Symposium NM13 : Functionalization of Topological Materials

In this talk I will give an introduction about how chemistry logic can be used to find new topological semimetals. After introducing how new Dirac semimetals can be found, I will show how we can use solid state chemistry to tune the electronic structure to the desired needs, form shifting Dirac cones to the Fermi level, to breaking time reversal symmetry in different ways, and thus split degeneracies. This way a multitude of different non trivial states is accessible.

HgTe is so far mostly known for its topological insulator properties. Recently, however, it became apparent that HgTe can also host a Weyl semimetalic phase. Applying compressive strain to bulk HgTe will result in a band overlap of the Gamma-8 bands with 3-dimensional Dirac points emerging at the band crossings. The inversion symmetry breaking due to the zinc-blende crystal structure will than result in a further splitting into Weyl points. The experimental realization of such a Weyl semimetalic state relies on controlling the strain in the HgTe layer. For this purpose we developed the growth of HgTe layers on artificial substrate structures based on CdTe/ZnTe superlattices. Magnetoresistance measurements of such HgTe layers reveal a strongly anisotropic negative magnetoresistance consistent with the proposed chiral anomaly in Weyl systems.

In this talk we will discuss angle-resolved photoemission experiments resolving the distinct electronic structure of the inequivalent top and bottom (001) surfaces of WTe₂ and MoTe₂. We further use the identification of the two different surfaces to clarify the number of Fermi surface sheets presenting a unifying picture of the surface and bulk electronic structure of both compounds. We identify surface states on both surfaces, some of which form large Fermi arcs emerging out of the bulk electron pocket. All surface states observed experimentally are reproduced by electronic structure calculations. In the case of WTe₂ the existence of Fermi arcs is independent of the presence of type-II Weyl points in the bulk band structure. This implies that the observation of surface Fermi arcs alone does not allow the identification of a material as a topological Weyl semimetal. However, the surface states observed in MoTe₂ could only be reproduced by electronic structure calculations for the experimental crystal structure that predicts a topological Weyl semimetal state with eight type-II Weyl points. We further use systematic electronic structure calculations simulating different Weyl point arrangements to discuss the robustness of the identified Weyl semimetal state and the topological character of Fermi arcs in MoTe₂.
F.Y. Bruno, et al, Phys Rev B 94, 121112(R) (2016).
A. Tamai, F.Y. Bruno, et al, Phys Rev X, 6, 031021 (2016).

Tungsten ditelluride is a layered transition-metal dichalcogenide that crystalizes in a distorted hexagonal net with an orthorhombic unit cell. The lack of inversion symmetry in this phase leads to a predicted new topological semimetal hosting the so-called type-II Weyl points. Here, we use intense THz pulses to trigger a structural deformation in WTe2, and probe its dynamics using an ultrafast electron diffraction (UED) technique. We observe large amplitude interlayer shear oscillations that occur along the in-plane motion between the orthorhombic and monoclinic phases of the material. We will discuss the driving mechanism that can lead to such structural deformation and its implication toward ultrafast THz field control over the topological properties in solids.

Materials with strongly-correlated electrons exhibit interesting phenomena such as metal-insulator transitions and high-temperature superconductivity. In stark contrast to ordinary metals, electron transport in these materials is thought to resemble the flow of viscous fluids. Despite their differences, it is predicted that transport in both, conventional and correlated materials, is fundamentally limited by the uncertainty principle applied to energy dissipation.
Here we discover hydrodynamic electron flow in the Weyl-semimetal tungsten phosphide (WP₂). Using thermal and magneto-electric transport experiments, we observe the transition from a conventional metallic state, at higher temperatures, to a hydrodynamic electron fluid below 20 K. The hydrodynamic regime is characterized by a viscosity-induced dependence of the electrical resistivity on the square of the channel width, and by the observation of a strong violation of the Wiedemann-Franz law. From magneto-hydrodynamic experiments and complementary Hall measurements, the relaxation times for momentum and thermal energy dissipating processes are extracted. Following the uncertainty principle, both are limited by the Planckian bound of dissipation, independent of the underlying transport regime.
[1] J. Gooth, F. Menges, C. Shekhar, V. Süβ, N. Kumar, Y. Sun, U. Drechsler, R. Zierold, C. Felser, B. Gotsmann, arXiv:1706.05925

Topology in various guises plays a central role in modern condensed matter physics. Although the original applications of topological ideas to band structures in semiconductors relied on the existence of a fully gapped bulk spectrum, more recently it has been recognized that protected surface states can arise even in gapless systems. The prototypical example of a gapless topological phase is a Weyl semi-metal showing linear dispersion around nodes termed as Weyl points, as the three-dimensional analog of graphene. Surface Fermi arcs are the most prominent manifestation of the topological nature of Weyl semi-metals. I will present predictions of the emergence of Weyl semimetal phase in two distinct cases:
(1)The topological crystalline insulator, Pb_1−x Sn_xTe exhibits topological phase transition upon the band inversion strength which can be tailored by the substitutional mixing ratio, strain, thermal expansion, ferroelectric displacement, and/or material thickness via quantum confinement effect. The SnTe building block of the compound is also known to exhibit a ferroelectric transition at low temperatures which leads to inversion symmetry breakdown. Using ab-initio-tight-binding calculations we have explored the parameter space associated with both band inversion and ferroelectric displacement. The calculated topological phase diagram shows the emergence of a Weyl semimetal phase which can be tuned with an external magnetic field.¹
(2)The interfacial phase-change memory (iPCM) GeTe/Sb2Te3 continues to attract a great deal of interest not only because they are promising candidates for the next generation non-volatile random-access memories but also for their fascinating topological properties. Depending on the atomic-layer-stacking sequence of the GeTe block the iPCM can be either in the ``SET'' (Ge-Te-Ge-Te) or ``RESET'' (Te-Ge-Ge-Te) states where the former exhibits a ferroelectric polarization and an electric conductivity which is two orders of magnitude higher than that of the RESET state. Ab initio electronic structure calculations reveal that the ferroelectric polarization in the "SET" phase which breaks the inversion symmetry results in the emergence of a Weyl semimetal phase with a large electric conductivity due to the gapless Weyl nodes.

¹T. Liang, S. Kushwaha, J. Kim, Q. Gibson, J. Lin, N. Kioussis, R. J. Cava, and N. P. Ong, A pressure-induced topological phase with large Berry curvature in Pb _1−xSn_xTe, Science Advances (2017), Vol. 3, no. 5, e1602510, DOI: 10.1126/sciadv.1602510

Antimony has been recently demonstrated to be amenable to standard exfoliation procedures [1], opening the possibility of studying the electronic properties of isolated few-layered flakes (generically referred to as antimonene). Antimony is a topological semimetal, meaning that its electronic structure presents topologically protected surface states, but it is still trivially metallic in bulk. Antimonene, on the other hand, may present a much reduced electronic bulk contribution for a small number of layers. A novel technique to make electrical contacts on the surface of individual thin flakes (5-10 monolayers) has allowed us to measure the (surface) conductivity of these in ambient conditions. Our measurements reveal a sheet resistance comparable to that of graphene, which we mainly attribute to the topologically protected surface electrons. We have carried out theoretical work to support this claim, addressing, in particular, the relative importance of bulk and surface conductivity and their scaling properties. Our calculations are based on density functional theory for the electronic structure and Kubo formalism for the conductivity, the latter considering random disorder and the presence of water [2].


References
[1] P. Ares et al., Advanced Materials 28, 6515 (2016)
[2] S. Pakdel et al, in preparation.

The historically first mixed-valence compound and first Kondo insulator SmB₆ features a low-temperature resistivity which has remained unexplained for over three decades. Recent predictions as the first topological insulator caused by electron correlation have been supported by a large number of angle-resolved photoemission studies. By proper distinction of Sm and B terminated samples we demonstrate that both types of surface states (at G and X) appear massive, most clearly the one at the zone center which develops a Rashba spin spitting for B termination excluding an odd number of Dirac cones and topological insulator behavior. Even more importantly, it is shown that the metallic surface at low temperature is due to a surface shift of the 4f and a reduced f-d hybridization at the surface which keeps the surface state at X metallic. The present work thus shows that the long-standing problem of the anomalous conductivity of SmB₆ has a conventional solution. This result is crucially important in the search for correlated topological insulators.

[1] P. Hlawenka, K. Siemensmeyer, E. Weschke, A. Varykhalov, J. Sánchez-Barriga, N. Y. Shitsevalova, A. V. Dukhnenko, V. B. Filipov, S. Gabáni, K. Flachbart, O. Rader, and E. D. L. Rienks, http://arxiv.org/abs/1502.01542 (2015)

Topological insulators constitute a new phase of matter protected by symmetries. Time-reversal symmetry protects strong topological insulators of the Z₂ class, which possess an odd number of metallic surface states with dispersion of a Dirac cone. Topological crystalline insulators are less robust and merely protected by individual crystal symmetries. They show an even number of Dirac cones. In this work, it is demonstrated that Bi-doping of Pb1−xSnxSe (111) epilayers induces a quantum phase transition from a topological crystalline insulator to a Z₂ topological insulator. This occurs because Bi-doping lifts the fourfold valley degeneracy and induces a gap at Γ, while the three Dirac cones at the M points of the surface Brillouin zone remain intact. We interpret this new phase transition as caused by a lattice distortion. It implies that the system becomes ferroelectric. Our results demonstrate that strong topological insulators can be switchable by distortions or electric fields.

[1] P. S. Mandal, G. Springholz, V. V. Volobuev, O. Caha, A. Varykhalov, E. Golias, G. Bauer, O. Rader, J. Sánchez-Barriga, Nat. Commun. 8, 968 (2017)

Magnetic topological insulators enable the quantum anomalous Hall effect with edge states for lossless charge transport. These edge states are hosted by a magnetic band gap at the Dirac point which, however, never been observed directly by angle-resolved photoelectron spectroscopy (ARPES) despite its importance for the achievable operation temperature of devices. Here, ARPES is employed to demonstrate a magnetic gap at the Dirac point of Mn-doped Bi₂Te₃ films [1]. The gap is 32 meV wide [1] and thus twice as large as predicted by density functional theory [2]. We discuss reasons for this discrepancy. Moreover, the control system Mn-doped Bi₂Se₃ does not show a magnetic gap [3].

[1] P. S. Mandal, S. Wimmer, E. D. L. Rienks, O. Caha, V. V. Volobuiev, G. Springholz, G. Bauer, A. Ney, S. Khan, J. Minár, J. Sánchez-Barriga, A. Varykhalov, O. Rader et al. (unpublished)
[2] J. Henk, M. Flieger, I. V. Maznichenko, I. Mertig, A. Ernst, S. V. Eremeev, and E. V. Chulkov, Phys. Rev. Lett. 109, 076801 (2012)
[3] J. Sánchez-Barriga, A. Varykhalov, G. Springholz, H. Steiner, R. Kirchschlager, G. Bauer, O. Caha, E. Schierle, E. Weschke, A. A. Ünal, S. Valencia, M. Dunst, J. Braun, H. Ebert, J. Minár, E. Golias, L.V. Yashina, A. Ney, V. Holý, O. Rader, Nat. Commun. 7, 10559 (2016)

Bismuth telluride (Bi₂Te₃) has been recently established as an archetype for the three-dimensional topological insulator with a single Dirac cone on the surface, as determined experimentally from angle-resolved photoemission spectroscopy. Topological insulators are insulating in the bulk and exhibit gapless metallic surface states with linear energy-momentum dispersion shaped like a Dirac cone. Due to the strong spin-orbit coupling, these conducting surface states have electron momentum locked to the spin orientation and are protected from scattering mechanisms by time reversal symmetry. Consequently, high-mobility spin polarized surface currents can be produced without external magnetic fields, offering possibilities to new applications in spintronics or quantum computing [1].
Conductivity measurement of the metallic surface states in Bi₂Te₃ is hindered by the bulk conductivity due to intrinsic defects, like vacancies and anti-sites. Counter doping (Ca, Sn or Pb) is a way to control the Fermi level and suppress the bulk contribution [2]. Another way is to grow films of high structural quality. Intrinsic conduction through topological surface states has been obtained in very thin insulating Bi₂Te₃ films grown by molecular beam epitaxy (MBE) [3,4].
Structural defects determine the n/p type and density of electrical carriers in the bulk. In MBE growth, the most probable structural defect to be formed are vacancies. Bismuth vacancies act like an acceptor (holes), while tellurium vacancies result in free electrons in the bulk. Depending on the growth kinetics, determined by the experimental parameters (substrate temperature, extra Te offer and deposition rate), different electrical behavior can be obtained. Theoretical modeling based solely on vacancy formation as a function of substrate temperature predicts gradual transitions from p-type (holes) to n-type (electrons) of charge carrier. However, experimental data have show different behaviour, implying in more complex structure of defects in epitaxial films than can be seen by either local probes or X-ray diffraction along the growth direction [5,6].
Here a multi-axis single crystal diffractometer is used to access diffraction vectors with different in-plane and out-plane components, revealing another dimension in terms of crystalline perfection to be taken into account when synthesizing epitaxic films of Bi₂Te₃. A more sensitive probe of latteral coherence in the films—based on second-order X-ray dynamical diffraction—is also used to shown that there is a very narrow gap in terms of growth parameters where in-plane long-range order in the films can be achieved.

[1] Y. Ando, J. Phys. Soc. Japan 82, 1 (2013).
[2] Y.L. Chen et al., Science 325, 178 (2009).
[3] C.I. Fornari et al. J. Appl. Phys. 119, 165303 (2016).
[4] C.I. Fornari et al., APL Mat. 4, 106107 (2016).
[5] H. Steiner et al., J. Appl. Cryt. 47, 1889 (2014).
[6] S.L. Morelhão et al, J. Appl. Cryst. 50, 1 (2017).

Thermodynamic and transport properties are reported on single crystals of the hexagonal antiferromagnet Mn₃Sn grown by the Sn flux technique. Magnetization measurements reveal two magnetic phase transitions at T₁ = 275 K and T₂ = 200 K, below the antiferromagnetic phase transition at T_N ≈ 420 K. The Hall conductivity in zero magnetic field is suppressed dramatically from 4.7 Ω^-1cm^-1 to near zero below T₁, coincident with the vanishing of the weak ferromagnetic moment. This illustrates that the large anomalous Hall effect (AHE) arising from the Berry curvature can be switched on and off by a subtle change in the symmetry of the magnetic structure near room temperature.

In this talk I will give an introduction about how chemistry logic can be used to find new topological semimetals. After introducing how new Dirac semimetals can be found, I will show how we can use solid state chemistry to tune the electronic structure to the desired needs, form shifting Dirac cones to the Fermi level, to breaking time reversal symmetry in different ways, and thus split degeneracies. This way a multitude of different non trivial states is accessible.

The established diversity of electronic topology classes lends the opportunity to pair them into dual topological complexes. Bulk-surface correspondence then ensures the coexistence of a combination of boundary states that cannot be realized but only at the various surfaces of such a dual topological material. We show that the layered compound Bi₂TeI realizes a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band which classify it as a weak topological insulator with metallic states on its ‘side’ surfaces. Additional mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. Bi₂TeI is therefore predicted to host a pair of Dirac cones protected by time reversal symmetry on its ’side’ surfaces and three pairs of Dirac cones protected by mirror symmetry on its top and bottom surfaces. We spectroscopically map the top cleaved surface of Bi₂TeI, and crystallographic step edges therein. We show the existence of both two dimensional surface states which are susceptible to mirror symmetry breaking, as well as one dimensional channels that resides along the step edges. Their mutual coexistence on the step edge where both facets join is facilitated by momentum and energy segregation. Our observations of a dual topological insulator make way to additional pairing of other dual topology classes with distinct surface manifestations coexisting at their boundaries.

We will present our recent combined experimental and theoretical results on the band structure engineering in 3D topological insulator (3D TI) bilayers [1] and superlattices [2] grown by molecular beam epitaxy (MBE) on Si(111). These studies show how new topologies emerge in complex structures, as compared to the routine Fermi level control by alloying [3, 4]. Our results provide a starting point in search for novel topological phases.
MBE growth of Sb₂Te₃ and Bi₂Te₃ leads to the p-type and n-type material respectively, due to the low formation energy of charged vacancies and antisites. We have succeeded in growing high quality heterostructures of Sb₂Te₃ grown on Bi₂Te₃ as confirmed by atomic resolution transmission electron microscopy images. The heterostructures form a vertical p-n junction where the Fermi level position at the surface can be controlled by the thicknesses of the two layers, which has been confirmed by photoemission [1].
Bi-Te compounds can be grown at various stoichiometries, which at the atomic level are combinations of Bi₂Te₃ quintuple layers and Bi bilayers. The Bi₁Te₁ stoichiometry results from combining two Bi₂Te₃ quintuple layers with one Bi bilayer in the unit cell. In such superlattice new dual topological properties emerge. According to our theoretical predictions the material is simultaneously a topological crystalline insulator (TCI) and a weak topological insulator (WTI), and our photoemission results demonstrate the existence of TCI crossings away from the Brillouin zone center [2]. This opens up the possibility of controlling the topological protection on different surfaces selectively by breaking respective (mirror or time-reversal) symmetries.
Encouraged by these results we propose future research directions, which include preparation of heterostructures based on ferromagnetic insulators, and search for 2D materials which exhibit non-trivial topologies. In particular we are optimizing EuO thin films as ferromagnetic insulator substrates which may enable realization of QAHE by deposition of monolayers of heavy metals. With high-resolution photoemission we are searching for band crossings in ferromagnets which locally exhibit non-zero Berry curvature, as these contribute to the intrinsic contribution to AHE, with one example being demonstration of spin-orbit gaps in Fe(001) thin film [5]. With novel photoemission microscope we demonstrate how the band structure of single flakes of 2D materials can be probed [6], which enables microscopic band structure mapping of 2D materials where non-trivial phases have been predicted.

[1] M. Eschbach et al., Nature Comm. 6, 8816 (2015)
[2] M. Eschbach et al., Nature Comm. 8, 14976 (2017)
[3] C. Weyrich et al., J. Phys. Cond. Matter 28, 495501 (2016)
[4] J. Kellner et al., Appl. Phys. Lett. 107, 251603 (2015)
[5] E. Mlynczak et al., Phys. Rev. X 6, 041048 (2016)
[6] M. Gehlmann et al., Nano Letters 17, 5187 (2017)

The quantum anomalous Hall (QAH) effect is a quantum Hall effect induced by spontaneous magnetization instead of an external magnetic field. The effect occurs in two-dimensional (2D) insulators with topologically nontrivial electronic band structure characterized by a non-zero Chern number. The experimental observation of the QAH effect in thin films of magnetically doped (Bi,Sb)₂Te₃ topological insulators (TIs) paves the way not only for practical applications of dissipationless quantum Hall edge states, but also for exploration of other novel quantum states of matter such as axion insulator, quantum spin Hall insulator, Weyl semimetal, and topological superconductor. In this talk, I will introduce our recent progresses on constructing and engineering heterostructures and multilayers based on magnetically doped (Bi,Sb)₂Te₃ QAH films. The QAH heterostructures and multilayers enable us to obtain and investigate various topological quantum states of matter and lay the foundation for studies on topological electronics and topological quantum computation.

Quantm anomalous Hall effect in magnetic topological insulator (TI) heterostructures has attracted much attention for demonstrating an edge current conduction at zero magnetic field [1-3]. Magnetic topological insulator contains spontaneous magnetization along z-direction that interacts with surface states, resulting in a formation of exchange gap in the surface states. When Fermi energy locates in the exchange gap at low temperature, longitudinal and Hall resistances are quantized. We have shown that magnetic/non-magnetic modulated heterostructures are nice platforms to observe QAHE-related phenomena at relatively high temperature about 2 K [4]. In this talk, two schemes will be discussed for a control of edge current conduction; the one is in-plane magnetic domain control with magnetic force microscopy technique [5] and the other is out-of-plane antiparallel magnetization control in tricolor superlattice composed of Cr-doped and V-doped TI heterostructures [6]. In the former study, an edge current conduction was controlled by domain arrangement in Hall-bar structures. In the latter, antiparallel alignment of magnetization at top and bottom magnetic layers corresponds to axion insulator states, demonstrating colossal magnetoresistance. This talk will cover growth optimization of the heterostructures as well as device operations.
This work has been carried out in RIKEN CEMS under the collaboration with Prof. Tokura and Prof. M. Kawasaki group.

[1] C.-Z. Chang et al., Science 340, 167 (2013). [2] J. Checkelsky et al., Nature Phys. 10, 731 (2014). [3] C.-Z. Chang et al., Nature Mater. 14, 473 (2015). [4] M. Mogi et al., Appl. Phys. Lett. 107, 182401 (2015). [5] K. Yasuda et al., arXiv. 1707.09105v1 (2017). [6] M. Mogi et al., Sci. Adv. 3, eaa01669 (2017).

An interplay of spin-orbit coupling and intrinsic magnetism is known to give rise to the quantum anomalous Hall and topological magnetoelectric effects under certain conditions. Their realization could open access to low power consumption electronics as well as many fundamental phenomena like image magnetic monopoles, Majorana fermions and others. Unfortunately, being realized very recently, these effects are only accessible at extremely low temperatures and the lack of appropriate materials that would enable the temperature increase is a most severe challenge. Presented in this talk is a novel material platform with unique combination of properties that is perfectly suitable for the realization of both effects at elevated temperatures. The key element of the computational material design is a magnetic extension of a topological insulator surface by a thin film of ferromagnetic insulator, which is both structurally and compositionally compatible with the topological insulator [1, 2]. Following this proposal, we suggest a variety of specific systems and discuss their numerous advantages, in particular wide band gaps with the Fermi level located in the gap. A recent experimental realization of the magnetic extension approach [3] is also described in the talk.
References
M. M. Otrokov, et al. JETP Lett. 105, 297 (2017)
M. M. Otrokov, et al. 2D Materials 4, 025082 (2017)
T. Hirahara, S. V. Eremeev, et al. Nano Lett. 17 (6), 3493 (2017)

Spintronics research based on topological insulators (TIs) has shown rapid progress during the past few years. Due to the strong spin-orbit coupling (SOC) and particularly the spin-momentum locked Dirac states on the surface, TIs are expected to be very promising materials for spintronic applications ranging from ultralow power memory/logic devices to new ultrafast computation technologies. In this talk, we will review the recent progress in the spintronics research based on TIs. First, we will go over the research on the detection of the spin-momentum locked surface states and the associated current-induced spin polarization on TIs, which provides a first step for the aftermentioned spintronic applications. Secondly, we will focus on the spin-orbit torque (SOT) research in different TI-based magnetic structures, including the magnetic TI bilayers and TI/ferro(or ferri-)magnet structures, and discuss the phenomena such as spin-torque ferromagnetic resonance and magnetization switching, which have significant implications on the potential memory/logic devices based on TIs. Thirdly, we will describe the spin pumping and spin to charge conversion effects in different TI/magnet structures, which show that TIs can serve as efficient spin detector/sensor in applications. Furthermore, we will elaborate the emerging topological antiferromagnetic research which combines TIs with antiferromagnetic materials. The merits of antiferromagnets, such as immunity to external field, absence from stray field, and their intrinsic ultrahigh-frequency dynamics, could bring many new topological physics and significantly enrich the landscape of spintronics research when they are combined with TIs. Finally, we will discuss the challenges and opportunities in the TI-based spintronics research and highlight the potential applications in ultralow-power and ultrafast-speed devices.

The topological magnetoelectric (TME) effect is a special version of the magnetoelectric effect, showing quantized response functions. The Z₂ topological insulators (TIs) with gapped surface states and time reversal invariant bulk states are predicted to show the TME effect, and are called axion insulators. We present our recent observation of the axion insulator state in a magnetically doped TI ((Bi_x, Sb_1-x)₂Te₃) sandwich heterostructure, where the top and bottom layers are doped with V and Cr respectively, and are separated by an undoped TI middle layer. Magnetic force microscopy measurements confirm the existence of parallel and antiparallel magnetization of two magnetic layers by sweeping the external magnetic field. Transport measurements unambiguously demonstrate the quantum anomalous Hall (QAH) state (parallel), and the axion insulator state (antiparallel), where we observe a large longitudinal resistance and vanishing longitudinal and Hall conductance. Our findings thus show evidence for a phase of matter distinct from the established QAH state and provide a promising platform for the realization of the TME effect.
Funded by ONR, ARO MURI, and NSF MIP.

Topological band structures are well-known to induce exotic bound states at their surfaces. With this in mind, it is natural to expect that magnetic domain walls can play a similar role *inside* a material. Here we report on theoretical studies of the transport in magnetic Weyl systems with domain walls, and how this leads to a number of physical effects. The applications to experiments on Mn3Sn and CeAlGe will be discussed.

The recently discovered heterostructures between topological-insulator (TI) and ferromagnetic metals (FM) are expected to pave the way for developing a plethora of novel technologically relevant spintronic effects due to the strong spin-orbit coupling (SOC) present at the TI/FM interface [1,2]. However, the lack of realistic models to describe the proximity effects on the electronic structure and on the spin-textures at the interface of the TI/FM heterostructure prevents their fundamental understanding.
In this talk I will discuss a novel approach which combines first-principles density functional theory (DFT) including non-collinear SOC effects and the non-equilibrium Green’s function (NEGF) technique. This DFT-NEGF method allows us to go beyond the traditional slab models used in DFT simulations and achieve an unprecedented insight into the electronic and spin properties of truly semi-infinite TI surfaces and TI/FM
interfaces [3,4].
We show how the proposed DFT-NEGF formalism provides an accurate description of the topologically protected surface states present at a single Bi2Se3(111) surface, which are free from spurious effects due to the interaction between surface states at the two surfaces of the slab [3]. Furthermore, we examine the band structure and the spin-texture at the interface between the Bi2Se3(111) surface and ferromagnetic cobalt, and show how the Rashba ferromagnetic model describes the spectral function on the surface of Bi2Se3(111) in contact with the cobalt film near the Fermi level, where circular and snowflake-like constant energy contours coexist which spin locks to momentum. The remnant of the Dirac cone is hybridized with evanescent wave functions injected by the metallic layer and pushed, due to charge transfer from the cobalt layer, tenths of eV below the Fermi level while hosting a distorted helical spin texture [4].
[1] Mellnik et al., Nature 511, 449 (2014)
[2] Fan et al. Nat. Mater., 13, 699 (2014)
[3] Smidstrup et al., Phys. Rev. B 96, 195309 (2017)
[4] Marmolejo-Tejada et al., Nano Lett. 2017, 17, 5626 (2017)

LaPtBi is a Half-Heusler compound which is recently predicted to exhibit multi-functionalities: the superconductivity and topological edge states, namely topological superconductor. ^{[1, 2]} LaPtBi has been shown to superconduct in the bulk. ^[3] However, and importantly, its topological property can only be stimulated by applying substantial uniaxial strain. In this talk, we report the observation of superconductivity in MBE grown epitaxial non-centrosymmetric LaPtBi film on MgO (001). Transport measurement shows T_c(onset) at 0.7 K and an upper critical field (B_c2 (0)) of 2.1 T. Magnetoresistance in the normal state exhibits a cusp-like minima at low magnetic fields which only depends on the total magnetic field. This is attributed to a weak anti-localization effect arising from the nanocrystalline structure of the film. Linear dependence of the critical magnetic field on temperature down to 50 mK, a non BCS like behavior, is observed. The critical current decreases linearly with magnetic field as well. The I-V characteristics indicate the presence of intrinsic Josephson effect in these nanocrystalline structured films. By optimizing the growth parameters, a compressive uniaxial strain of 17% was introduced into the film. In such a strained LaPtBi film, the predicted topological non-trivial gap at G point is expected to emerge. Characterization of these strained films, including ARPES, will be presented. The realization of superconducting phase in the strained LaPtBi films is an important step towards obtaining a topological superconductor in order to seek other predicted exotic properties such as Majorana states.
Work at MIT is supported by STC Center for Integrated Quantum Materials under NSF Grant No. DMR-1231319, NSF Grant DMR-1700137 and ONR Grant N00014-16-1- 2657
Reference:
[1] D. Xiao et al., Phys. Rev. Lett. 105, 25–28 (2010).
[2] T. Graf et al., Prog. Solid State Chem. 39, 1–50 (2011).
[3] G. Goll et al., Physica B. 403, 1065–1067 (2008).

Josephson junctions based on topological insulators have recently received a lot of attention due to their potential of hosting topologically protected, gapless Andreev bound states, so called Majorana fermions. However, detecting such Majorana fermions experimentally via the measurement of a 4π-periodic Josephson current is rather challenging due to issues with quasiparticle poisoning and the presence of additional trivial modes.
Here, we propose phase-dependent heat currents through topological Josephson junctions as an alternative way to probe the existence of Majorana fermions [1]. In particular, we demonstrate that the latter manifest themselves by a minimal thermal conductance at phase difference π. The effect is immune to quasiparticle poisoning and persists in the presence of trivial modes. We propose a simple experimental setup to verify our predictions.
Furthermore, we demonstrate that topological Josephson junctions subject to a magnetic flux form highly efficient thermal switches that offer a temperature variation of up to 40% between the on and off state [2]. While short junctions provide a sharp switching behaviour, in long junctions the switching with magnetic flux is smooth.

[1] B. Sothmann and E. M. Hankiewicz, Phys. Rev. B 94, 081407(R) (2016).
[2] B. Sothmann, F. Giazotto and E. M. Hankiewicz, New J. Phys. 19, 023056 (2017).

I will discuss the renormalization of the charging energy in a topological superconductor islands connected to a ground by a weak link. I will show analytical results on the almost transparent junction and numerical results in a range of parameters. I will discuss the consequences of the results to the design of topological qubits and scalable quantum computer architectures.

Nanowires with helical surface states represent key prerequisites for observing and exploiting phase-coherent
topological conductance phenomena, such as spin-momentum locked quantum transport or topological super-
conductivity. We demonstrate in a joint experimental and theoretical study that gated nanowires fabricated from
high-mobility strained HgTe, known as a bulk topological insulator, indeed preserve the topological nature of
the surface states, that moreover extend phase-coherently across the entire wire geometry. The phase-coherence
lengths are enhanced up to 5 μm when tuning the wires into the bulk gap, so as to single out topological trans-
port. The nanowires exhibit distinct conductance oscillations, both as a function of the flux due to an axial
magnetic field, and of a gate voltage. The observed h/e-periodic Aharonov-Bohm-type modulations indicate
surface-mediated quasi-ballistic transport. Furthermore, an in-depth analysis of the scaling of the observed
gate-dependent conductance oscillations reveals the topological nature of these surface states. To this end we
combined numerical tight-binding calculations of the quantum magneto-conductance with simulations of the
electrostatics, accounting for the gate-induced inhomogenous charge carrier densities around the wires. We
find that helical transport prevails even for strongly inhomogeneous gating and is governed by flux-sensitive
high-angular momentum surface states that extend around the entire wire circumference.

Topological crystalline insulators are materials in which the crystalline symmetry leads to topologically protected surface states with a chiral spin texture, rendering them potential candidates for spintronics applications. Using scanning tunneling spectroscopy, we uncover the existence of one-dimensional (1D) midgap states at odd-atomic surface step edges of the three-dimensional topological crystalline insulator (Pb,Sn)Se. A minimal toy model and realistic tight-binding calculations identify them as spin-polarized flat bands connecting two Dirac points. This nontrivial origin provides the 1D midgap states with inherent stability and protects them from backscattering. We experimentally show that this stability results in a striking robustness to defects, strong magnetic fields, and elevated temperature

Due to its large bulk band gap, bismuthene on SiC offers intriguing new opportunities for room-temperature quantum spin Hall (QSH) applications. Although edge states have been observed in the local density of states (LDOS), there has been no experimental evidence until now that they are spin polarized and topologically protected. We predict experimentally testable fingerprints of these properties originating from magnetic fields, such as changes in the LDOS and in ballistic magnetotransport. In particular, for armchair edges, experimentally accessible, we find a distinct difference of behavior under out-of-plane (gap opening of a few meV between the QSH states) and in-plane (no or tiny gap) fields. While we focus here on bismuthene on SiC, our main findings should also be applicable to other honeycomb-lattice-based QSH systems.

Topological insulators (TI) are new class of materials exhibiting Dirac-like surface states protected by time reversal symmetry for Z2 TIs or by crystalline symmetries for topological crystalline insulators (TCIs). Functional applications requires thin film heterostructures to control the properties of the topological surface states (TSS) by means of strain, finite size hybridization, composition, as well as by magnetic and non-magnetic doping. Here, we present our recent results on molecular beam epitaxy, photoemission spectroscopy [1-3] and magneto-optical and transport investigations [4] of bismuth-based TI and PbSnSe(Te) TCI films and quantum well structures grown by molecular beam epitaxy. We compare Mn doping of Bi2Se3 and Bi2Te3, revealing peculiar incorporation sites and a striking difference in the gap opening of the TSS [1]. For non-magnetic doping of IV-VI TCIs with four-fold valley-degeneracy, a gap is opened at one Dirac cone at center of the surface Brillouin zone, whereas the three cones at the M-points remain intact. This is the manifestation of a new topological phase transition between a TCI a TI state controlled by Bi doping [2]. In the case of PbSnTe, however, Bi doping rather leads to a giant Rashba splitting of the surface states that is controlled by changes in the bulk Fermi level [3]. We also show that the topology of TCIs can be effectively tuned by strain imposed in heterostructures and moreover, in the thin-film limit a strong hybridization of the opposite TSS occurs that persist up to large thicknesses of more than 50 monolayers. The resulting quantum well show pronounced multiple 2D subband levels in ARPES due to the quantum confinement that can be further tuned by surface doping. This opens a wide playground for device applications.
[1] J. Sánchez-Barriga, A. Varykhalov, G. Springholz, et al., Nat. Commun. 7, 10559 (2016).
[2] P. S. Mandal, G. Springholz, V. V. Volobuev, et al., Nat. Commun. 8, 968 (2017).
[3] V. Volobuev , P. S. Mandal, M. Galicka, O. Caha, et al., Adv. Mater. 29, 1604185 (2017).
[4] B. Assaf, T. Phuphachong, E. Kampert, et al., Phys. Rev. Lett. 119, 10602 (2017).

Research in thermoelectric quantum structures was greatly powered by the prediction of a significant boost of the thermoelectric efficiency by quantum size effects in the early 90ies. Recently the research interest shifted from quantum size effects in trivial semiconductors towards new types of quantum materials, i.e. topological insulators (TI), Weyl and Dirac semimetals, characterized by their non-trivial electronic topology. Bi₂Te₃, Sb₂Te₃ and Bi₂Se₃, established thermoelectric materials, are also TIs exhibiting a bulk band gap and highly conductive and robust gapless surface states. The signature of the non-trivial electronic band structure on the thermoelectric transport properties can be best verified in transport experiments using nanowires and thin films. In that cases a two channel transport model could accout for the observed thermoelectric behaviour [1]. But even in nanograined bulk, the typical peculiarities in the transport properties of TIs can be seen [2], evidencing potential for enhancement of the thermoelectric performance of materials. Finally, Dirac and Weyl semimetals [3,4,5], as for instance Bi_1-xSb_x, TaAs, NbP, or Cd₃As₂, are two recently discovered classes of 3-dimensional topological materials in which conduction and valence bands touch linearly close to the Fermi energy. This has revitalized the interest in Weyl fermions that were first discovered in high energy experiments. The investigation of the thermoelectric transport properties of Weyl semimetals currently opens the door for an advanced understanding of these exotic states of matter in which even the Ohm's law is fundamentally violated.

[1] Shin, HS; Hamdou, B; Reith, H; Osterhage, H; Gooth, J; Damm, C; Rellinghaus, B; Pippel, E; Nielsch, K, Nanoscale 2016, 8, 13552.
[2] Sun, G. L.; Li, L. L.; Qin, X. Y.; Li, D.; Zou, T. H.; Xin, H. X.; Ren, B. J.; Zhang, J.; Li, Y. Y.; Li, X. J. Appl. Phys. Lett. 2015, 106, 053102 .
[3] Moll, P. J. W.; Nair, N. L.; Helm, T.; Potter, A. C.; Kimchi, I.; Vishwanath, A.; Analytis, J. G. Nature 2016, 535, 266.
[4] Sergelius, P.; Gooth, J.; Bäßler, S.; Zierold, R.; Wiegand, C.; Niemann, A.; Reith, H.; Shekhar, C.; Felser, C.; Yan, B.; Nielsch, K. Scientific Reports 2016, 6, 33859.
[5] Niemann, A. C.; Gooth, J.; Wu, S. C.; Bäßler, S.; Sergelius, P.; Hühne, R.; Rellinghaus, B.; Shekhar, C.; Süß, V.; Schmidt, M.; Felser, C.; Yan, B.; Nielsch, K. Scientific Reports 2017, 7, 43394.

Hybrid devices comprised of topological insulator (TI) nanostructures in proximity to superconductors (SC) are expected to pave the way towards topological quantum computation. Fabrication under ultra-high vacuum conditions is necessary to attain high quality of TI-SC hybrid devices because the physical surfaces of V-VI three-dimensional TIs suffer from degradation at ambient conditions. I will present an in-situ process, which allows to fabricate such hybrids by combining molecular beam epitaxy and stencil lithography. Here, we prepare a Si/SiO₂/Si₃N₄ substrate by means of e-beam lithography and reactive ion etching to process Si₃N₄ bridges. A dip hydrofluoric acid removes the SiO₂ underneath the Si₃N₄ to obtain freestanding Si₃N₄ bridges above the Si substrate. These Si₃N₄ bridges function as a shadow mask during the MBE growth that allow to realize high-quality in-situ grown (Bi,Sb)₂Te₃/Nb Josephson junctions on the nanometer scale. These in-situ Josephson junctions show nearly perfect interface transparency and very large products. The Shapiro response of radio frequency measurements indicates the presence of gapless Andreev bound states, so-called Majorana bound states.

A novel approach on quantum information processing based on exotic Majorana zero modes in solid state matter holds the great promise to perform fault tolerant computations. Extensive error correction being the bottleneck of other solid state qubits, drives the research on these so-called Majorana qubits. Majorana zero modes reside at the interface of a topological insulator (TI) towards a superconductor (SC). Signatures thereof have already been realized based on tunnel-spectroscopy^[1], Josephson irradiation^[2] as well as Shapiro response^[3] measurements on TI-SC hybrid devices.
Here, we present Majorana signatures in low temperature experiments found in Shapiro response measurements. The three dimensional Bi₂Te₃ topological insulator thin films were grown by molecular beam epitaxy. TI-SC hybrid devices are fabricated under ultra-high vacuum conditions, yielding a very high interface quality. The interface transparency and the characteristic I_CR_N product of in-situ defined Josephson junctions have been determined to show superior quantities, when compared to ex-situ fabricated devices.
Next to highly transparent interfaces, thin films need being confined to nanostructures for Majorana devices. A preparation technique to selectively define TI nanoribbons is presented. Measurements on these nanoribbons show conductance fluctuations, when a magnetic field is applied Using Fourier analysis, the origin of these oscillations is investigated. Superconductivity has as well successfully been induced in these selectively grown TI nanoribbons in proximity to an ex-situ deposited SC. Shapiro response measurements on the nanoribbon based Josephson devices will be presented.
A combination of both processes, the selective growth of TI nanoribbons as well as the in-situ fabrication of superconductive electrodes has been established. This novel preparation technique does not only allow for high quality Josephson devices but allows to fabricate highly complex TI-SC hybrids, due to its scalability. This will ultimately result in a reproducible process to define in-situ deposited qubit architectures based on selectively deposited TI nanoribbons.

[1] V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. Bakkers, L. P. Kouwenhoven, Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science, 336 (6084), 2012
[2] J. Wiedenmann, E. Bocquillon, R. S. Deacon, S. Hartinger, O. Herrmann, T. M. Klapwijk, L. Maier, C. Ames, C. Brüne, C. Gould, A. Oiwa, K. Ishibashi, S. Tarucha, H. Buhmann and L. W. Molenkamp, 4π-periodic Josephson supercurrent in HgTe-based topological Josephson junctions, Nat. Com., 10303, 2016
[3] R. S. Deacon, J. Wiedenmann, E. Bocquillon, F. Dominguez, T. M. Klapwijk, P. Leubner, C. Brüne, E. M. Hankiewicz, S. Tarucha, K. Ishibashi, H. Buhmann and L. W. Molenkamp, Josephson Radiation from Gapless Andreev Bound States in HgTe-Based Topological Junctions, Phys. Rev. X 7, 021011, 2017

It is well-known that braiding Majorana/Ising anyons does not lead to a universal quantum computation model. However they have several other useful properties such as entanglement resources, localizability and possibly error-correction. I will discuss these properties from a computational/mathematics perspective.

We introduce a new platform based on spin transitions in the fractional quantum Hall effect regime where parafermions - higher order non-abelian excitations - can be realized. Local (gate) control of spin transition allows formation of isolated domain walls, which consist of counter-propagating edge states of opposite polarization with fractional charge excitations. When superconductivity is induced into such a domain wall from superconducting contacts via proximity effect, arafermions are expected to be formed at the domain wall boundaries. In a multi-gate device a re-configurable network of domain walls can be formed allowing creation, braiding, manipulation and fusion of parafermions. In respect to the quantum computing application parafermons are more computationally intense han Majoranas and are a building block for Fibonacci fermions, even high order non-Abelian particles that can perform universal gate operations within the opologically protected subspace.

As a significant advance towards implementing topological quantum computation, a pressing goal for the community is to successfully demonstrate the functioning of Majorana fermio -based topological qubits. Non-local pairs of such fermions share an electronic state that can be either occupied or empty, making such a pair a parity qubit. Semiconducting nanowires, and more recently, chains of ferromagnetic atoms, in proximity to a superconductor, have received prominent attention for their ability to nucleate Majorana fermion states bound to their ends. As with conventional quantum computing, implementing topological quantum computation in a materials system can be best achieved by investigating multiple routes. Here we present an alternative approach, networks of lateral superconductor-topological insulator-superconductor Josephson junctions as a viable, highly promising candidate that has several advantages for supporting Majorana fermion-based topological qubits. The architecture consists of superconducting islands deposited on a topological insulator substrate forming long Josephson junction pathways. Magnetic fields threading the junction nucleate Majorana fermions localized in the junction whose locations can be controlled by applied currents. We propose protocols essential for topological qubit operations involving: i) tuning the coupling between the Majorana states to affect braiding and non-Abelian rotations, and ii) measurement of non-local parity transitions induced by such a rotation. The proposal makes use of local magnetic field or currents pulses to control the spacing of Josephson vortices that host MFs to perform operations and quantum dots to readout the parity of Majorana fermion pairs. We report our progress in the experimental realization of this architecture.

Abstract not available.

Majorana bound states are zero-energy excitations that are predicted to exhibit non-Abelian statistics upon exchange. While spectroscopic signatures of these excitations were reported in several experimental platforms including semiconducting wires and atomic chains, controlling Majorana bound states in these platforms is still an elusive goal. In this talk, I will describe our current efforts aiming to address challenges elated to establish control over Majorana bound states realized in arrays of magnetic atoms placed on a superconducting island of a nanoscale size.

Abstract not available.

Tunneling spectroscopy measurements on one-dimensional superconducting hybrid materials have revealed signatures of Majorana fermions which are the edge states of a bulk topological superconducting phase. We couple strong spin-orbit semiconductor InSb nanowires to conventional superconductors (NbTiN, Al) to obtain additional signatures of Majorana fermions and to explore the topological phase transition. A potent alternative explanation for many of the recent experimental Majorana reports is that a non-topological Andreev state localizes near the end of a nanowire. We compare Andreev and Majorana modes and investigate ways to clearly distinguish the two phenomena. We are also building circuits that incorporate microwave resonators and nanowires to ultimately perform control and readout of Majorana states based on magnetic flux.