Imaging currents in HgTe quantum wells in the quantum spin Hall regime
TL;DR: This work directly confirms the existence of the edge channels of the quantum spin Hall state by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells, providing input to the question of how ballistic transport may be limited in the edge channel.
Abstract: The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels 1‐5 . The QSH state was predicted 6 and experimentally demonstrated 7 to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices 7‐9 . Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems 10‐13 . Like an ordinary insulator, the QSH state has a bulk energy gap, but the QSH state supports within the gap a pair of counter-propagating spin-polarized edge modes 15 . The QSH state is predicted in HgTe/(Hg,Cd)Te quantum wells thicker than a critical thickness of 6.3nm, whereas thinner quantum wells should beordinaryinsulators 6,7 .Theedgemodesaretheoreticallyprotected against backscattering by their orthogonal spin states 1416 , and therefore should have a quantized conductance of e 2 =h, where e is
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TL;DR: Bychkov and Rashba as discussed by the authors introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors, which has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductor devices.
Abstract: In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.
1,533 citations
TL;DR: In this paper, the authors discuss the underpinnings of the topological band theory and its materials applications, and propose a framework for predicting new classes of topological materials.
Abstract: First-principles band theory, properly augmented by topological considerations, has provided a remarkably successful framework for predicting new classes of topological materials. This Colloquium discusses the underpinnings of the topological band theory and its materials applications.
1,179 citations
SLAC National Accelerator Laboratory1, Geballe Laboratory for Advanced Materials2, University of California, Berkeley3, Max Planck Society4, Pusan National University5, Lawrence Berkeley National Laboratory6, Pohang University of Science and Technology7, ShanghaiTech University8, University of Oxford9, Ikerbasque10, Chinese Academy of Sciences11
TL;DR: A combination of photoemission and scanning tunnelling spectroscopy measurements provide compelling evidence that single layers of 1T'-WTe2 are a class of quantum spin Hall insulator as mentioned in this paper.
Abstract: A combination of photoemission and scanning tunnelling spectroscopy measurements provide compelling evidence that single layers of 1T'-WTe2 are a class of quantum spin Hall insulator. A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin–orbit coupling1,2. By investigating the electronic structure of epitaxially grown monolayer 1T'-WTe2 using angle-resolved photoemission (ARPES) and first-principles calculations, we observe clear signatures of topological band inversion and bandgap opening, which are the hallmarks of a QSH state. Scanning tunnelling microscopy measurements further confirm the correct crystal structure and the existence of a bulk bandgap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Our results establish monolayer 1T'-WTe2 as a new class of QSH insulator with large bandgap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).
628 citations
TL;DR: In this article, the Weyl semimetal WTe2 was shown to become a 2DTI in monolayer form if a bulk gap opens and the edge conduction was suppressed by an in-plane magnetic field.
Abstract: Experiments showing that a single layer of WTe2 can conduct electricity along its edges while insulating in the interior suggests that this material is a two-dimensional topological insulator A two-dimensional topological insulator (2DTI) is guaranteed to have a helical one-dimensional edge mode1,2,3,4,5,6,7,8,9,10,11 in which spin is locked to momentum, producing the quantum spin Hall effect and prohibiting elastic backscattering at zero magnetic field No monolayer material has yet been shown to be a 2DTI, but recently the Weyl semimetal WTe2 was predicted12 to become a 2DTI in monolayer form if a bulk gap opens Here, we report that, at temperatures below about 100 K, monolayer WTe2 does become insulating in its interior, while the edges still conduct The edge conduction is strongly suppressed by an in-plane magnetic field and is independent of gate voltage, save for mesoscopic fluctuations that grow on cooling due to a zero-bias anomaly, which reduces the linear-response conductance Bilayer WTe2 also becomes insulating at low temperatures but does not show edge conduction Many of these observations are consistent with monolayer WTe2 being a 2DTI However, the low-temperature edge conductance, for contacts spacings down to 150 nm, never reaches values higher than ∼20 μS, about half the predicted value of e2/h, suggesting significant elastic scattering in the edge
515 citations
TL;DR: In this article, the authors mainly focus on recent progress in the engineering of topologically nontrivial phases (such as topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems.
Abstract: Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as [Formula: see text] topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.
389 citations
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TL;DR: In this paper, the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topologically insulators have been observed.
Abstract: Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on $\mathrm{Hg}\mathrm{Te}∕\mathrm{Cd}\mathrm{Te}$ quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.
15,562 citations
TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.
11,092 citations
TL;DR: Graphene is converted from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator and the spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.
Abstract: We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are nonchiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.
6,058 citations
TL;DR: In this article, the quantum spin Hall (QSH) effect can be realized in mercury-cadmium telluride semiconductor quantum wells, a state of matter with topological properties distinct from those of conventional insulators.
Abstract: We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride–cadmium telluride semiconductor quantum wells. When the thickness of the quantum well is varied, the electronic state changes from a normal to an “inverted” type at a critical thickness d c . We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss methods for experimental detection of the QSH effect.
5,187 citations
TL;DR: The Z2 order of the QSH phase is established in the two band model of graphene and a generalization of the formalism applicable to multiband and interacting systems is proposed.
Abstract: The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.
4,973 citations