Quantum Spin Hall and Quantum Anomalous Hall States Realized in Junction Quantum Wells

Chapter 5 - Quantum Spin Hall State in HgTe

The quantum spin Hall (QSH) state, observed in a zero magnetic field in HgTe quantum wells, respects the time-reversal symmetry and is distinct from quantum Hall (QH) states. We show that the QSH state persists in strong quantizing fields and is identified by counterpropagating (helical) edge channels with nonlinear dispersion inside the band gap. If the Fermi level is shifted into the Landau-quantized conduction or valence band, we find a transition between the QSH and QH regimes. Near the transition the longitudinal conductance of the helical channels is strongly suppressed due to the combined effect of the spectrum nonlinearity and enhanced backscattering. It shows a power-law decay B(-2N) with magnetic field B, determined by the number of backscatterers on the edge N. This suggests a rather simple and practical way to probe the quality of quasiballistic QSH devices using magnetoresistance measurements.

A large bulk band gap is critical for the applications of quantum spin hall (QSH) insulators in spintronics at room temperature. Based on first-principles calculations, we predict that the methyl-functionalized III-Bi monolayers, namely III-Bi-(CH3)2 (III=Ga, In, Tl) thin films, own QSH states with band gap as large as 0.260, 0.304 and 0.843 eV, respectively, making them suitable for room-temperature applications. The topological characteristics are confirmed by s-px,y band inversion, topological invariant Z2, and the topologically protected edge states. Noticeably, for GaBi/InBi-(CH3)2 films, the s-px,y band inversion occurred in the progress of spin-orbital coupling (SOC), while for TlBi(CH3)2 film, the s-px,y band inversion happened in the progress of chemical bonding. Significantly, the QSH states in III-Bi-(CH3)2 films are robust against the mechanical strains and various methyl coverages, making these films particularly flexible to substrate choice for device applications. Besides, the h-BN substrate is an ideal substrate for III-Bi-(CH3)2 films to realize large gap nontrivial topological states.. These findings demonstrate that the methyl-functionalized III-Bi films may be good QSH effect platforms for topological electronic devices design and fabrication in spintronics.

Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

Quantum spin Hall (QSH) effect, a fundamentally new quantum state of matter and topological phase transitions are characteristics of a kind of electronic material, popularly referred to as topological insulators (TIs). TIs are similar to ordinary insulator in terms of their bulk bandgap, but have gapless conducting edge-states that are topologically protected. These edge-states are facilitated by the time-reversal symmetry and they are robust against nonmagnetic impurity scattering. Recently, the quest for new materials exhibiting non-trivial topological state of matter has been of great research interest, as TIs find applications in new electronics and spintronics and quantum-computing devices. Here, we propose and demonstrate as a proof-of-concept that QSH effect and topological phase transitions can be realized in /InSb semiconductor quantum wells (QWs). The simultaneous incorporation of nitrogen and bismuth in InSb is instrumental in lowering the bandgap, while inducing opposite kinds of strain to attain a near-lattice-matching conducive for lattice growth. Phase diagram for bandgap shows that as we increase the QW thickness, at a critical thickness, the electronic bandstructure switches from a normal to an inverted type. We confirm that such transition are topological phase transitions between a traditional insulator and a TI exhibiting QSH effect—by demonstrating the topologically protected edge-states using the bandstructure, edge-localized distribution of the wavefunctions and edge-state spin-momentum locking phenomenon, presence of non-zero conductance in spite of the Fermi energy lying in the bandgap window, crossover points of Landau levels in the zero-mode indicating topological band inversion in the absence of any magnetic field and presence of large Rashba spin-splitting, which is essential for spin-manipulation in TIs.

Electrically switchable quantum anomalous and spin Hall states in two-dimensional honeycomb lattices with non-Dirac bands

We theoretically study the helical edge states in the quantum spin Hall (QSH) effect based on an effective 4-band tight-binding model for HgTe/CdTe quantum wells. We microscopically describe the spatial dependence of the helical edge modes in the QSH state. It is found that the helical edge states are gapped when the width of sample narrows. This is because the edge states on the opposite boundary of the sample overlap each other, and then the backward scattering channel opens up.

The quantum spin Hall state is a topologically nontrivial insulator state protected by the time-reversal symmetry. We show that such a state always leads to spin-charge separation in the presence of a pi flux. Our result is generally valid for any interacting system. We present a proposal to experimentally observe the phenomenon of spin-charge separation in the recently discovered quantum spin Hall system.

We consider the quantum spin hall (QSH) state in a three-orbital model, with a certain spin loop current order which is induced by spin-dependent interactions. This type of order is motivated by the loop current model, which was proposed long ago to describe the pseudogap phase of cuprates. It is shown that this model has nontrivial Chern parity by directly counting the zeros of the Pfaffian of the time reversal operator. By connecting to the second Chern number, we explicitly show the property of singularities of the wave-functions, and also their dependance on the gauge choices. Also it is shown that the Berry phase of the QSH state can be mapped to a non-Abelian instanton.

As one type of important topological quantum states, the quantum spin Hall (QSH) effect realized in two-dimensional (2D) materials still maintains sufficient attractiveness due to its promising spintronic applications. By using the first-principles calculations, we theoretically investigate the structural, electronic and topological properties of a newly 2D honeycomb-Kagome WI3 monolayer (ML). The WI3 ML possesses the excellent dynamical, thermal and mechanical stabilities, as has been confirmed by phonon spectra, molecular dynamics simulations and elastic constants calculations, respectively. It is found that the WI3 ML behaves a type-II quadratic non-Dirac band dispersion around the Fermi level in the absence of spin–orbit coupling (SOC), while that may be adjusted to the type-I and/or type-III case based on the half-unilateral hydrogenation method. In the presence of SOC, the system may transform from the quadratic non-Dirac semimetal state into an intrinsic QSH state with nonzero topological invariant and Dirac-like edge states. The nontrivial topology of the system should originate from the strong SOC interaction of the degenerate W dx 2–y2/dxy states at Γ point, and a nearly 0.10 eV nontrivial global band gap has been obtained under the 4% compressive strain. The half/fully-substitutional Mo doping, hydrogenation modulation as well as substrate effect on the electronic structures and topological states of the WI3 ML have been explored. Intriguingly, the unilateral hydrogenated WI3 ML present a topological semimetal phase with robust nontrivial edge stets against SOC and in-plane biaxial strain, while the fully hydrogenated one exhibits a Dirac-type QSH state around the high-symmetry K/K′ points. Therefore, the honeycomb-Kagome WI3 ML should be the potential candidate platform for future low-power nanoelectronic and spintronic applications.

We present the first experimental evidence of a topological phase transition in a monoelemental quantum spin Hall insulator. Particularly, we show that low-buckled epitaxial germanene is a quantum spin Hall insulator with a large bulk gap and robust metallic edges. Applying a critical perpendicular electric field closes the topological gap and makes germanene a Dirac semimetal. Increasing the electric field further results in the opening of a trivial gap and disappearance of the metallic edge states. This electric field-induced switching of the topological state and the sizable gap make germanene suitable for room-temperature topological field-effect transistors, which could revolutionize low-energy electronics.

Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e(2)/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

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.

The anomalous valley Hall (AVH) effect, characterized by a polarized valley degree of freedom, provides a route toward a valley-dependent quantum anomalous Hall (QAH) state. Yet, realizing both in one material remains challenging due to their distinct Chern number requirements. We propose a general strategy for a strain-tunable topological transition in hexagonal ferromagnets. In the inversion-broken system, spin–orbit coupling yields valley polarization with valley-contrasted Chern numbers (C = ±1/2). Strain closes and reopens the gap at one valley, driving band inversion that switches the total Chern number to C = −1, transforming the system into a QAH phase with a single chiral edge channel. This strain-driven transition is demonstrated in monolayers of FeXY (X ≠ Y; Cl, Br, I), ScBr2, and VSi2P4. These results highlight the key role of strain engineering in controlling valley topology and provide a viable route toward valleytronic and topotronic applications.

Electronic and topological properties of silicene adsorbed with 4$d$ transition metal (TM) atoms are investigated by using $ab$ $initio$ methods together with tight-binding models. All six kinds of TM adatoms (Y to Ru) we studied prefer hollow sites of silicene. The interplay of TM-induced exchange interactions, spin-orbit coupling, and staggered $AB$-sublattice potential triggers abundant topological states, including quantum anomalous Hall (QAH) states, valley Hall states, and valley-polarized metallic states. Particularly, QAH states with different Chern numbers are obtained, which is $\ensuremath{-}2$ in the Nb/Ru doped system and 1 in the Y doped system. Our results indicate that great potential for information processing applications exists in these systems of silicene adsorbed with TM atoms.