Quantum Spin Hall Insulator Phase Research Articles

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers. II. Zero-field topological superconductivity

It has been proposed that band-inverted electron-hole bilayers support a phase transition from an insulating phase with spontaneously broken time-reversal symmetry to a quantum spin Hall insulator phase as a function of increasing electron and hole densities. Here we show that in the presence of proximity-induced superconductivity, it is possible to realize Majorana zero modes in the time-reversal symmetry broken phase in the absence of magnetic field. We develop an effective low-energy theory for the system in the presence of a time-reversal symmetry-breaking order parameter to obtain analytically the Majorana zero modes and we find good agreement between the numerical and analytical results in the limit of weakly broken time-reversal symmetry. We show that the Majorana zero modes can be detected in superconductor/time-reversal symmetry broken insulator/superconductor Josephson junctions through the measurement of a $4\ensuremath{\pi}$ Josephson current. Finally, we demonstrate that the Majorana fusion-rule detection is feasible by utilizing the gate voltage dependence of the spontaneous time-reversal symmetry breaking order parameter.

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers. I. Transport properties

The band-inverted electron-hole bilayers, such as InAs/GaSb, are an interesting playground for the interplay of quantum spin Hall effect and correlation effects because of the small density of electrons and holes and the relatively small hybridization between the electron and hole bands. It has been proposed that Coulomb interactions lead to a time-reversal symmetry broken phase when the electron and hole densities are tuned from the trivial to the quantum spin Hall insulator regime. We show that the transport properties of the system in the time-reversal symmetry broken phase are consistent with recent experimental observations in InAs/GaSb. Moreover, we carry out a quantum transport study on a Corbino disk where the bulk and edge contributions to the conductance can be separated. We show that the edge becomes smoothly conducting and the bulk is always insulating when one tunes the system from the trivial to the quantum spin Hall insulator phase, providing unambiguous transport signatures of the time-reversal symmetry broken phase.

Correlated disorder induced anomalous transport in magnetically doped topological insulators

We examine the transport properties of magnetically doped topological insulator (TI) thin films subject to correlated non-magnetic disorder. For the disorder we choose a quasi-periodic potential with a random phase. We restrict the disorder to a central region, which is coupled to two leads in a clean quantum spin Hall insulator (QSHI) state and concentrate on different orientations of the quasi-periodicity in the two-dimensional central region. In the case of a diagonally oriented or purely longitudinal quasi-periodicity we find different topological Anderson insulator (TAI) phases, with a quantum anomalous Hall insulator (QAHI), a quantum spin Chern insulator (QSCI), or a QSHI phase being realized before the Anderson insulation takes over at large disorder strength. Quantized transport from extended bulk states is found for diagonal quasi-periodicity in addition to the above TAI phases that are also observed for the case of uncorrelated disorder. For a purely transverse orientation of the quasi-periodicity the emerging QSHI and QSCI phases persist to arbitrarily strong disorder potential. These topological phase transitions (except to the Anderson insulator phase), can be understood from a self consistent Born approximation.

Phase transitions in intrinsic magnetic topological insulator with high-frequency pumping

In this work, we investigate the topological phase transitions in an effective model for a topological thin film with high-frequency pumping. In particular, our results show that the circularly polarized light can break the time-reversal symmetry and induce the quantum anomalous Hall insulator (QAHI) phase. Meanwhile, the bulk magnetic moment can also break the time-reversal symmetry. Therefore, it shows rich phase diagram by tuning the intensity of the light and the thickness of the thin film. Using the parameters fitted by experimental data, we give the topological phase diagram of the Cr-doped Bi2Se3 thin film, showing that by modulating the strength of the polarized optical field in an experimentally accessible range, there are four different phases: the normal insulator phase, the time-reversal-symmetry-broken quantum spin Hall insulator phase, and two different QAHI phases with opposite Chern numbers. Comparing with the non-doped Bi2Se3, it is found that the interplay between the light and bulk magnetic moment separates the two different QAHI phases with opposite Chern numbers. The results show that an intrinsic magnetic topological insulator with high-frequency pumping is an ideal platform for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.

Tunable valley filter efficiency by spin–orbit coupling in silicene nanoconstrictions* *Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LQ17A040001), the National Natural Science Foundation of China (Grant Nos. 61874078, 11647046, and 61904125), the National Key Research and Development Program of China (Grant No. 2018YFB2202100), and the Science and Technology Planning Project of Wenzhou City (Grant

Valley filter is a promising device for producing valley polarized current in graphene-like two-dimensional honeycomb lattice materials. The relatively large spin–orbit coupling in silicene contributes to remarkable quantum spin Hall effect, which leads to distinctive valley-dependent transport properties compared with intrinsic graphene. In this paper, quantized conductance and valley polarization in silicene nanoconstrictions are theoretically investigated in quantum spin-Hall insulator phase. Nearly perfect valley filter effect is found by aligning the gate voltage in the central constriction region. However, the valley polarization plateaus are shifted with the increase of spin–orbit coupling strength, accompanied by smooth variation of polarization reversal. Our findings provide new strategies to control the valley polarization in valleytronic devices.

Electrical tuning of helical edge states in topological multilayers

Mainstream among topological insulators, GaSb/InAs quantum wells present a broken gap alignment for the energy bands which supports the quantum spin Hall insulator phase and forms an important building block in the search of exotic states of matter. Such structures allow the band-gap inversion with electrons and holes confined in adjacent layers, providing a fertile ground to tune the corresponding topological properties. Using a full 3D eight-band method we investigate the inverted band structure of GaSb/InAs/GaSb and InAs/GaSb/InAs multilayers and the behavior of the helical edge states, under the influence of an electric field applied along the growth direction. By tuning the electric field modulus, we induce the change of the energy levels of both conduction and valence bands, resulting in a quantum spin Hall insulator phase where the helical edge states are predominantly confined in the GaSb layer. In particular, we found that InAs/GaSb/InAs has a large hybridization gap of about and, therefore, are promising to observe massless Dirac fermions with a large Fermi velocity. Our comprehensive characterization of GaSb/InAs multilayers creates a basis platform upon which further optimization of III–V heterostructures can be contrasted.

Unified low-energy effective Hamiltonian and the band topology of p -block square-net layer derivatives

In recent years, low-dimensional materials with tetragonal $P4/nmm$ (orthorhombic $Pnma$) space group having square-net (chain-like) substructure of $p$-block elements have been studied extensively. By using a first-principles calculation and a two-sites $\otimes$ two-orbitals tight-binding model, we construct the unified low-energy effective Hamiltonian and the $\mathbb{Z}_{2}$ topological phase diagram for such materials with different filling factors. Near the chemical potential, we show that the staggered arrangement of ions at 2c (4c) site yields the virtual hopping that have the same form with the second nearest-neighbor hopping between the square-net (chain-like) ions. We show that this hybridization and low-symmetry of the chain-like structure protects the quantum spin Hall insulator phase. Finally, the second order spin-orbit coupling on top of the atomic spin-orbit coupling is considered to clarify the origin of the non-zero Berry phase signals reported in recent quantum oscillation experiments.

Two- and three-dimensional topological phases in BiTeX compounds

Recently, it was shown that quantum spin Hall insulator phase with a gap wide enough for practical applications can be realized in the ultrathin films constructed from two inversely stacked structural elements of trivial band insulator BiTeI. Here, we study the edge states in nanoribbons made of the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}{\mathrm{I}}_{2}$ sextuple layer (SL) and the electronic structure of the SL deposited on the natural BiTeI substrate as well as sandwiched between two thick BiTeI films. We show that the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}{\mathrm{I}}_{2}$ SL keeps nontrivial topological properties. We also demonstrate that ultrathin centrosymmetric films constructed in a similar manner from related material BiTeBr are trivial band insulators up to five-SL film thickness. In contrast to ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}{\mathrm{I}}_{2}$ for which the stacking of nontrivial SLs in a three-dimensional (3D) limit results in a strong topological insulator (TI) phase, a 3D TI ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}{\mathrm{Br}}_{2}$ is formed by trivial SLs. For the last material of the $\mathrm{BiTe}X$ ($X=\text{I}$,Br,Cl) series, BiTeCl, both 2D and 3D centrosymmetric phases are characterized by topologically trivial band structure.

Quantum spin Hall insulator phase in monolayer WTe2 by uniaxial strain

Monolayer WTe2, which is predicted to be large-gap quantum spin Hall (QSH) insulators with distorted 1T (1T’) structure, attracts rapidly growing interests. However, the intrinsic semimetallic nature of the monolayer 1T’-WTe2 limits their direct applications based on QSH effect. By first-principles density functional theoretical calculations, we demonstrate a phase transition from semimetal to QSH insulator under the uniaxial strains along a and b axis in monolayer 1T’-WTe2. The electronic phase transition results from the geometric structure deformation upon the uniaxial strains. This suggests monolayer 1T’-WTe2 as a promising material for application in strain-tunable topological quantum electronics.

Multiple unpinned Dirac points in group-Va single-layers with phosphorene structure

AbstractEmergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitutes one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black phosphorous, has been a subject of intense investigations recently, and it was found that other group-Va elements could also form 2D layers with similar puckered lattice structure. Here, by a close examination of their electronic band structure evolution, we discover two types of Dirac fermion states emerging in the low-energy spectrum. One pair of (type-I) Dirac points is sitting on high-symmetry lines, while two pairs of (type-II) Dirac points are located at generic k-points, with different anisotropic dispersions determined by the reduced symmetries at their locations. Such fully-unpinned (type-II) 2D Dirac points are discovered for the first time. In the absence of spin-orbit coupling (SOC), we find that each Dirac node is protected by the sublattice symmetry from gap opening, which is in turn ensured by any one of three point group symmetries. The SOC generally gaps the Dirac nodes, and for the type-I case, this drives the system into a quantum spin Hall insulator phase. We suggest possible ways to realise the unpinned Dirac points in strained phosphorene.

Dimensional crossover of transport characteristics in topological insulator nanofilms

We show how the two-dimensional (2D) topological insulator evolves, by stacking, into a strong or weak topological insulator with different topological indices, proposing a new conjecture that goes beyond an intuitive picture of the crossover from quantum spin Hall to the weak topological insulator. Studying the conductance under different boundary conditions, we demonstrate the existence of two conduction regimes in which conduction happens through either surface- or edge-conduction channels. We show that the two conduction regimes are complementary and exclusive. Conductance maps in the presence and absence of disorder are introduced, together with 2D $\mathbb{Z}_2$-index maps, describing the dimensional crossover of the conductance from the 2D to the 3D limit. Stacking layers is an effective way to invert the gap, an alternative to controlling the strength of spin-orbit coupling. The emerging quantum spin Hall insulator phase is not restricted to the case of odd numbers of layers.

Interplay of exciton condensation and the quantum spin hall effect in InAs/GaSb bilayers.

We study the phase diagram of the inverted InAs/GaSb bilayer quantum wells. For a small tunneling amplitude between the layers, we find that the system is prone to the formation of an s-wave exciton condensate phase, where the spin structure of the order parameter is uniquely determined by the small spin-orbit coupling arising from the bulk inversion asymmetry. The phase is topologically trivial and does not support edge transport. On the contrary, for a large tunneling amplitude, we obtain a topologically nontrivial quantum spin Hall insulator phase with a p-wave exciton order parameter, which enhances the hybridization gap. These topologically distinct insulators are separated by an insulating phase with spontaneously broken time-reversal symmetry. Close to the phase transition between the quantum spin Hall and time-reversal broken phases, the edge transport shows quantized conductance in small samples, whereas in long samples the mean free path associated with the backscattering at the edge is temperature independent, in agreement with recent experiments.

Topological phase transition in a graphene system with a coexistence of Coulomb interaction, staggered potential, and intrinsic spin-orbit coupling

Using a mean-field approximation of the Hubbard model, we investigate the topological phase transition of the graphene system with an intrinsic spin-orbit coupling undergoing a coexistence of a Coulomb interaction and a staggered potential. We find that in an infinite system the antiferromagnetic phase can be classified into four types according to their topological properties: Two of them belong to the normal band-insulator phase, the third type is the quantum spin Hall insulator phase, although the inversion symmetry and the time-reversal symmetry are broken, and the fourth is the spin-polarized quantum Hall insulator phase, a different state of matter possessing Chern number 1 and spin Chern numbers $\frac{1}{2}$, which emerges due to the interplay between the Coulomb repulsion and the breaking of the sublattice symmetry. In addition, the number of edge states in a zigzag graphene ribbon whose parameters belong to one of these types confirms the validity of the analysis of the four phases. All the results obtained from a simplified toy model agree with those acquired from the self-consistent calculation. This indicates that the proposed toy model can exactly and analytically provide the essential information on the phase transition process of such graphene systems.