Tuning Edge States in Strained-Layer InAs/GaInSb Quantum Spin Hall Insulators

Exciton Condensation in Landau Levels of Quantum Spin Hall Insulators

We theoretically study the quantum spin Hall insulator (QSHI) in a perpendicular magnetic field. In the noninteracting case, the QSHI with space inversion and/or uniaxial spin rotation symmetry undergoes a topological transition into a normal insulator phase at a critical magnetic field B_{c}. The exciton condensation in the lowest Landau levels is triggered by Coulomb interactions in the vicinity of B_{c} at low temperature and spontaneously breaks the inversion and the spin rotation symmetries. We propose that the electron spin resonance spectroscopy with the ac magnetic field also aligned in the perpendicular direction can directly probe the exciton condensation order. Our results should apply to QSHIs such as the InAs/GaSb quantum wells and monolayer transition-metal dichalcogenides.

Quantum Spin Hall Effect in Two-Monolayer-Thick InN/InGaN Coupled Multiple Quantum Wells

In this study, we present a theoretical study of the quantum spin Hall effect in InN/InGaN coupled multiple quantum wells with the individual well widths equal to two atomic monolayers. We consider triple and quadruple quantum wells in which the In content in the interwell barriers is greater than or equal to the In content in the external barriers. To calculate the electronic subbands in these nanostructures, we use the eight-band k∙p Hamiltonian, assuming that the effective spin-orbit interaction in InN is negative, which represents the worst-case scenario for achieving a two-dimensional topological insulator. For triple quantum wells, we find that when the In contents of the external and interwell barriers are the same and the widths of the internal barriers are equal to two monolayers, a topological insulator with a bulk energy gap of 0.25 meV can appear. Increasing the In content in the interwell barriers leads to a significant increase in the bulk energy gap of the topological insulator, reaching about 0.8 meV. In these structures, the topological insulator can be achieved when the In content in the external barriers is about 0.64, causing relatively low strain in quantum wells and making the epitaxial growth of these structures within the range of current technology. Using the effective 2D Hamiltonian, we study the edge states in strip structures containing topological triple quantum wells. We demonstrate that the opening of the gap in the spectrum of the edge states caused by decreasing the width of the strip has an oscillatory character regardless of whether the pseudospin-mixing elements of the effective Hamiltonian are omitted or taken into account. The strength of the finite size effect in these structures is several times smaller than that in HgTe/HgCdTe and InAs/GaSb/AlSb topological insulators. Therefore, its influence on the quantum spin Hall effect is negligible in strips with a width larger than 150 nm, unless the temperature at which electron transport is measured is less than 1 mK. In the case of quadruple quantum wells, we find the topological insulator phase only when the In content in the interwell barriers is larger than in the external barriers. We show that in these structures, a topological insulator with a bulk energy gap of 0.038 meV can be achieved when the In content in the external barriers is about 0.75. Since this value of the bulk energy gap is very small, quadruple quantum wells are less useful for realizing a measurable quantum spin Hall system, but they are still attractive for achieving a topological phase transition and a nonlocal topological semimetal phase.

Excitonic topological order in imbalanced electron-hole bilayers

Correlation and frustration play essential roles in physics, giving rise to novel quantum phases^1-6. A typical frustrated system is correlated bosons on moat bands, which could host topological orders with long-range quantum entanglement⁴. However, the realization of moat-band physics is still challenging. Here, we explore moat-band phenomena in shallowly inverted InAs/GaSb quantum wells, where we observe an unconventional time-reversal-symmetry breaking excitonic ground state under imbalanced electron and hole densities. We find that a large bulk gap exists, encompassing a broad range of density imbalances at zero magnetic field (B), accompanied by edge channels that resemble helical transport. Under an increasing perpendicular B, the bulk gap persists, and an anomalous plateau of Hall signals appears, which demonstrates an evolution from helical-like to chiral-like edge transport with a Hall conductance approximately equal to e²/h at 35 tesla, where e is the elementary charge and h is Planck's constant. Theoretically, we show that strong frustration from density imbalance leads to a moat band for excitons, resulting in a time-reversal-symmetry breaking excitonic topological order, which explains all our experimental observations. Our work opens up a new direction for research on topological and correlated bosonic systems in solid states beyond the framework of symmetry-protected topological phases, including but not limited to the bosonic fractional quantum Hall effect.

Polarization-Induced Phase Transitions in Ultra-Thin InGaN-Based Double Quantum Wells

We investigate the phase transitions and the properties of the topological insulator in InGaN/GaN and InN/InGaN double quantum wells grown along the [0001] direction. We apply a realistic model based on the nonlinear theory of elasticity and piezoelectricity and the eight-band k·p method with relativistic and nonrelativistic linear-wave-vector terms. In this approach, the effective spin−orbit interaction in InN is negative, which represents the worst-case scenario for obtaining the topological insulator in InGaN-based structures. Despite this rigorous assumption, we demonstrate that the topological insulator can occur in InGaN/GaN and InN/InGaN double quantum wells when the widths of individual quantum wells are two and three monolayers (MLs), and three and three MLs. In these structures, when the interwell barrier is sufficiently thin, we can observe the topological phase transition from the normal insulator to the topological insulator via the Weyl semimetal, and the nontopological phase transition from the topological insulator to the nonlocal topological semimetal. We find that in InGaN/GaN double quantum wells, the bulk energy gap in the topological insulator phase is much smaller for the structures with both quantum well widths of 3 MLs than in the case when the quantum well widths are two and three MLs, whereas in InN/InGaN double quantum wells, the opposite is true. In InN/InGaN structures with both quantum wells being three MLs and a two ML interwell barrier, the bulk energy gap for the topological insulator can reach about 1.2 meV. We also show that the topological insulator phase rapidly deteriorates with increasing width of the interwell barrier due to a decrease in the bulk energy gap and reduction in the window of In content between the normal insulator and the nonlocal topological semimetal. For InN/InGaN double quantum wells with the width of the interwell barrier above five or six MLs, the topological insulator phase does not appear. In these structures, we find two novel phase transitions, namely the nontopological phase transition from the normal insulator to the nonlocal normal semimetal and the topological phase transition from the nonlocal normal semimetal to the nonlocal topological semimetal via the buried Weyl semimetal. These results can guide future investigations towards achieving a topological insulator in InGaN-based nanostructures.

Topological spintronics and magnetoelectronics

Topological electronic materials, such as topological insulators, are distinct from trivial materials in the topology of their electronic band structures that lead to robust, unconventional topological states, which could bring revolutionary developments in electronics. This Perspective summarizes developments of topological insulators in various electronic applications including spintronics and magnetoelectronics. We group and analyse several important phenomena in spintronics using topological insulators, including spin-orbit torque, the magnetic proximity effect, interplay between antiferromagnetism and topology, and the formation of topological spin textures. We also outline recent developments in magnetoelectronics such as the axion insulator and the topological magnetoelectric effect observed using different topological insulators.

Charge transport spectra in superconductor-InAs/GaSb-superconductor heterostructures

Charge transport physics in InAs/GaSb bi-layer systems has recently attracted attention for the experimental search for two-dimensional topological superconducting states in solids. Here we report measurement of charge transport spectra of nano devices consisting of an InAs/GaSb quantum well sandwiched by tantalum superconductors. We explore the current-voltage relation as a function of the charge-carrier density in the quantum well controlled by a gate voltage and an external magnetic field. We observe three types of differential resistance peaks, all of which can be effectively tuned by the external magnetic field, and, however, two of which appear at electric currents independent of the gate voltage, indicating a dominant mechanism from the superconductor and the system geometry. By analyzing the spectroscopic features, we find that the three types of peaks identify Andreev reflections, quasi-particle interference, and superconducting transitions in the device, respectively. Our results provide a basis for further exploration of possible topological superconducting state in the InAs/GaSb system.

Higher-order topological insulator in cubic semiconductor quantum wells

The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order topological insulator state in quantum wells based on the most common semiconducting materials. By successively deriving the bulk and boundary Hamiltonians, we theoretically prove the existence of topological corner states due to cubic symmetry in quantum wells with double band inversion. We show that the appearance of corner states does not depend solely on the crystallographic orientation of the meeting edges, but also on the growth orientation of the quantum well. Our theoretical results significantly extend the application potential of topological quantum wells based on IV, II–VI and III–V semiconductors with diamond or zinc-blende structures.

Dissipative Hot-Spot-Enabled Shock and Bounce Dynamics via Terahertz Quantum Quenches in Helical Edge States

We study quantum quenches of helical liquids with spin-flip inelastic scattering. Counterpropagating charge packets in helical edges can be created by an ultrashort electric pulse applied across a 2D topological insulator. Localized "hot spots" that form due to scattering enable two types of strongly nonlinear wave dynamics. First, propagating packets develop self-focusing shock fronts. Second, colliding packets with opposite charge can exhibit near-perfect retroreflection, despite strong dissipation. This leads to frequency doubling that could be detected experimentally from emitted terahertz radiation.

In-Plane Zeeman-Field-Induced Majorana Corner and Hinge Modes in an s-Wave Superconductor Heterostructure

Second-order topological superconductors host Majorana corner and hinge modes in contrast to conventional edge and surface modes in two and three dimensions. However, the realization of such second-order corner modes usually demands unconventional superconducting pairing or complicated junctions or layered structures. Here we show that Majorana corner modes could be realized using a 2D quantum spin Hall insulator in proximity contact with an s-wave superconductor and subject to an in-plane Zeeman field. Beyond a critical value, the in-plane Zeeman field induces opposite effective Dirac masses between adjacent boundaries, leading to one Majorana mode at each corner. A similar paradigm also applies to 3D topological insulators with the emergence of Majorana hinge states. Avoiding complex superconductor pairing and material structure, our scheme provides an experimentally realistic platform for implementing Majorana corner and hinge states.

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 [Formula: see text] 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 [Formula: see text] 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.

Real Space Imaging of Topological Edge States in InAs/GaSb and InAs/InxGa1-xSb Quantum Wells

Structure dependent differential tunneling conductance, dI/dV, profiles obtained using scanning tunneling microscopy on both (110)-cleaved surfaces and (001)-growth surfaces in InAs/GaSb and InAs/In_xGa_1-xSb quantum wells (QWs), which are platforms of two-dimensional topological insulator (2D-TI), clearly demonstrated the edge states formed on the 2D-TI surfaces. The results were confirmed by kp-based electronic structure calculations, which demonstrated that the edge states extended to the 10 nm range from cleaved surfaces generated in the appropriately designed InAs/(In)GaSb QW systems.

Anomalous Conductance Oscillations in the Hybridization Gap of InAs/GaSb Quantum Wells

We observe the magnetic oscillation of electric conductance in the two-dimensional InAs/GaSb quantum spin Hall insulator. Its insulating bulk origin is unambiguously demonstrated by the antiphase oscillations of the conductance and the resistance. Characteristically, the in-gap oscillation frequency is higher than the Shubnikov-de Haas oscillation close to the conduction band edge in the metallic regime. The temperature dependence shows both thermal activation and smearing effects, which cannot be described by the Lifshitz-Kosevich theory. A two-band Bernevig-Hughes-Zhang model with a large quasiparticle self-energy in the insulating regime is proposed to capture the main properties of the in-gap oscillations.

Noise-Induced Backscattering in a Quantum Spin Hall Edge

Time-reversal symmetry suppresses electron backscattering in a quantum-spin-Hall edge, yielding quantized conductance at zero temperature. Understanding the dominant corrections in finite-temperature experiments remains an unsettled issue. We study a novel mechanism for conductance suppression: backscattering caused by incoherent electromagnetic noise. Specifically, we show that an electric potential fluctuating randomly in time can backscatter electrons inelastically without constraints faced by electron-electron interactions. We quantify noise-induced corrections to the dc conductance in various regimes and propose an experiment to test this scenario.

Time-Reversal Symmetry-Breaking Nematic Insulators near Quantum Spin Hall Phase Transitions

We study the phase diagram of a model quantum spin Hall system as a function of band inversion and band-coupling strength, demonstrating that when band hybridization is weak, an interaction-induced nematic insulator state emerges over a wide range of band inversion. This property is a consequence of the long-range Coulomb interaction, which favors interband phase coherence that is weakly dependent on momentum and therefore frustrated by the single-particle Hamiltonian at the band inversion point. For weak band hybridization, interactions convert the continuous gap closing topological phase transition at inversion into a pair of continuous phase transitions bounding a state with broken time-reversal and rotational symmetries. At intermediate band hybridization, the topological phase transition proceeds instead via a quantum anomalous Hall insulator state, whereas at strong hybridization interactions play no role. We comment on the implications of our findings for InAs/GaSb and HgTe/CdTe quantum spin Hall systems.

Quantum spin Hall insulator with a large bandgap, Dirac fermions, and bilayer graphene analog

The search for room temperature quantum spin Hall insulators (QSHIs) based on widely available materials and a controlled manufacturing process is one of the major challenges of today's topological physics. We propose a new class of semiconductor systems based on multilayer broken-gap quantum wells, in which the QSHI gap reaches 60 meV and remains insensitive to temperature. Depending on their layer thicknesses and geometry, these novel structures also host a graphene-like phase and a bilayer graphene analog. Our theoretical results significantly extend the application potential of topological materials based on III-V semiconductors.