Transport through a quantum spin Hall quantum dot

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 study the interplay between Dirac and Schrödinger fermions in the polarization properties of a two-dimensional electron gas (2DEG). Specifically, we analyze the low-energy sector of narrow-gap semiconductors described by a two-band Kane model. In the context of quantum spin Hall insulators, particularly, in Hg(Cd)Te quantum wells, this model is named the Bernevig-Hughes-Zhang model. Interestingly, it describes electrons with intermediate properties between Dirac and Schrödinger fermions. We calculate the dynamical dielectric function of such a model at zero temperature within random phase approximation. Surprisingly, plasmon resonances are found in the intrinsic (undoped) limit, whereas they are absent-in that limit-in graphene as well as ordinary 2DEGs. Additionally, we demonstrate that the optical conductivity offers a quantitative way to identify the topological phase of Hg(Cd)Te quantum wells from a bulk measurement.

Topological insulators (TIs) are promising for achieving dissipationless transport devices due to the robust gapless states inside the insulating bulk gap. However, currently realized two-dimensional (2D) TIs, quantum spin Hall (QSH) insulators, suffer from ultrahigh vacuum and extremely low temperature. Thus, seeking for desirable QSH insulators with high feasibility of experimental preparation and large nontrivial gap is of great importance for wide applications in spintronics. On the basis of the first-principles calculations, we predict a novel family of 2D QSH insulators in transition-metal halide MX (M = Zr, Hf; X = Cl, Br, and I) monolayers, especially, which is the first case based on transition-metal halide-based QSH insulators. MX family has the large nontrivial gaps of 0.12-0.4 eV, comparable with bismuth (111) bilayer (0.2 eV), stanene (0.3 eV), and larger than ZrTe5 (0.1 eV) monolayers and graphene-based sandwiched heterstructures (30-70 meV). Their corresponding 3D bulk materials are weak topological insulators from stacking QSH layers, and some of bulk compounds have already been synthesized in experiment. The mechanism for 2D QSH effect in this system originates from a novel d-d band inversion, significantly different from conventional band inversion between s-p, p-p, or d-p orbitals. The realization of pure layered MX monolayers may be prepared by exfoliation from their 3D bulk phases, thus holding great promise for nanoscale device applications and stimulating further efforts on transition metal-based QSH materials.

The properties of HgTe/Hg1−x Cdx Te superlattices (SLs) and quantum wells, (QWs), are of fundamental interest; SLs are potentially useful for infrared opto-electronic applications and QWs have aroused much interest due to recent evidence that they are topological insulators with dissipation less transport in edge states in the absence of a magnetic field. Depending on the HgTe thickness , the band structure has either the normal sequence of quantum well states or an inverted one when nm, in which the electron E1 subband is a valence subband and lies below the heavy hole H1 subband. This has been shown to lead to a very large Rashba spin–orbit (s–o) splitting of up to meV in HgTe/Hg1−x Cdx Te QWs with an inverted band structure. This as well as other transport results will be presented. These properties of the HgTe/Hg1−x Cdx Te QW, large s–o splitting and an inverted band structure, have recently been shown to result in the quantum spin Hall effect. In the quantum spin Hall effect, carriers with opposite spin move in opposite directions on a given edge in an insulator in the absence of a magnetic field. Convincing evidence for non-local edge channel transport in HgTe based QWs has been recently published. The results demonstrate that quantum transport through helical edge channels is dissipation less at zero magnetic field and agree quantitatively with the theory of the quantum spin Hall effect. Images of current in the edge channels by means of scanning gate microscopy have revealed well localized scattering sites which perturb the quantum spin Hall edge states on a sub-micrometer scale. In the micrometer sized regions between the scattering sites, current appeared to propagate unperturbed Recently, images of edge channels in HgTe QWs in the quantum spin Hall regime have been obtained by means of their magnetic fields with a scanning superconducting quantum interference device (SQUID). The edge channels were observed to dominate transport in devices with edges much longer than the scattering length, and to persist even in the presence of bulk conduction.

We present the theory and numerical evaluations of the backscattering rate determined by acceptor holes or Mn spins in HgTe and (Hg,Mn)Te quantum wells in the quantum spin Hall regime. The role of anisotropic s-p and sp-d exchange interactions, Kondo coupling, Luttinger liquid effects, precessional dephasing, and bound magnetic polarons is quantified. The determined magnitude and temperature dependence of conductance are in accord with experimental results for HgTe and (Hg,Mn)Te quantum wells.

Quantum spin Hall (QSH) insulator with large gap is highly desirable for potential spintronics application. Here we realize electrically tunable QSH insulator with large gap in van der Waals heterobilayer of monolayer transition metal dichalcogenide (TMD) and hexagonal boron arsenide (BAs), in particular the WSe2/BAs heterobilayer. When the type II band alignment gets inverted in an electric field, the hybridization by interlayer hopping between the spin-valley locked valence band edges in TMD and the BAs conduction band edges leads to a stacking-configuration dependent topological band inversion. In the non-interacting limit, the double spin degeneracy of BAs leaves an un-hybridized conduction band inside the gap, so the heterobilayer is a spin-valley locked metal instead of a QSH insulator. With the Coulomb interaction accounted in the double-layer geometry, the interaction with the hybridization induced electric dipole shifts this un-hybridized conduction band upwards in energy, giving rise to a sizable global QSH gap. Consequently, this heterobilayer provides a platform for engineering electrically tunable QSH insulator with sizable band gap. In the long-period moiré pattern with the spatial variation of local stacking-configurations, the competition between Coulomb interaction and interlayer hopping leads to superstructures of QSH insulators and excitonic insulators.

Topologically protected edge states of 2D quantum spin Hall (QSH) insulators have paved the way for dissipationless transport. In this regard, one of the key challenges is to find suitable QSH insulators with large bandgaps. Group IV analogues of graphene such as silicene, germanene, stanene, plumbene etc. are promising materials for QSH insulators. This is because their high spin–orbit coupling (SOC) and large bandgap opening may be possible by chemically decorating these group IV graphene analogues. However, finding suitable chemical groups for such decoration has always been a demanding task. In this work, we investigate the performance of a plumbene monolayer with –CX3 (X = H, F, Cl) chemical decoration and report very large bandgaps in the range of 0.8414 eV to 0.9818 eV with spin–orbit coupling, which is much higher compared to most other topological insulators and realizable at room temperature. The topological invariants of the samples are calculated to confirm their topologically nontrivial properties. The existence of edge states and topological nontrivial property are illustrated by investigating PbCX3 nanoribbons with zigzag edges. Lastly, the structural and electronic stability of the topological materials against strain are demonstrated to extend the scope of using these materials. Our findings suggest that these derivatives are promising materials for spintronic and future high performance nanoelectronic devices.

Spin‐polarized conducting edge currents counterpropagate in quantum spin Hall (QSH) insulators and are protected against disorder‐driven localizations by the time‐reversal symmetry. Using these spin‐currents for device applications requires materials with a large bandgap and fast switchable QSH states. By means of in‐depth first‐principles calculations, this study demonstrates the large bandgap and fast switchable QSH state in a newly introduced 2D material family with 1T′‐MGe2Z4 (M = Mo or W and Z = P or As). These Ge‐based compounds show superior properties with respect to other members of the same family. For the WGe2As4 monolayer it can stabilize the 1T′‐phase, while for the other members of the family, this study needs an appropriate strain. The dynamically stable 1T′‐MGe2Z4 monolayers have a large energy gap up to 237 meV for WGe2As4. These materials undergo a phase transition from a QSH insulator to a trivial insulator with a Rashba‐like spin splitting under the influence of an out‐of‐plane electric field, demonstrating a fast tunability of the bandgap and its band topology for the Ge‐based compounds. Fast topological phase switching in a large gap 1T′‐MGe2Z4 QSH insulators have potential applications in low‐power devices, quantum computation, and quantum communication.

We study the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary. We calculate various edge properties in an N\to\inftyN→∞ limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as ``fractional’’ degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the quantum spin Hall state but with the full SU(2)SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped.

The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators, here we investigate topological phase transitions to/from quantum spin Hall (QSH) insulators driven by non-Hermiticity. We show that a trivial to QSH insulator phase transition can be induced by solely varying non-Hermitian terms, and there exists exceptional edge arcs in QSH phases. We establish two topological invariants for characterizing the non-Hermitian phase transitions: i) with time-reversal symmetry, the biorthogonal $\mathbb{Z}_2$ invariant based on non-Hermitian Wilson loops, and ii) without time-reversal symmetry, a biorthogonal spin Chern number through biorthogonal decompositions of the Bloch bundle of the occupied bands. These topological invariants can be applied to a wide class of non-Hermitian topological phases beyond Chern classes, and provides a powerful tool for exploring novel non-Hermitian topological matter and their device applications.

Quantum Spin Hall (QSH) insulators with a large topologically nontrivial bulk gap are crucial for future applications of the QSH effect. Among these, group III-V monolayers and their halides with chair structure (regular hexagonal framework, RHF) were widely studied. Using first-principles calculations, we propose a new structure model for the functionalized group III-V monolayers, which consist of rectangular GaBi-X2 (X=I, Br, Cl) monolayers with a distorted hexagonal framework (DHF). These structures have a much lower energy than the GaBi-X2 monolayers with chair structure. Remarkably, the DHF GaBi-X2 monolayers are all QSH insulators, which exhibit sizeable nontrivial band gaps ranging from 0.17 eV to 0.39 eV. Those band gaps can be widely tuned by applying different spin-orbit coupling (SOC) strengths, resulting in a distorted Dirac cone.

Quantum spin Hall insulators are two-dimensional materials that host conducting helical electron states strictly confined to the one-dimensional boundaries. These edge channels are protected by time-reversal symmetry against single-particle backscattering, opening new avenues for spin-based electronics and computation. However, the effect of the interelectronic Coulomb repulsion also has to be taken into account, as two-particle scattering is not impeded by topological protection and may strongly affect the edge state conductance. Here, we explore the impact of electronic correlations on highly localized edge states of the unique quantum spin Hall material bismuthene on SiC(0001) (ref. 1). Exploiting the advantage of having an accessible monolayer substrate system, we use STM/STS to visualize the close-to-perfect one-dimensional confinement of the edge channels and scrutinize their suppressed density of states at the Fermi level. On the basis of the observed spectral behaviour and its universal scaling with energy and temperature, we demonstrate the correspondence with a (helical) Tomonaga–Luttinger liquid. In particular, the extracted interaction parameter K is directly relevant to the fundamental question of the temperatures at which the quantized conductance (a hallmark of quantum spin Hall materials) will become obscured by correlations2. Scanning tunnelling microscopy and spectroscopy study of the conductive edge state in a two-dimensional topological insulator reveals the interplay of topology and electronic correlations.

Achieving combination of spin and valley polarized states with topological insulating phase is pregnant to promote the fantastic integration of topological physics, spintronics and valleytronics. In this work, a spin-valley-coupled quantum spin Hall insulator (svc-QSHI) is predicted in Janus monolayer CSb1.5Bi1.5 with dynamic, mechanical and thermal stabilities. Calculated results show that the CSb1.5Bi1.5 is a direct band gap semiconductor with and without spin–orbit coupling, and the conduction-band minimum and valence-band maximum are at valley point. The inequivalent valleys have opposite Berry curvature and spin moment, which can produce a spin-valley Hall effect. In the center of Brillouin zone, a Rashba-type spin splitting can be observed due to missing horizontal mirror symmetry. The topological characteristic of CSb1.5Bi1.5 is confirmed by the Z 2 invariant and topological protected conducting helical edge states. Moreover, the CSb1.5Bi1.5 shows unique Rashba-splitting edge states. Both energy band gap and spin-splitting at the valley point are larger than the thermal energy of room temperature (25 meV) with generalized gradient approximation level, which is very important at room temperature for device applications. It is proved that the spin-valley-coupling and nontrivial quantum spin Hall state are robust again biaxial strain. Our work may provide a new platform to achieve integration of topological physics, spintronics and valleytronics.

We study the quantum beats in the polarization of the photon echo from\ndonor-bound exciton ensembles in semiconductor quantum wells. To induce these\nquantum beats, a sequence composed of a circularly polarized and a linearly\npolarized picosecond laser pulse in combination with an external transverse\nmagnetic field is used. This results in an oscillatory behavior of the photon\necho amplitude, detected in the $\\sigma^+$ and $\\sigma^-$ circular\npolarizations, occurring with opposite phases relative to each other. The\nbeating frequency is the sum of the Larmor frequencies of the resident electron\nand the heavy hole when the second pulse is polarized along the magnetic field.\nThe beating frequency is, on the other hand, the difference of these Larmor\nfrequencies when the second pulse is polarized orthogonal to the magnetic\nfield. The measurement of both beating frequencies serves as a method to\ndetermine precisely the in-plane hole $g$ factor, including its sign. We apply\nthis technique to observe the quantum beats in the polarization of the photon\necho from the donor-bound excitons in a 20-nm-thick\nCdTe/Cd$_{0.76}$Mg$_{0.24}$Te quantum well. From these quantum beats we obtain\nthe in-plane heavy hole $g$ factor $g_h=-0.143\\pm0.005$.\n

Resonant reflectivity study of exciton oscillator strength in CdTe/(Cd,Mn)Te quantum wells and superlattices