Quantum Spin Hall Insulator Research Articles

Real-space obstruction in quantum spin Hall insulators

The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic Wannier functions and the ionic positions. We extend this notion to quantum spin Hall insulators in which the ground state cannot be described in terms of time-reversal symmetric localized Wannier functions. A system equivalent to graphene in all its relevant electronic and topological properties except for a real-space obstruction is identified and studied via symmetry analysis as well as with density functional theory. The low-energy model comprises a local spin-orbit coupling and a non-local symmetry breaking potential, which turn out to be the essential ingredients for an obstructed quantum spin Hall insulator. An experimental fingerprint of the obstruction is then measured in a large-gap triangular quantum spin Hall material.

Direct Observation of the Topological Surface State in the Topological Superconductor 2M-WS2.

The quantum spin Hall (QSH) effect has attracted extensive research interest because of the potential applications in spintronics and quantum computing, which is attributable to two conducting edge channels with opposite spin polarization and the quantized electronic conductance of 2e2/h. Recently, 2M-WS2, a new stable phase of transition metal dichalcogenides with a 2M structure showing a layer configuration identical to that of the monolayer 1T' TMDs, was suggested to be a QSH insulator as well as a superconductor with a critical transition temperature of around 8 K. Here, high-resolution angle-resolved photoemission spectroscopy (ARPES) and spin-resolved ARPES are applied to investigate the electronic and spin structure of the topological surface states (TSS) in the superconducting 2M-WS2. The TSS exhibit characteristic spin-momentum-locking behavior, suggesting the existence of long-sought nontrivial topological states therein. We expect that 2M-WS2 with coexisting superconductivity and TSS might host the promising Majorana bound states.

Bipolar spin-conversion diode and quantum entanglement induced by the valley and pseudoparity mixing

Herein, we report on a zigzag graphene superconducting junction with a superconductor sandwiched in between two magnetized zigzag graphene nanoribbons, where the valley and pseudoparity mixing are shown to bring about peculiar properties. We find that the bipolar spin diode and spin-conversion diode in the ferromagnetic configuration as well as quantum entanglement in the antiferromagnetic one are exhibited. The noncollinear angle combined with the valley and pseudoparity mixing in arbitrary magnetic configurations exerts a significant influence on the transport properties. In addition, not only the bipolar spin diode and magnetic storage with high efficiencies but also the bipolar spin-conversion diode and quantum entanglement can coexist in one setup. Particularly, the bipolar spin-conversion diode can be used to directly detect and confirm the helical spin texture of the edge state in a quantum spin Hall insulator.

Two-dimensional antiferromagnetic nodal-line semimetal and quantum anomalous Hall state in the van der Waals heterostructure germanene/Mn2S2

Materials with interactions between the topology and magnetism are triggering increasing interest. We constructed a two-dimensional (2D) van der Waals heterostructure germanene/Mn2S2, where the germanene is a quantum spin Hall insulator and Mn2S2 provides antiferromagnetic (AFM) interactions. In this structure, a 2D AFM nodal-line semimetal (NLSM) phase is expected without the spin–orbit coupling (SOC), which is of a high density of states around the Fermi level. The band touching rings originate from the intersection between different spin components of p orbitals of germanene. This result provides a possible 2D realization of NLSMs, which are usually realized in three-dimensional systems. When the SOC is present, a quantum anomalous Hall (QAH) state emerges with the annihilation of the band-touching rings. The nontrivial topology is determined by calculating the Chern number and Wannier charge centers. This provides an alternative platform to realize QAH states. These results could also provide the possibility of further understanding the topological states in NLSM and electronic applications.

Effect of C3v symmetry breaking on the noncentrosymmetric quantum spin Hall insulating phase and optical characteristics of monolayer PbBiI

Due to the rise of applications in several optoelectronic and spintronic platforms, theoretically engineering the propagation of light in low-dimensional systems dealing with both charge and spin degrees of freedom has recently triggered considerable interest. By breaking the ${C}_{3v}$ symmetry through external exchange fields, we engineer the propagation of an incident circularly polarized light in a noncentrosymmetric quantum spin Hall insulator, monolayer PbBiI, that is active in the near-infrared region of the electromagnetic spectrum. The Kubo formalism is ideal for optical properties. We endeavor to thoroughly demonstrate that a critical-breaking regime of three types of fields leads to various anisotropic electronic phases and optical interband transitions. We find various near-to-far infrared shifts for the optical activity of the system when the ${C}_{3v}$ symmetry breaking fields are turned on. This is proven in the ensuing two ways: The spectrum of optical conductivity components and the intensities of scattered/absorbed light. We further find the criteria under which the system is transparent. Finally, depending on the exchange fields, we engineer the eccentricities for the reflected and transmitted lights in monolayer PbBiI to see how the polarization of incident circular light becomes linear and elliptical. The applicability of results in industry and medicine is also briefly discussed.

Observation of room temperature excitons in an atomically thin topological insulator

Optical spectroscopy of ultimately thin materials has significantly enhanced our understanding of collective excitations in low-dimensional semiconductors. This is particularly reflected by the rich physics of excitons in atomically thin crystals which uniquely arises from the interplay of strong Coulomb correlation, spin-orbit coupling (SOC), and lattice geometry. Here we extend the field by reporting the observation of room temperature excitons in a material of non-trivial global topology. We study the fundamental optical excitation spectrum of a single layer of bismuth atoms epitaxially grown on a SiC substrate (hereafter bismuthene or Bi/SiC) which has been established as a large-gap, two-dimensional (2D) quantum spin Hall (QSH) insulator. Strongly developed optical resonances are observed to emerge around the direct gap at the K and K’ points of the Brillouin zone, indicating the formation of bound excitons with considerable oscillator strength. These experimental findings are corroborated, concerning both the character of the excitonic resonances as well as their energy scale, by ab-initio GW and Bethe-Salpeter equation calculations, confirming strong Coulomb interaction effects in these optical excitations. Our observations provide evidence of excitons in a 2D QSH insulator at room temperature, with excitonic and topological physics deriving from the very same electronic structure.

Electrical control of spin-polarized topological currents in monolayer WTe2

We evidence the possibility for coherent electrical manipulation of the spin orientation of topologically protected edge states in a low-symmetry quantum spin Hall insulator. By using a combination of ab initio simulations, symmetry-based modeling, and large-scale calculations of the spin Hall conductivity, it is shown that small electric fields can efficiently vary the spin textures of edge currents in monolayer 1T'-${\mathrm{WTe}}_{2}$ by up to a 90-degree spin rotation, without jeopardizing their topological character. These findings suggest a new kind of gate-controllable spin-based device, topologically protected against disorder and of relevance for the development of topological spintronics.

Tuning the many-body interactions in a helical Luttinger liquid

In one-dimensional (1D) systems, electronic interactions lead to a breakdown of Fermi liquid theory and the formation of a Tomonaga-Luttinger Liquid (TLL). The strength of its many-body correlations can be quantified by a single dimensionless parameter, the Luttinger parameter K, characterising the competition between the electrons’ kinetic and electrostatic energies. Recently, signatures of a TLL have been reported for the topological edge states of quantum spin Hall (QSH) insulators, strictly 1D electronic structures with linear (Dirac) dispersion and spin-momentum locking. Here we show that the many-body interactions in such helical Luttinger Liquid can be effectively controlled by the edge state’s dielectric environment. This is reflected in a tunability of the Luttinger parameter K, distinct on different edges of the crystal, and extracted to high accuracy from the statistics of tunnelling spectra at tens of tunnelling points. The interplay of topology and many-body correlations in 1D helical systems has been suggested as a potential avenue towards realising non-Abelian parafermions.

Band inversion induced large-gap quantum spin Hall states in III-Bi-monolayer/ SiO2

We extend the ${p}_{x}\ensuremath{-}{p}_{y}$ large-gap scenario to the band inversion systems and exemplify the mechanism with a family of III-Bi honeycomb monolayers on $\mathrm{Si}{\mathrm{O}}_{2}$, which can be the next generation of large-gap quantum spin Hall (QSH) systems. First, it suggests a topological gap of the same order as the current record kept of bismuthene/SiC(0001). Second, the band inversion mechanism in which these QSH insulators originate is qualitatively distinct from the Kane-Mele paradigm. Our work demonstrates that the ${p}_{x}\text{\ensuremath{-}}{p}_{y}$ scenario can be utilized to promote large-gap QSH states with both Kane-Mele and band inversion mechanisms, providing an efficient building principle for future topological device construction.

Critical topology and pressure-induced superconductivity in the van der Waals compound AuTe2Br

The study on quantum spin Hall effect and topological insulators formed the prologue to the surge of research activities in topological materials in the past decade. Compared to intricately engineered quantum wells, three-dimensional weak topological insulators provide a natural route to the quantum spin Hall effect, due to the adiabatic connection between them and a stack of quantum spin Hall insulators, and the convenience in exfoliation of samples associated with their van der Waals-type structure. Despite these advantages, both theoretical prediction and experimental identification of weak topological insulators remain scarce. Here, based on first-principles calculations, we show that AuTe2Br locates at the boundary between a strong and a weak topological semimetal state. We identify the key structural parameter that dictates the traversal of the topological transition, which can be easily realized in experiments. More interestingly, the critical topology of AuTe2Br persists up to an applied pressure of ~15.4 GPa before a structural phase transition accompanied by a change of electronic topology and the onset of superconductivity. Our results establish AuTe2Br as a new candidate for an effective tuning between weak and strong topological phases in a single material, with the potential to realize various other topological phases of matter.

Indium Epitaxy on SiC(0001): A Roadmap to Large Scale Growth of the Quantum Spin Hall Insulator Indenene

Indium Epitaxy on SiC(0001): A Roadmap to Large Scale Growth of the Quantum Spin Hall Insulator Indenene

Proximity-magnetized quantum spin Hall insulator: monolayer 1 T’ WTe2/Cr2Ge2Te6

Van der Waals heterostructures offer great versatility to tailor unique interactions at the atomically flat interfaces between dissimilar layered materials and induce novel physical phenomena. By bringing monolayer 1 T’ WTe2, a two-dimensional quantum spin Hall insulator, and few-layer Cr2Ge2Te6, an insulating ferromagnet, into close proximity in an heterostructure, we introduce a ferromagnetic order in the former via the interfacial exchange interaction. The ferromagnetism in WTe2 manifests in the anomalous Nernst effect, anomalous Hall effect as well as anisotropic magnetoresistance effect. Using local electrodes, we identify separate transport contributions from the metallic edge and insulating bulk. When driven by an AC current, the second harmonic voltage responses closely resemble the anomalous Nernst responses to AC temperature gradient generated by nonlocal heater, which appear as nonreciprocal signals with respect to the induced magnetization orientation. Our results from different electrodes reveal spin-polarized edge states in the magnetized quantum spin Hall insulator.

Quantum spin Hall effect in two-dimensional transition-metal chalcogenides MX5 (M = Zr, Hf and X = S, Se, Te)

Based on first-principles calculations, we have found a family of two-dimensional (2D) transition-metal (TM) chalcogenides MX5 (M = Zr, Hf and X = S, Se, Te) can host quantum spin Hall (QSH) effect. The molecular dynamics (MD) simulations indicate that they are all thermal-dynamically stable at room and high temperature. We have investigated MX5’s electronic properties and found their properties are very similar. The single-layer MX5 are all gapless semimetals without consideration of spin–orbit coupling (SOC). With consideration of SOC, they are all insulators with maximum band gap of 0.187 eV. The evolution of Wannier charge centers (WCC) and edge states confirm they are all QSH insulators. The mechanisms for QSH effect in MX5 originate from the special nonsymmorphic space group features. In addition, the QSH state of MX5 survives at a large range of strain as long as the interchain coupling is not strong enough to reverse the band ordering. Monolayer MX5 expand the TI materials based on TM chalcogenides and may open up a new way to fabricate novel low power spintronic devices.

Direct coupling-induced pseudoparity nonconservation scattering: bipolar spin diode and unipolar spin entanglement pairing

The zigzag graphene nanoribbon (ZR) is characterized by the distinct pseudoparity combined with valley-selection rule, which could feature exotic transport phenomena, especially in ZR-based superconducting spintronic devices. However, the ZR with superconductivity induced by proximity of a bulk superconductor (SC) on it still keeps original band properties. Herein, we present a superconducting heterostructure with an SC directly coupling to two ZRs, which is characteristic of pseudoparity-mixing, resulting in pseudoparity nonconservation elastic cotunneling (EC) and crossed Andreev reflection (CAR) processes. It is shown that the mixing leads to the switch effect of the EC and CAR processes manipulated by the SC length, particularly the full spin polarization. In the context of only one magnetized ZR lead, a novel bipolar spin diode behavior on a scale of small SC length and unipolar spin entanglement pairing at some large SC lengths, are both exhibited on a large scale of forward and/or reverse bias voltages. More importantly, the spin-diode can be combined with the quantum spin Hall (QSH) insulator to provide smoking gun evidence for the helical spin texture of the (QSH) insulator, which is still lacking.

Ultra-strong spin–orbit coupling and topological moiré engineering in twisted ZrS2 bilayers

We predict that twisted bilayers of 1T-ZrS2 realize a novel and tunable platform to engineer two-dimensional topological quantum phases dominated by strong spin-orbit interactions. At small twist angles, ZrS2 heterostructures give rise to an emergent and twist-controlled moiré Kagome lattice, combining geometric frustration and strong spin-orbit coupling to give rise to a moiré quantum spin Hall insulator with highly controllable and nearly-dispersionless bands. We devise a generic pseudo-spin theory for group-IV transition metal dichalcogenides that relies on the two-component character of the valence band maximum of the 1T structure at Γ, and study the emergence of a robust quantum anomalous Hall phase as well as possible fractional Chern insulating states from strong Coulomb repulsion at fractional fillings of the topological moiré Kagome bands. Our results establish group-IV transition metal dichalcogenide bilayers as a novel moiré platform to realize strongly-correlated topological phases in a twist-tunable setting.

Theory of superconductivity mediated by topological phonons

Topological phononic insulators are the counterpart of three-dimensional quantum spin Hall insulators in phononic systems and, as such, their topological surfaces are characterized by Dirac cone-shaped gapless edge states arising as a consequence of a bulk-boundary correspondence. We propose a theoretical framework for the possible superconducting phase in these materials, where the attractive interaction between electrons is mediated by topological phonons in nontrivial boundary modes. Within the BCS limit, we develop a self-consistent two-band gap equation, whose solutions show that the superconducting critical temperature has a non-monotonic behaviour with respect to the phononic frequency in the Kramers-like point. This remarkable behaviour is produced by a resonance, that occurs when electrons and phonons on the topological surfaces have the same energy: this effectively increases the electron-phonon interaction and hence the Cooper pair binding energy, thus establishing an optimal condition for the superconducting phase. With this mechanism, the $T_{c}$ can be increased by well over a factor two, and the maximum enhancement occurs in the degenerate phononic flat-band limit.

Chiral detection of Majorana bound states at the edge of a quantum spin Hall insulator

A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the Zeeman-field-induced boost of the helical edge state is then proposed for the detection of the MBS. Two-dimensional transport simulations of our proposed setup are compared with the corresponding setup in the absence of the QAH region, when moderate potential and magnetic disorder are included. The remarkable contrast between the two results demonstrates the possibility for an unprecedented immunity from disorder-induced masking of the MBS detection in our proposed setup.

Two-dimensional anisotropic Dirac materials PtN4C2 and Pt2N8C6 with quantum spin and valley Hall effects

We propose two different two-dimensional topological Dirac materials, planar ${\mathrm{PtN}}_{4}{\mathrm{C}}_{2}$ and ${\mathrm{Pt}}_{2}{\mathrm{N}}_{8}{\mathrm{C}}_{6}$, which exhibit graphenelike electronic structures with linearly dispersive Dirac-cone states exactly at the Fermi level. Moreover, the Dirac cone is anisotropic, resulting in anisotropic Fermi velocities and making it possible to realize orientation-dependent quantum devices. Using first-principles electronic structure calculations, we have systemically studied the structural, electronic, and topological properties. We find that spin-orbit coupling opens a sizable topological band gap so that the materials can be classified as quantum spin Hall insulators as well as quantum valley Hall insulators. Helical edge states that reside in the insulating band gap connecting the bulk conduction and valence bands are observed. Our work not only expands the Dirac-cone material family, but also provides another avenue to search for more two-dimensional topological quantum spin and valley Hall insulators.

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.

Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites

Higher-order topological superconductors and superfluids (SFs) host lower-dimensional Majorana corner and hinge states since novel topology exhibitions on boundaries. While such topological nontrivial phases have been explored extensively, more possible schemes are necessary for engineering Majorana states. In this paper we propose Majorana corner states could be realized in a two-dimensional attractive quantum spin-Hall insulator with opposite in-plane Zeeman energy at two sublattice sites. The appropriate Zeeman field leads to the opposite Dirac mass for adjacent edges of a square sample, and naturally induce Majorana corner states. This topological phase can be characterized by Majorana edge polarizations, and it is robust against perturbations on random potentials and random phase fluctuations as long as the edge gap remains open. Our work provides a new possibility to realize a second-order topological SF in two dimensions and engineer Majorana corner states.