The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin-...The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin--orbit coupling due to bulk-inversion asymmetry is taken into account, the energy gap Eg of the edge states features an oscillating exponential decay as a function of the strip width of the inverted HgTe quantum well. In this paper, we investigate the effects of the interface between a topological insulator and a normal insulator on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. Two different types of boundary conditions, i.e., the symmetric and asymmetric geometries, are considered. It is found that due to the existence of the interface between topological insulator and normal insulator this oscillatory pattern on the exponential decay induced by bulk-inversion asymmetry is modulated by the width of normal insulator regions. With the variation of the width of normal insulator regions, the shift of the Dirac point of the edge states in the spectrum and the energy gap Eg closing point in the oscillatory pattern can occur. Additionally, the effect of the spin-orbit coupling due to structure-inversion asymmetry on the finite size effects is also investigated.展开更多
Using the natural orbitals renormalization group（NORG）method,we investigate the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator.It is fou...Using the natural orbitals renormalization group（NORG）method,we investigate the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator.It is found that there is a local spin formed at the impurity site and the local spin is completel.y screened by electrons in the quantum spin Hall insulator.Meanwhile,the local spin is screened dominantly by a single active natural orbital.We then show that the Kondo screening mechanism becomes transparent and simple in the framework of the natural orbitals formalism.We project the active natural orbital respectively into real space and momentum space to characterize its structure.We conilrm the spin-momentum locking property of the edge states based on the occupancy of a Bloch state on the edge to which the impurity couples.Furthermore,we study the dynamical property of the active natural orbital represented by the local density of states,from which we observe the Kondo resonance peak.展开更多
There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite wi...There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.展开更多
The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the ...The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.展开更多
For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit（ISO）coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall（QSH） e...For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit（ISO）coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall（QSH） effect characterized by two pairs of gapless helical edge states within the bulk gap.Generally,due to the finite size effect in QSH systems,the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum.In this paper,we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions,i.e.,the straight,bearded and asymmetry edges.The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice.For a strip Lieb lattice with two straight edges,the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum.Moreover,it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice,and no gap is opened in the edge band.It is concluded that the finite size effect of QSH states is absent in the case with the straight edges.However,in the other two cases with the bearded and asymmetry edges,the energy gap induced by the finite size effect is still opened with decreasing the width of the strip.It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.展开更多
It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin ...It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron–electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling(SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state.展开更多
The exchange field effects on topological Dirac semimetal（DSM） films are discussed in this article. A topological phase transition can be controlled by tuning the exchange field together with the quantum confinement...The exchange field effects on topological Dirac semimetal（DSM） films are discussed in this article. A topological phase transition can be controlled by tuning the exchange field together with the quantum confinement effects. What is more interesting is that the system can transit into the quantum anomalous Hall（QAH） state from the topologically trivial state（Z2 = 0） or from the topologically nontrivial state（Z2 = 1）, depending on the thickness of the DSM films. This provides a useful mechanism to realize the QAH state from the DSM.展开更多
A Kramers pair of helical edge states in quantum spin Hall effect(QSHE) is robust against normal dephasing but not robust to spin dephasing. In our work, we provide an effective spin dephasing mechanism in the puddles...A Kramers pair of helical edge states in quantum spin Hall effect(QSHE) is robust against normal dephasing but not robust to spin dephasing. In our work, we provide an effective spin dephasing mechanism in the puddles of two-dimensional(2D) QSHE, which is simulated as quantum dots modeled by 2D massive Dirac Hamiltonian. We demonstrate that the spin dephasing effect can originate from the combination of the Rashba spin-orbit coupling and electron-phonon interaction, which gives rise to inelastic backscattering in edge states within the topological insulator quantum dots, although the time-reversal symmetry is preserved throughout. Finally,we discuss the tunneling between extended helical edge states and local edge states in the QSH quantum dots, which leads to backscattering in the extended edge states. These results can explain the more robust edge transport in In As/Ga Sb QSH systems.展开更多
Monolayer transition metal dichalcogenides(TMDCs) with the 1 T0 structure are a new class of large-gap two-dimensional(2 D) topological insulators, hosting topologically protected conduction channels on the edges. How...Monolayer transition metal dichalcogenides(TMDCs) with the 1 T0 structure are a new class of large-gap two-dimensional(2 D) topological insulators, hosting topologically protected conduction channels on the edges. However, the 1 T0 phase is metastable compared to the 2 H phase for most of 2 D TMDCs, among which the 1 T0 phase is least favored in monolayer MoS2. Here we report a clean and controllable technique to locally induce nanometer-sized 1 T0 phase in monolayer 2 H-MoS2 via a weak Argon-plasma treatment,resulting in topological phase boundaries of high density. We found that the stabilization of 1 T0 phase arises from the concerted effects of S vacancies and the tensile strain. Scanning tunneling spectroscopy(STS) clearly reveals a spin-orbit band gap(~60 meV) and topologically protected in-gap states residing at the 1 T0-2 H phase boundary, which are corroborated by density-functional theory(DFT) calculations.The strategy developed in this work can be generalized to a large variety of TMDCs materials, with potentials to realize scalable electronics and spintronics with low dissipation.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11274102)the Program for New Century Excellent Talents in University of the Ministry of Education of China(Grant No.NCET-11-0960)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20134208110001)
文摘The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin--orbit coupling due to bulk-inversion asymmetry is taken into account, the energy gap Eg of the edge states features an oscillating exponential decay as a function of the strip width of the inverted HgTe quantum well. In this paper, we investigate the effects of the interface between a topological insulator and a normal insulator on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. Two different types of boundary conditions, i.e., the symmetric and asymmetric geometries, are considered. It is found that due to the existence of the interface between topological insulator and normal insulator this oscillatory pattern on the exponential decay induced by bulk-inversion asymmetry is modulated by the width of normal insulator regions. With the variation of the width of normal insulator regions, the shift of the Dirac point of the edge states in the spectrum and the energy gap Eg closing point in the oscillatory pattern can occur. Additionally, the effect of the spin-orbit coupling due to structure-inversion asymmetry on the finite size effects is also investigated.
基金Supported by National Natural Science Foundation of China under Grant Nos 11474356 and 11774422supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China
文摘Using the natural orbitals renormalization group（NORG）method,we investigate the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator.It is found that there is a local spin formed at the impurity site and the local spin is completel.y screened by electrons in the quantum spin Hall insulator.Meanwhile,the local spin is screened dominantly by a single active natural orbital.We then show that the Kondo screening mechanism becomes transparent and simple in the framework of the natural orbitals formalism.We project the active natural orbital respectively into real space and momentum space to characterize its structure.We conilrm the spin-momentum locking property of the edge states based on the occupancy of a Bloch state on the edge to which the impurity couples.Furthermore,we study the dynamical property of the active natural orbital represented by the local density of states,from which we observe the Kondo resonance peak.
基金Project supported by the National Natural Science Foundation of China(Grant No.11274102)the Program for New Century Excellent Talents in Universities,China(Grant No.NCET-11-0960)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20134208110001)
文摘There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.
基金supported by the National Basic Research Program of China (Grant Nos. 2009CB929504,2011CB922103,and 2010CB923400)the National Natural Science Foundation of China (Grant Nos. 11225420,11074110,11174125,11074109,and 91021003)+1 种基金the Priority Academic Program Development of Jiangsu Higher Education Institutions,China,the US NSF (Grant Nos. DMR-0906816 and DMR-1205734)Princeton MRSEC (Grant No. DMR-0819860)
文摘The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.
基金Project supported by the National Natural Science Foundation of China(Grant No.11274102)the Program for New Century Excellent Talents in University of the Ministry of Education of China(Grant No.NCET-11-0960)the Specialized Research Fund for the Doctoral Program of the Higher Education of China(Grant No.20134208110001)
文摘For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit（ISO）coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall（QSH） effect characterized by two pairs of gapless helical edge states within the bulk gap.Generally,due to the finite size effect in QSH systems,the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum.In this paper,we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions,i.e.,the straight,bearded and asymmetry edges.The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice.For a strip Lieb lattice with two straight edges,the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum.Moreover,it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice,and no gap is opened in the edge band.It is concluded that the finite size effect of QSH states is absent in the case with the straight edges.However,in the other two cases with the bearded and asymmetry edges,the energy gap induced by the finite size effect is still opened with decreasing the width of the strip.It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.
基金supported by the National Key Basic Research Program of China(Grant Nos.2014CB920903,2013CB921903,2011CBA00108,and 2012CB937500)the National Natural Science Foundation of China(Grant Nos.11021262,11172303,11404022,11225418,and 11174337)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20121101110046)the Excellent Young Scholars Research Fund of Beijing Institute of Technology(Grant No.2014CX04028)the Basic Research Funds of Beijing Institute of Technology(Grant No.20141842001)
文摘It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron–electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling(SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state.
基金supported by the National Natural Science Foundation of China(Grant No.11574019)
文摘The exchange field effects on topological Dirac semimetal（DSM） films are discussed in this article. A topological phase transition can be controlled by tuning the exchange field together with the quantum confinement effects. What is more interesting is that the system can transit into the quantum anomalous Hall（QAH） state from the topologically trivial state（Z2 = 0） or from the topologically nontrivial state（Z2 = 1）, depending on the thickness of the DSM films. This provides a useful mechanism to realize the QAH state from the DSM.
基金the Deutsche Forschungsgemeinschaft (grant SFB 410)the German-Israeli Foundation for Scientific Research and Development (grant 881/05)+4 种基金the NSF(grant DMR-0342832)the U.S.Department of EnergyOffice of Basic Energy Sciencesunder contract DE-AC03-76SF00515Focus Center Research Program (FCRP) Center on Functional Engineered Nanoarchitectonics (FENA)
基金supported by the National Basic Research Program of China(Grant Nos.2015CB921102,2012CB821402 and 2012CB921303)the National Natural Science Foundation of China(Grant Nos.11534001 and11274364)
文摘A Kramers pair of helical edge states in quantum spin Hall effect(QSHE) is robust against normal dephasing but not robust to spin dephasing. In our work, we provide an effective spin dephasing mechanism in the puddles of two-dimensional(2D) QSHE, which is simulated as quantum dots modeled by 2D massive Dirac Hamiltonian. We demonstrate that the spin dephasing effect can originate from the combination of the Rashba spin-orbit coupling and electron-phonon interaction, which gives rise to inelastic backscattering in edge states within the topological insulator quantum dots, although the time-reversal symmetry is preserved throughout. Finally,we discuss the tunneling between extended helical edge states and local edge states in the QSH quantum dots, which leads to backscattering in the extended edge states. These results can explain the more robust edge transport in In As/Ga Sb QSH systems.
基金financially supported by the National Natural Science Foundation of China (11888101, 11634001, 11834017 and 61888102)the National Key R&D Program (2016YFA0300901 and 2017YFA0205003)+3 种基金the Strategic Priority Research Program of Chinese Academy of Sciences (XDB28000000 and XDB30000000)Beijing Municipal Science & Technology Commissionsupport from National Science Fund for Distinguished Young Scholars (21725302)Cheung Kong Young Scholar Program
文摘Monolayer transition metal dichalcogenides(TMDCs) with the 1 T0 structure are a new class of large-gap two-dimensional(2 D) topological insulators, hosting topologically protected conduction channels on the edges. However, the 1 T0 phase is metastable compared to the 2 H phase for most of 2 D TMDCs, among which the 1 T0 phase is least favored in monolayer MoS2. Here we report a clean and controllable technique to locally induce nanometer-sized 1 T0 phase in monolayer 2 H-MoS2 via a weak Argon-plasma treatment,resulting in topological phase boundaries of high density. We found that the stabilization of 1 T0 phase arises from the concerted effects of S vacancies and the tensile strain. Scanning tunneling spectroscopy(STS) clearly reveals a spin-orbit band gap(~60 meV) and topologically protected in-gap states residing at the 1 T0-2 H phase boundary, which are corroborated by density-functional theory(DFT) calculations.The strategy developed in this work can be generalized to a large variety of TMDCs materials, with potentials to realize scalable electronics and spintronics with low dissipation.
