A three-dimensional weak topological insulator (WTI) can be regarded as stacked layers of two-dimensional quantum spin-Hall insulators, each of which accommodates a one-dimensional helical edge mode. Massless Dirac electrons emerge on a side surface of WTIs as a consequence of the hybridization of such helical edge modes. We study the energy spectrum and transport of Dirac electrons on a side surface in the presence of step edges, which significantly modify the way of hybridization. It is shown that pseudo-helical modes with a nearly gapless linear dispersion can be created by manipulating step edges in a certain manner. We numerically calculate the average conductance of weakly disordered WTIs and show that it is markedly enhanced by pseudo-helical modes.
The nontrivial band topology can influence the Hofstadter spectrum. We investigate the Hofstadter spectrum for various models of Chern insulators under a rational flux $\frac{ϕ_{0}}{q}$, here $ϕ_{0}=\frac{h}{e}$ and $q$ being an integer. We find two major features. First, the number of splitting subbands is $|q-C|$ with Chern number $C$. Second, the anomalous open-orbit subbands with Chern numbers $q-1$ and $-q-1$ emerge, which are beyond the parameter window $(-q/2,q/2)$ of the Diophantine equation studied by Thouless-Kohmoto-Nightingale-den Nijs [Phys. Rev. Lett. \textbf{49}, 405 (1982)]. Th…
We study the influence of step defect on surface states in three-dimensional topological insulators subject to a perpendicular magnetic field. By calculating the energy spectrum of the surface states, we find that Landau levels (LLs) can form on flat regions of the surface and are distant from the step defect, and several subbands emerge at side surface of the step defect. The subband which connects to the two zeroth LLs is spin-polarized and chiral. In particular, when the electron transports along the side surface, the electron spin direction can be manipulated arbitrarily by gate voltage. A…
We have theoretically investigated the influence of interface roughness scattering on the low temperature mobility of electrons in quantum wires when electrons fill one or many subbands. We find the Drude conductance of the wire with length $\mathcal{L}$ first increases with increasing linear concentration of electrons $η$ and then decreases at larger concentrations. For small radius $R$ of the wire with length $\mathcal{L}$ the peak of the conductance $G_{max}$ is below $e^2/h$ so that electrons are localized. The height of this peak grows as a large power of $R$, so that at large $R$ the con…
In bilayer graphene rotationally faulted to theta=1.1 degrees, interlayer tunneling and rotational misalignment conspire to create a pair of low energy flat band that have been found to host various correlated phenomena at partial filling. Most work to date has focused on the zero magnetic field phase diagram, with magnetic field (B) used as a probe of the B=0 band structure. Here, we show that twisted bilayer graphene (tBLG) in a B as low as 2T hosts a cascade of ferromagnetic Chern insulators with Chern number |C|=1,2 and 3. We argue that the emergence of the Chern insulators is driven by th…
Three-dimensional topological insulator (TI) nanowires with quantized surface subband spectra are studied as a main component of Majorana bound states (MBS) devices. However, such wires are known to have large concentration $N \sim 10^{19}$ cm$^{-3}$ of Coulomb impurities. It is believed that a MBS device can function only if the amplitude of long-range fluctuations of the random Coulomb potential $Γ$ is smaller than the subband gap $Δ$. Here we calculate $Γ$ for recently experimentally studied large-dielectric-constant (Bi$_{1-x}$Sb$_x$)$_2$Te$_{3}$ wires in a small-dielectric-constant enviro…
A heterostructure consisting of a topological insulator (TI) nanowire brought into proximity with a superconducting layer provides a promising route to achieve topological superconductivity and associated Majorana bound states (MBSs). Here, we study effects caused by such a coupling between a thin layer of an $s$-wave superconductor and a TI nanowire. We show that there is a distinct phenomenology arising from the metallization of states in the TI nanowire by the superconductor. In the strong coupling limit, required to induce a large superconducting pairing potential, we find that metallizati…
The two-dimensional topological insulator phase has been observed previously in single HgTe-based quantum wells with inverted subband ordering. In double quantum wells (DQWs), coupling between the layers introduces additional degrees of freedom leading to a rich phase picture. By studying local and nonlocal resistance in HgTe-based DQWs, we observe both the gapless semimetal phase and the topological insulator phase, depending on parameters of the samples and according to theoretical predictions. Our work establishes the DQWs as a promising platform for realization of multilayer topological in…
Impurities embedded in electronic systems induce bound states which under certain circumstances can hybridize and lead to impurity bands. Doping of insulators with impurities has been identified as a promising route towards engineering electronic topological states of matter. In this paper we show how to realize tuneable Chern insulators starting from a three dimensional topological insulator whose surface is gapped and intentionally doped with magnetic impurities. The main advantage of the protocol is that it is robust, and in particular not very sensitive to the impurity configuration. We ex…
The double quantum well systems consisting of two HgTe layers separated by a tunnel-transparent barrier are expected to manifest a variety of phase states including two-dimensional gapless semimetal and two-dimensional topological insulator. The presence of several subbands in such systems leads to a rich filling factor diagram in the quantum Hall regime. We have performed magnetotransport measurements of the HgTe-based double quantum wells in both gapless and gapped state and observed numerous crossings between the Landau levels belonging to different subbands. We analyze the Landau level cro…
A tight-binding model of bcc tungsten that includes spin-orbit coupling is developed and applied to the surface states of (110) tungsten thin films. The model describes accurately the anisotropic Dirac cone-like dispersion and Rashba-like spin polarization of the surface states, including the crucial effect of the relaxation of the surface atomic layer of the tungsten towards the bulk. It is shown that the surface relaxation affects the tungsten surface states because it results in increased overlaps between atomic orbitals of the surface atomic layer and nearby layers whereas electric fields …
Floquet engineering is an important way to manipulate the electronic states of condensed matter physics. Recently, the discovery of the magnetic topological insulator MnBi$_2$Te$_4$ and its family provided a valuable platform to study magnetic topological phenomena, such as, the quantum anomalous Hall effect, the axion insulator state and the topological magnetoelectric effect. In this work, based on the effective model and first-principles calculations in combination with the Floquet theory, we reveal that the circularly polarized light (CPL) induces the sign reversal of the Chern number of o…
Three dimensional topological insulators are bulk insulators with $\mathbf{Z}_2$ topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by non-magnetic disorder, and have been adopted as the basis for a wide range of proposals to achieve new quasiparticle species and device functionality. Recent studies have yielded a surprise by showing that in spite of resisting localization, topological insulator surface electrons can be reshaped by defects into distinctive resonance states. Here we use numeri…
We theoretically demonstrate that the second-order topological insulator with robust corner states can be realized in two-dimensional $\mathbb{Z}_2$ topological insulators by applying an in-plane Zeeman field. Zeeman field breaks the time-reversal symmetry and thus destroys the $\mathbb{Z}_2$ topological phase. Nevertheless, it respects some crystalline symmetries and thus can protect the higher-order topological phase. By taking the Kane-Mele model as a concrete example, we find that spin-helical edge states along zigzag boundaries are gapped out by Zeeman field whereas in-gap corner state at…
We study the hybrid excitations due to the coupling between surface optical phonons of a polar insulator substrate and plasmons in the valley-spin-polarized metal phase of silicene under an exchange field. We perform the calculations within the generalized random-phase approximation where the plasmon-phonon coupling is taken into account by the long-range Fr$\ddot{\mathrm{o}}$hlich interaction. Our investigation on two hybridized plasmon branches in different spin and valley subbands shows distinct behavior compared to the uncoupled case. Interestingly, in one valley, it is found that while th…
We consider a system of spinless fermions on the honeycomb lattice with substrate-induced modulated electrostatic potentials tripling the unit cell. The resulting non-Abelian SU(2) gauge fields act cooperatively to realize a quadratic band crossing point (QBCP). Using a combination of mean-field theory and renormalization group techniques, we show that in the QBCP regime, arbitrarily weak repulsive electronic interactions drive the system into the quantum anomalous Hall state. This proves that substrate-induced local voltages are an effective knob to induce the spontaneous formation of a topol…
Transport evidence of surface states in magnetic topological insulator MnBi2Te4
Leibniz Institute for Solid State and Materials Research, IFW Dresden（德累斯顿铁电研究所）；Université Grenoble Alpes, CNRS, CEA, Grenoble-INP, Spintec（格勒诺布尔阿尔卑斯大学）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群ct.qmat）；CNRS, Laboratoire National des Champs Magnétiques Intenses, Université Grenoble-Alpes, Université Toulouse 3, INSA-Toulouse, EMFL（法国国家强磁场实验室）
We propose to Floquet-engineer Dirac cones at the surface of a three-dimensional topological insulator. We show that a large tunability of the Fermi velocity can be achieved as a function of the polarization, direction and amplitude of the driving field. Using this external control, the Dirac cones in the quasienergy spectrum may become elliptic or massive, in accordance to experimental evidences. These results help us to understand the interplay of surface states and external ac driving fields in topological insulators. In our work we use the full Hamiltonian for the three-dimensional system …
Topological insulator (TI) nanoribbons (NRs) provide a unique platform for investigating quantum interference oscillations combined with topological surface states. One-dimensional subbands formed along the perimeter of a TI NR can be modulated by an axial magnetic field, exhibiting Aharonov-Bohm (AB) and Altshuler-Aronov-Spivak (AAS) oscillations of magnetoconductance (MC). Using Sb-doped Bi2Se3 TI NRs, we found that the relative amplitudes of the two quantum oscillations can be tuned by varying the channel length, exhibiting crossover from quasi-ballistic to diffusive transport regimes. The …
: n-type Ge/SiGe asymmetric-coupled quantum wells represent the building block of a variety of nanoscale quantum devices, including recently proposed designs for a silicon-based THz quantum cascade laser. In this paper, we combine structural and spectroscopic experiments on 20-module superstructures, each featuring two Ge wells coupled through a Ge-rich tunnel barrier, as a function of the geometry parameters of the design and the P dopant concentration. Through the comparison of THz spectroscopic data with numerical calculations of intersubband optical absorption resonances, we demonstrated t…
Topological insulators are tunable waveguides for hyperbolic polaritons
层状拓扑绝缘体，例如Bi $_2$ Se $_3$，在THz频率范围内是光学双曲材料。这种材料具有深度亚衍射，高度定向的集体模式：双曲声子极化激元。在薄晶体中，这种模式的色散被分裂成离散的子带，并受到电子表面态的强烈影响。如果表面态被掺杂，则混合集体模式由声子-极化激元与表面等离子体激元的耦合产生。杂化的强度可以通过改变表面态的化学势的外部门来控制。等离子体-声子耦合的动量依赖性导致了古斯-汉兴效应的极化激元模拟。极化激元射线的方向性及其可调谐的古斯-汉欣位移可以通过太赫兹纳米成像观察到。
Studying the influence of breaking time-reversal symmetry on topological insulator surface states is an important problem of current interest in condensed matter physics and could provide a route toward proof-of-concept spintronic devices that exploit spin-textured surface states. Here, we develop a new model system for studying the effect of breaking time-reversal symmetry: a hybrid heterostructure wherein a ferromagnetic semiconductor Ga1-xMnxAs, with an out-of-plane component of magnetization, is cleanly interfaced with a three-dimensional topological insulator (Bi,Sb)2(Te,Se)3 by molecular…
We report the fabrication and characterization of superconducting quantum interference devices (SQUIDs) made of Sb-doped Bi2Se3 topological insulator (TI) nanoribbon (NR) contacted with PbIn superconducting electrodes. When an external magnetic field was applied along the NR axis, the TI NR exhibited periodic magneto-conductance oscillations, the so-called Aharonov-Bohm oscillations, owing to one-dimensional subbands. Below the superconducting transition temperature of PbIn electrodes, we observed supercurrent flow through TI NR-based SQUID. The critical current periodically modulates with a m…
Topological insulator ribbon: Surface states and dynamical response
从理论上研究了具有实际矩形截面的拓扑绝缘体带的电荷和自旋极化分布。由于在两个横向方向上的收缩，表面态离散成一系列的子带内的体带隙。电荷和自旋分布显示出不同于理想拓扑表面态的有趣特征。分析了四种不同的表面态合并成一个新的表面态的效果。研究了该带的光学电导率和动态自旋极化率。与单一理想表面不同，带的光学响应和动态自旋极化率之间并没有明确的对应关系。动力学自旋极化率可以用来确定Bi $_2$ Se $_3$更合适的模型。
Despite the broadband response, limited optical absorption at a particular wavelength hinders the development of optoelectronics based on Dirac fermions. Heterostructures of graphene and various semiconductors have been explored for this purpose, while non-ideal interfaces often limit the performance. The topological insulator is a natural hybrid system, with the surface states hosting high-mobility Dirac fermions and the small-bandgap semiconducting bulk state strongly absorbing light. In this work, we show a large photocurrent response from a field effect transistor device based on intrinsic…
(Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ topological insulators (TIs) are gathering increasing attention owing to their large charge-to-spin conversion efficiency and the ensuing spin-orbit torques (SOTs) that can be used to manipulate the magnetization of a ferromagnet (FM). The origin of the torques, however, remains elusive, while the implications of hybridized states and the strong material intermixing at the TI/FM interface are essentially unexplored. By combining interface chemical analysis and spin-transfer ferromagnetic resonance (ST-FMR) measurements, we demonstrate that intermixing plays a criti…
Dynamic manipulation of magnetism in topological materials is demonstrated here via a Floquet engineering approach using circularly polarized light. Increasing the strength of the laser field, besides the expected topological phase transition, the magnetically doped topological insulator thin film also undergoes a magnetic phase transition from ferromagnetism to paramagnetism, whose critical behavior strongly depends on the quantum quenching. In sharp contrast to the equilibrium case, the non-equilibrium Curie temperatures vary for different time scale and experimental setup, not all relying o…
Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have conductive surface or edge states. Topological materials show various unusual physical properties and are surmised to enable the creation of exotic Majorana-fermion quasiparticles. How the signatures of topological behavior evolve when the system size is reduced is interesting from both a fundamental and an application-oriented point of view, as such understanding …
In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport …
Electrically tunable interfacial thermal conduction via electronic structure engineering in ${Au}$/$Bi_{1-x}$$Sb_{x}$ topological insulators
The Ohio State University（俄亥俄州立大学）；Korea Institute of Science and Technology (KIST)（韩国科学技术院）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Pohang University of Science and Technology (POSTECH)（浦项科技大学）；Carnegie Mellon University（卡内基梅隆大学）；E. O. Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
We outline here how strong light-matter interaction can be used to induce quantum phase transition between normal and topological phases in two-dimensional topological insulators. We consider the case of a HgTe quantum well, in which band inversion occurs above a critical value of the well thickness, and demonstrate that coupling between electron states and the $E$ field from an off-resonant linearly polarized laser provides a powerful tool to control topological transitions, even for a thickness of the quantum well that is below the critical value. We also show that topological phase properti…
A three-dimensional (3D) nodal-loop semimetal phase is exploited to engineer a number of intriguing phases featuring different peculiar topological surface states. In particular, by introducing various two-dimensional gap terms to a 3D tight-binding model of a nodal-loop semimetal, we obtain a rich variety of topological phases of great interest to ongoing theoretical and experimental studies, including chiral insulator, degenerate-surface-loop insulator, second-order topological insulator, as well as Weyl semimetal with tunable Fermi arc profiles. The unique concept underlying our approach is…
Chiral edge state (CES) at zero magnetic field has already been realized in the magnetically doped topological insulator (TI). However, this scheme strongly relies on material breakthroughs, and in fact, most of the TIs cannot be driven into a Chern insulator in this way. Here, we propose to achieve the CESs in 2D TI/ferromagnetic insulator/TI sandwiched structures through spin-selective coupling between the helical edge states of the two TIs. Due to this coupling, the edge states of one spin channel are gapped and those of the other spin channel remain almost gapless, so that the helical edge…
Topological insulators (TIs) are characterized by the quantum anomalous Hall effect (QAHE) on the topological surface states under time-reversal symmetry breaking. Motivated by recent experiments on the magneto-optical effects induced by the QAHE, we develop a theory for the dynamical Hall conductivity for subgap optical frequency and intense optical fields using the Keldysh-Floquet Green's function formalism. Our theory reveals a nonlinear regime in which the Hall conductivity remains close to $e^2/2h$ at low frequencies. At higher optical fields, we find that the subsequent collapse of the h…
Screening and atomic-scale engineering of the potential at a topological insulator surface
利用扫描隧道显微镜（STM）研究了三维拓扑绝缘体Bi $_2$ Se $_3$（111）表面Rb原子的分布，研究了其静电行为.带正电荷的离子被驻留在拓扑表面状态中的自由电子以及导带的带弯曲诱导的量子阱状态两者屏蔽，导致令人惊讶的短屏蔽长度。结合基于STM的原子操作的势能的理论描述，我们证明了在具有原子尺度控制的拓扑表面上创建定制的电子势景观的能力。
