We consider weak topological insulators with a twofold rotation symmetry around the dark direction, and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by rotation symmetry. These hybrid-order weak topological insulators display surface Dirac cones on all surfaces. Translational symmetry breaking perturbations gap the Dirac cones on the side surfaces leaving anomalous helical hinge modes behind. We also prove that the existence of this topological phase comes about due to a hidden crystalline topological invariant of quantum spin-Hall insulators that can neither be revealed by symmetry indicators nor using Wilson loop invariants. Considering the minimal symmetry requirements, we anticipate that our findings could apply to a large number of weak topological insulators.
Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of wave functions are also at the heart of the topological classification of the gapped phases of matter. Despite identical singular features, topological insulators and topological defects in waves remain two distinct fields. Realising 1D microwave insulators, we experimentally observe a wavefront dislocation - a 2D phase singularity - in the local density of sta…
We investigate the impact of electrostatics on the proximity effect between a magnetic insulator and a semiconductor wire in semiconductor-superconductor-magnetic insulator hybrid structures. By performing self-consistent Schr$\ddot{\rm o}$dinger-Poisson calculations using an effective model of the hybrid system, we find that large effective Zeeman fields consistent with the emergence of topological superconductivity emerge within a large parameter window in wires with overlapping layers of magnetic insulator and superconductor, but not in non-overlapping structures. We show that this behavior…
Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological insulator is characterized by a fixed order topological invariant and exhibits associated bulk-boundary correspondence. Here, we realize a new type of topological insulator in a bilayer phononic crystal, which hosts simultaneously the first-order and second-order topologies, referred here as the hybrid-order topological insulator. The one-dimensional gapless heli…
An acoustic topological insulator (TI) is synthesized using topology optimization, a free material inverse design method. The TI appears spontaneously from the optimization process without imposing requirements on the existence of pseudo spin-1/2 states at the TI interface edge, or the Chern number of the topological phases. The resulting TI is passive; consisting of acoustically hard members placed in an air background and has an operational bandwidth of $\approx$12.5\% showing high transmission. Further analysis demonstrates confinement of more than 99\% of the total field intensity in the T…
We study laser driven spin-current effects at ferromagnet/topological-insulator interfaces by two complementary experimental approaches. The DC photocurrent is studied in ferromagnet/topological-insulator bilayers with high spatial resolution. Dynamic interface currents are explored via the emission of terahertz radiation emitted by these currents with high temporal resolution. From our experiments, we reveal a lateral and dynamic interaction of the ferromagnet and the topological insulator interface.
In this paper, a brief review of the history of topological insulators is given. After that,electronic transport experiments in topological insulator-superconductor hybrid structures, including experimental methods, physical properties and seemingly contradictory observations are discussed. Additionally, some new topological insulator hybrid structures are proposed.
Transition between one- and two-dimensional topology in a Chern insulator of finite width
Aarhus University（奥胡斯大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
We investigate the current-induced spin-orbit torque in thin topological insulator (TI) films in the presence of hybridization between the top and bottom surface states. We formulate the relation between spin torque and TI thickness, from which we derived the optimal value of the thickness to maximize the torque. We show numerically that in typical TI thin films made of $\mathrm{Bi_2Se_3}$, the optimal thickness is about 3-5 nm.
Twisting the stacking of layered materials leads to rich new physics. A three dimensional (3D) topological insulator film host two dimensional gapless Dirac electrons on top and bottom surfaces, which, when the film is below some critical thickness, will hybridize and open a gap in the surface state structure. The hybridization gap can be tuned by various parameters such as film thickness, inversion symmetry, etc. according to the literature. The 3D strong topological insulator Bi(Sb)Se(Te) family have layered structures composed of quintuple layers (QL) stacked together by van der Waals inter…
We show that the interplay of cyclotron motion and Andreev reflection experienced by massless-Dirac-like charge carriers in topological-insulator surface states generates a Majorana-particle excitation. Based on an envelope-function description of the Dirac-Andreev edge states, we discuss the kinematic properties of the Majorana mode and find them to be possible to be tuned by changing the superconductor's chemical potential and/or the magnitude of the perpendicular magnetic field. Our proposal opens up new possibilities for studying Majorana fermions in a controllable setup.
As the thickness of a three-dimensional (3D) topological insulator (TI) becomes comparable to the penetration depth of the surface states, quantum tunneling between surfaces turns their gapless Dirac electronic structure into a gapped surface state. Analytical formulation suggests that the hybridization gap scales exponentially with decrease in number of layers while the system oscillates between topologically trivial and non-trivial insulators. This work explores the transport properties of a 3D TI in the inter-surface hybridization regime. By experimentally probing the hybridization gap as a…
Studying deterministic operators, we define an appropriate topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall effect, and lastly we show why our "insulator" condition makes sense from the point of view of the localization theory using the fractional moments method.
In this work, we propose a ferromagnetic Bi$_2$Se$_3$ as a candidate to hold the coexistence of Weyl- and nodal-line semimetal phases, which breaks the time reversal symmetry. We demonstrate that the type-I Weyl semimetal phase, type-I-, type-II- and their hybrid nodal-line semimetal phases can arise by tuning the Zeeman exchange field strength and the Fermi velocity. Their topological responses under U(1) gauge field are also discussed. Our results raise a new way for realizing Weyl and nodal-line semimetals and will be helpful in understanding the topological transport phenomena in three-dim…
We show that the local in-gap Greens function of a band insulator $\mathbf{G}_0 (ε,\mathbf{k}_{\parallel},\mathbf{r}_{\perp}=0)$, with $\mathbf{r}_\perp$ the position perpendicular to a codimension-1 or -2 impurity, reveals the topological nature of the phase. For a topological insulator, the eigenvalues of this Greens function attain zeros in the gap, whereas for a trivial insulator the eigenvalues remain nonzero. This topological classification is related to the existence of in-gap bound states along codimension-1 and -2 impurities. Whereas codimension-1 impurities can be viewed as 'soft edg…
The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of boundary states in the insulating gap is not always necessary since they can be hidden in the bulk energy bands, obscured by boundary artifacts of non-topological origin, or, in the case of higher-order topology, they can be gapped altogether. Crucially, in such systems the interplay between symmetry-protected topology and the corresponding symmetry defects can p…
Bloch theory describes the electronic states in crystals whose energies are distributed as bands over the Brillouin zone. The electronic states corresponding to a (few) isolated energy band(s) thus constitute a vector bundle. The topological properties of these vector bundles provide new characteristics of the corresponding electronic phases. We review some of these properties in the case of (topological) insulators and semi-metals.
It has been known that an anti-unitary symmetry such as time-reversal or charge conjugation is needed to realize Z2 topological phases in non-interacting systems. Topological insulators and superconducting nanowires are representative examples of such Z2 topological matters. Here we report the first-known Z2 topological phase protected by only unitary symmetries. We show that the presence of a nonsymmorphic space group symmetry opens a possibility to realize Z2 topological phases without assuming any anti-unitary symmetry. The Z2 topological phases are constructed in various dimensions, which …
We study the multi-gap topology of the periodic spectra of Wilson loop operators (WLOs) in mirror symmetric insulators. We develop two topological invariants each associated with a mirror-invariant gap in the Wilson loop spectrum. We propose that both topological invariants in combination determine the general higher-order bulk-boundary correspondence in 2D mirror symmetric, boundary-obstructed topological insulators. Finally, we demonstrate that these new multi-gap topological invariants apply to anomalous cases beyond those captured by the nested Wilson loop, and we subsequently develop an u…
Topology plays a central role in nearly all disciplines of physics, yet its applications have so far been restricted to closed, lossless systems in thermodynamic equilibrium. Given that many physical systems are open and may include gain and loss mechanisms, there is an eminent need to reexamine topology within the context of non-Hermitian theories that describe open, lossy systems. The recent generalization of the Chern number to non-Hermitian Hamiltonians initiated this reexamination; however, there is so far no established connection between a non-Hermitian topological invariant and the qua…
Thermoelectric coefficients of an ultra-thin topological insulator are presented here. The hybridization between top and bottom surface states of a topological insulator plays a significant role. In absence of magnetic field, thermopower increases and thermal conductivity decreases with increase of the hybridization energy. In presence of magnetic field perpendicular to the ultra-thin topological insulator, thermoelectric coefficients exhibit quantum oscillations with inverse magnetic field, whose frequency is strongly modified by the Zeeman energy and phase factor is governed by the product o…
We theoretically investigate the surface plasmon polariton (SPP) at the interface between 3D strong topological insulator (TI) and layered superconductor-magnetic insulator structure. The tunability of SPP through electronic doping can be enhanced when the magnetic permeability of the layered structure becomes higher. When the interface is gapped by superconductivity or perpendicular magnetism, SPP dispersion is further distorted, accompanied by a shift of group velocity and penetration depth. Such a shift of SPP reaches maximum when the magnitude of Fermi level approaches the gap value, and m…
We study the low-energy edge states of a superconductor -- 3D topological-insulator hybrid structure (NS junction) in the presence of a perpendicular magnetic field. The hybridization of electron-like and hole-like Landau levels due to Andreev reflection gives rise to chiral edge states within each Landau level. We show that by changing the chemical potential of the superconductor, this junction can be placed in a regime where the sign of the effective charge of the edge state within the zeroth Landau level changes more than once resulting in neutral edge modes with a finite value of the guidi…
We determine the optical response of topological insulator thin films in the presence of a quantizing, external magnetic field. We explicitly take into account hybridization between the states of top and bottom surface. The interplay between hybridization and Zeeman energies gives rise to topological and normal insulator phases and phase transitions between them. The optical response in the two phases and at the phase transition point is investigated. We show that the difference in magneto-optical response can be used to distinguish the topological phase from the normal phase of the system. Fu…
Spin-Hall nano-oscillators (SHNOs) are promising spintronic devices to realize current controlled GHz frequency signals in nanoscale devices for neuromorphic computing and creating Ising systems. However, traditional SHNOs -- devices based on transition metals -- have high auto-oscillation threshold currents as well as low quality factors and output powers. Here we demonstrate a new type of hybrid SHNO based on a permalloy (Py) ferromagnetic-metal nanowire and low-damping ferrimagnetic insulator, in the form of epitaxial lithium aluminum ferrite (LAFO) thin films. The superior characteristics …
Topological insulators (TIs) and Weyl semimetals (WSMs) are two realizations of topological matter usually appearing separately in nature. However, they are directly related to each other via a topological phase transition. In this paper, we investigate the question whether these two topological phases can exist together at the same time, with a combined, hybrid surface state at the joint boundaries. We analyze effective models of a 3D TI and an inversion symmetric WSM and couple them in a way that certain symmetries, like inversion, are preserved. A tunnel coupling approach enables us to obta…
We calculate the phonon, electron and magnon temperature profiles in yttrium iron garnet/platinum bilayers by diffusive theory with appropriate boundary conditions, in particular taking into account interfacial thermal resistances. Our calculations show that in thin film hybrids, the interface magnetic heat conductance qualitatively affects the magnon temperature. Based on published material parameters we assess the degree of non-equilibrium at the yttrium iron garnet/platinum interface. The magnitude of the spin Seebeck effect derived from this approach compares well with experimental results…
The disorder effects on higher-order topological phases in periodic systems have attracted much attention. However, in aperiodic systems, such as quasicrystalline systems, the interplay between disorder and higher-order topology is still unclear. In this paper, we investigate the effects of disorder on two types of second-order topological insulators, including a quasicrystalline quadrupole insulator and a modified quantum spin Hall insulator, in a two-dimensional Amman-Beenker tiling quasicrystalline lattice. We demonstrate that the higher-order topological insulators are robust against weak …
In this paper we discuss the role of material parameters and external field effects on a thin film topological insulator(TI) in the context of quantum phase transition(QPT). First, we consider an in-plane tilted magnetic field and determine the band structure of the surface states as a function of the tilt angle. We show that the presence of either a hybridization term or hexagonal warping or a combination of both leads to a semi-metal to insulator phase transition which is facilitated by their ${\cal PT}$ symmetry breaking character. We then note that while the introduction of an electric fie…
A pair of Dirac points (analogous to a vortex-antivortex pair) associated with opposite topological numbers (with $\pmπ$ Berry phases) can be merged together through parameter tuning and annihilated to gap the Dirac spectrum, offering a canonical example of a topological phase transition. Here, we report transport studies on thin films of BiSbTeSe$_2$ (BSTS), which is a 3D TI that hosts spin-helical gapless (semi-metallic) Dirac fermion surface states (SS) for sufficiently thick samples, with an observed resistivity close to $h/4e^2$ at the charge neutral point. When the sample thickness is re…
We theoretically investigate the RKKY exchange coupling between two ferromagnets (FM) separated by a thin topological insulator film (TI). We find an unusual dependence of the RKKY exchange coupling on the TI thickness ($t_{TI}$). First, when $t_{TI}$ decreases, the coupling amplitude increases at first and reaches its maximum value at some critical thickness, below which the amplitude turns to diminish. This trend is attributed to the hybridization between surfaces of the TI film, which opens a gap below critical thickness and thus turns the surfaces into insulating state from semi-metal stat…
The axion insulator (AXI) has long been recognized as the simplest example of a 3D magnetic topological insulator (TI). The most familiar AXI results from magnetically gapping the surface states of a 3D $\mathbb{Z}_{2}$ TI while preserving the bulk gap. Like the 3D TI, it exhibits a quantized magnetoelectric polarizability of $θ=π$, and can be diagnosed from bulk symmetry eigenvalues when inversion symmetric. However, whereas a 3D TI is characterized by bulk Wilson loop winding, 2D surface states, and the pumping of the 2D $\mathbb{Z}_{2}$ TI index, we show that an AXI with a large number of b…
We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator and three-dimensional topological fullerenes, which involve multi-leg junctions. As a consequence of bulk-edge correspondence, these edge networks can faithfully predict properties such as the energy and fractional charge related to the bound states (edge solitons) in the aforementioned systems, including several aspects that were previously complicated or …
We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite non-zero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently-reported broken-symmetry spontane…
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…
The study of two-dimensional (2D) electronic systems is of great fundamental significance in physics. Atomic layers containing hybridized domains of graphene and hexagonal boron nitride (h-BNC) constitute a new kind of disordered 2D electronic system. Magneto-electric transport measurements performed at low temperature in vapor phase synthesized h-BNC atomic layers show a clear and anomalous transition from an insulating to a metallic behavior upon cooling. The observed insulator to metal transition can be modulated by electron and hole doping and by the application of an external magnetic fie…
Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of photonic topological insulators as an inverse design problem and use topology optimization to maximize the transmission through an edge mode with a sharp bend. Two design domains composed of two different, but initially identical, C$_\text{6v}$-symmetric unit cells define the geometrical design problem. Remarkabl…
We study transport properties of a topological insulator nanowire when a magnetic field is applied along its length. We predict that with strong surface disorder, a characteristic signature of the band topology is revealed in Aharonov Bohm (AB) oscillations of the conductance. These oscillations have a component with anomalous period $Φ_0=hc/e$, and with conductance maxima at odd multiples of $\frac12Φ_0$, i.e. when the AB phase for surface electrons is $π$. This is intimately connected to the band topology and a surface curvature induced Berry phase, special to topological insulator surfaces.…
We report on transport properties of Josephson junctions in hybrid superconducting-topological insulator devices, which show two striking departures from the common Josephson junction behavior: a characteristic energy that scales inversely with the width of the junction, and a low characteristic magnetic field for suppressing supercurrent. To explain these effects, we propose a phenomenological model which expands on the existing theory for topological insulator Josephson junctions.
We experimentally investigate and quantitatively analyze the spin Hall magnetoresistance effect in ferromagnetic insulator/platinum and ferromagnetic insulator/nonferromagnetic metal/platinum hybrid structures. For the ferromagnetic insulator we use either yttrium iron garnet, nickel ferrite or magnetite and for the nonferromagnet copper or gold. The spin Hall magnetoresistance effect is theoretically ascribed to the combined action of spin Hall and inverse spin Hall effect in the platinum metal top layer. It therefore should characteristically depend upon the orientation of the magnetization …
We study electronic transport in graphene/ferromagnetic insulator hybrid devices. The system comprises an armchair graphene nanoribbon with a lens-shaped EuO ferromagnetic insulator layer deposited on top of it. When the device supports a large number of propagating modes, the proximity exchange interaction of electrons with the magnetic ions of the ferromagnetic insulator results in electrons being spatially localised at different spots depending on their spin. We found the spin-dependent electron focusing is robust under moderate edge disorder. A spin-polarised electric current can be genera…
Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically nontrivial phases. We show how this picture generalizes to multiband critical models belonging to any of the chiral symmetry classes AIII, BDI, or CII of noninteracting fermions in one dimension.
Established forms of electromagnetic coupling are usually conservative (in insulators) or dissipative (in metals and semiconductors). Here we point out the possibility of nondissipative electric driving of magnetization dynamics, if the valence electronic states have nontrivial topology in the combined space of crystal momentum and magnetization configuration. We provide a hybrid insulator system to demonstrate that the topology-based nonconservative electrical generalized force is capable of supporting sustained magnetization motion in the presence of Gilbert damping, with quantized and stead…
High-order topological insulators are a recent development extending the topological theory of charge polarization to higher multipole moments. Since their theoretical proposal, several experimental realizations of high-order topological insulators have been reported. However, high order topological transitions have not been observed. In this letter, we report on the observation of a high-order topological transition in a quadrupole topological insulator implemented in an LC circuit with nonlinear couplings. This system presents the ability to confine electromagnetic energy in its corner state…
We theoretically show that the coupling of inhomogeneous strains to the Dirac fermions of three-dimensional topological insulators (3DTI) in thin film geometries results in the occurrence of phase transitions between topologically distinct insulating phases. By means of minimal k dot p models for strong 3DTI in the Bi 2 Se 3 materials class, we find that in thin films of stoichiometric materials a strain-gradient induced structure inversion asymmetry drives a phase transition from a quantum spin-Hall phase to a topologically trivial insulating phase. Interestingly, in alloys with strongly redu…
We study nonlocal resistance in an H-shaped two-dimensional HgTe/CdTe quantum well consist of injector and detector, both of which can be tuned in the quantum spin Hall or metallic spin Hall regime. Because of strong spin-orbit interaction, there always exist spin Hall effect and the nonlocal resistance in HgTe/CdTe quantum well. We find that when both detector and injector are in the quantum spin Hall regime, the nonlocal resistance is quantized at $0.25\frac{h}{e^2}$, which is robust against weak disorder scattering and small magnetic field. While beyond this regime, the nonlocal resistance …
We study the axion in three-dimensional topological insulators with magnetic impurities under finite temperature. We find a stable antiferromagnetic ground state and ferromagnetic metastable state. In both magnetic states, the mass of the axion is found to be up to eV scale and it approaches zero near the phase boundary of the magnetic state. This result applies to both normal and topological insulator phases, i.e., the axion mass is insensitive to the topological states, and it will have a direct impact on the targeted mass range of particle axion dark matter in future experiments.
Magnetic materials in which it is possible to control the topology of their magnetic order in real space or the topology of their magnetic excitations in reciprocal space are highly sought-after as platforms for alternative data storage and computing architectures. Here we show that multiferroic insulators, owing to their magneto-electric coupling, offer a natural and advantageous way to address these two different topologies using laser fields. We demonstrate that via a delicate balance between the energy injection from a high-frequency laser and dissipation, single skyrmions -- archetypical …
We report on a study of an ultrathin topological insulator film with hybridization between the top and bottom surfaces, placed in a quantizing perpendicular magnetic field. We calculate the full Landau level spectrum of the film as a function of the applied magnetic field and the magnitude of the hybridization matrix element, taking into account both the orbital and the Zeeman spin splitting effects of the field. For an undoped film, we find a quantum phase transition between a state with a zero Hall conductivity and a state with a quantized Hall conductivity equal to $e^2/h$, as a function of…
