Surface Of Topological Insulator Research Articles

Reflection and Refraction of a Spin at the Edge of a Quasi-Two-Dimensional Semiconductor Layer (Quantum Well) and a Topological Insulator

We derive the reflection and refraction laws for an electron spin incident from a quasi-two-dimensional semiconductor region (with no spin–orbit interaction) on the metallic surface of a topological insulator (TI) when the two media are in contact edge to edge. For a given incident angle, there can generally be two different refraction angles for refraction into the two spin eigenstates in the TI surface, resulting in two different ‘spin refractive indices’ (birefringence) and the possibility of two different critical angles for total internal reflection. We derive expressions for the spin refractive indices and the critical angles, which depend on the incident electron’s energy for given effective masses in the two regions and a given potential discontinuity at the TI/semiconductor interface. For some incident electron energies, there is only one critical angle, in which case 100% spin polarized injection can occur into the TI surface from the semiconductor if the angle of incidence exceeds that critical angle. The amplitudes of reflection of the incident spin with and without spin flip at the interface, as well as the refraction (transmission) amplitudes into the two spin eigenstates in the TI, are derived as functions of the angle of incidence.

Anomalous Josephson Effect of s-Wave Pairing States in Chiral Double Layers.

We consider s-wave pairing in a double layer of two chiral metals due to interlayer Coulomb interaction and study the Josephson effect near a domain wall, where the sign of the order parameter jumps. The domain wall creates two evanescent modes at the exceptional zero-energy point, whose superposition is associated with currents flowing in different directions in the two layers. Assuming a toroidal geometry, the effective Josephson current winds around the domain walls, whose direction is determined by the phase difference of the complex coefficients of the superimposed zero-energy modes. Thus, the zero-energy mode is directly linked to a macroscopic current. This result can be understood as an interplay of the conventional Josephson current perpendicular and the edge current parallel to a domain wall in a double layer of two chiral metals. As a realization we suggest the surface of a ring-shaped topological insulator. The duality between electron-electron and electron-hole double layers indicates that this effect should also be observable in excitonic double layers.

Nonlinear antidamping spin-orbit torque originating from intraband transport on the warped surface of a topological insulator

Motivated by recent experiments observing a large antidamping spin-orbit torque (SOT) on the surface of a three-dimensional topological insulator, we investigate the origin of the current-induced SOT beyond linear-response theory. We find that a strong antidamping SOT arises from intraband transitions in non-linear response, and does not require interband transitions as is the case in linear transport mechanisms. The joint effect of warping and an in-plane magnetization generates a non-linear antidamping SOT which can exceed the intrinsic one by several orders of magnitude, depending on warping parameter and the position of Fermi energy, and exhibits a complex dependence on the azimuthal angle of the magnetization. This nonlinear SOT provides an alternative explanation of the observed giant SOT in recent experiments.

Electron beam splitting at topological insulator surface states and a proposal for electronic Goos-Hänchen shift measurement

The hexagonal warping effect on transport properties and Goos-H\"anchen (GH) lateral shift of electrons on the surface of a topological insulator with a potential barrier is investigated theoretically. Due to the warped Fermi surface for incident electron beams, we can expect two propagating transmitted beams corresponding to the occurrence of double refraction. The transmitted beams have spin orientations locked to their momenta so one of the spin directions rotates compared to the incident spin direction. Based on a low-energy Hamiltonian near the Dirac point and considering Gaussian beams, we derive expressions for calculating lateral shifts in the presence of warping effect. We study the dependence of transmission probabilities and GH shifts of transmitted beams on system parameters in detail by giving an explanation for the appearance of large peaks in the lateral shifts corresponding to their transmission peaks. It is shown that the separation between two transmitted beams through their different GH shifts can be as large as a few micrometers, which is large enough to be observed experimentally. Finally, we propose a method to measure the GH shift of electron beams based on the transverse magnetic focusing technique in which, by tuning an applied magnetic field, a detectable resonant path for electrons can be induced.

Andreev spectroscopy of nonhelical spin textures in topological insulators

We study how nonhelical spin textures affect the proximity-induced superconductivity of topological insulator (TI)-superconductor (SC) interface states. In particular we calculate the conductance of lateral heterojunctions which comprise a TI surface that is only partially covered by a superconducting material. Interface potentials at the TI-SC interface may lead to a Fermi velocity and spin texture mismatch between the two regions of the lateral heterojunction. By enforcing the hermiticity of the total Hamiltonian, we derive the boundary conditions and calculate the conductance of the structure in both the normal and superconducting state. The total Andreev conductance is calculated for both $s$-wave and spin-triplet parent SCs, and for several examples of nonhelical spin textures which lead to different Fermi surface mismatches between the two planar regions of the heterojunction. We find that for spin-triplet SCs, nonzero conductance signatures only appear for certain combinations of nonhelical spin textures and parent superconducting material.

Absence of induced magnetic monopoles in Maxwellian magnetoelectrics

The electromagnetic response of topological insulators is governed by axion electrodynamics, which features a topological magnetoelectric term in the Maxwell equations. As a consequence magnetic fields become the source of electric fields and vice versa, a phenomenon that is general for any material exhibiting a linear magnetoelectric effect. Axion electrodynamics has been associated with the possibility to create magnetic monopoles, in particular, by an electrical charge that is screened above the surface of a magnetoelectric material. Here we explicitly solve for the electromagnetic fields in this geometry and show that while vortexlike magnetic screening fields are generated by the electrical charge their divergence is identically zero at every point in space, which implies an absence of induced magnetic monopoles. Nevertheless magnetic image charges can be made explicit in the problem, and even if no bound state with electric charges yielding a dyon arises, a dyonlike angular momentum follows from our analysis. Because of its dependence on the dielectric constant this angular momentum is not quantized, which is consistent with a general argument that precludes magnetic monopoles to be generated in Maxwell magnetoelectrics. We also solve for topologically protected zero modes in the Dirac equation induced by the point charge. Since the induced topological defect on the topological insulator's surface carries an electric charge as a result of the axion term, these zero modes are not self-conjugated.

Signatures of nontopological patches on the surface of topological insulators

The non-trivial topology in the layered $\text{FeTe}_{0.55}\text{Se}_{0.45}$ (FTS) superconductor has been suggested by both theory and experiment to be strongly dependent on the Te concentration. Motivated by this together with the Te fluctuations expected from alloy disorder, we develop a simple layered model for a strong topological insulator that allows us to describe a scenario where topologically trivial domains permeate the sample. We refer to such a phase as topological domain disordered and study the local density (LDOS) of the topological surface states that can be measured using scanning tunneling spectroscopy (STS) in this phase. We find that topologically trivial domains on the surface, where one would expect the topological surface state to be absent, appear as regions of suppressed LDOS surrounded by domain walls with enhanced LDOS. Furthermore, we show that studying the energy dependence of the STS should allow us to distinguish the topologically trivial parts of the surface from other forms of disorder. Finally, we discuss implications of such local disappearance of the topological surface states for the observation of Majorana modes in vortices.

Transmission in Through a Super Lattice of Magnetic Structure on Surface Oftopological Insulator

Transmission in Through a Super Lattice of Magnetic Structure on Surface Oftopological Insulator

Signature of anomalous Andreev bound states in magnetic Josephson junction of noncentrosymmetric superconductor on a topological insulator

We study the Josephson effect in a clean noncentrosymmetric superconductor/half-metal/noncentrosymmetric superconductor junction, which is grown on the surface of a three-dimensional Topological Insulator (TI) in the ballistic limit. We find the signature of anomalous Andreev Bound States (ABS) and band splitting for a spin-active barrier whose barrier magnetic moment is misaligned with the bulk moment. The chiral Majorana mode and 4$\pi$ periodic ABS are found to exist on the surface of TI for parallel orientation of the moments in the normal incidence condition. But for anti-parallel misalignment, we observe the 2$\pi$ periodic ABS. There exist a gap in ABS for oblique incidence. We find the splitting of Andreev levels in the presence of RSOC and also for unequal mixing of singlet-triplet correlations present in NCSC. The Majorana mode, ABS and Josephson supercurrent can be controlled by the ratio of barrier magnetic and non-magnetic moments. The critical current is found to be maximum for singlet or triplet dominated NCSC, while it is minimum in the equal mixing condition. The ABS is found to be barrier thickness dependent and is suppressed for an opaque barrier. We observe a monotonic decay in critical current with a finite length of the junction for all the singlet-triplet mixings and magnetic moments. The current-phase relation is found to be sinusoidal with no phase shift in the half-metallic limit, however, for different orientations of the bulk moment, an anomalous characteristic is also observed.

Irreversible thermodynamics at surfaces: inverse Edelstein effect for topological insulator

We employ Onsager’s irreversible thermodynamics to study the inverse Edelstein effect (IEE) for a non-magnetic material (NM) adjacent to a topological insulator (TI) with a strong spin–orbit interaction. The TI surface state region is treated as quasi two-dimensional (2D). For the IEE, the source is a 3D spin flux incident from the NM that converts, at the NM–TI interface, to a quasi-2D charge current in the TI. For the Edelstein effect (EE), the source is a quasi-2D charge flux incident from the TI that converts, at the interface, to a three-dimensional (3D) spin flux in the NM. For strong spin–orbit coupling, as considered here, when the 3D spin flux crosses to the 2D TI, the quasi-2D charge current is produced along with a quasi-2D spin accumulation. (For weak spin–orbit coupling, production of charge current and of spin accumulation are distinct processes.) We compute the associated rates of heating.

Effect of Dilute Magnetism in a Topological Insulator

Three-dimensional (3D) topological insulator (TI) has emerged as a unique state of quantum matter and generated enormous interests in condensed matter physics. The surfaces of a 3D TI consist of a massless Dirac cone, which is characterized by the Z2topological invariant. Introduction of magnetism on the surface of a TI is essential to realize the quantum anomalous Hall effect and other novel magneto-electric phenomena. Here, by using a combination of first-principles calculations, magneto-transport and angle-resolved photoemission spectroscopy (ARPES), we study the electronic properties of gadolinium (Gd)-doped Sb2Te3. Our study shows that Gd doped Sb2Te3is a spin-orbit-induced bulk band-gap material, whose surface is characterized by a single topological surface state. Our results provide a new platform to investigate the interactions between dilute magnetism and topology in magnetic doped topological materials.

Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators

The recent observations of nonlinear Hall effect in time-reversal symmetry protected systems and on the surface of three-dimensional topological insulators due to an in-plane magnetic field have attracted immense experimental and theoretical investigations in two-dimensional transition metal dichalcogenides and Weyl semimetals. The origin of this type of second order effect has been attributed to the emergence of a Berry curvature dipole, which requires a low-symmetry environment. Here, we propose a mechanism for generating such a second order nonlinear Hall effect in Kane-Mele two-dimensional topological insulators due to spatial and time reversal symmetry breaking in the presence of Zeeman and Rashba couplings. By actively tuning the energy gaps with external electromagnetic fields we also demonstrate that the nonlinear Hall effect shows remarkable signatures of topological phase transitions existing in the considered two-dimensional systems.

Impurity effect on hysteric magnetoconductance: holographic approach

In this paper we study a hysteric phase transition from weak localization phase to hysteric magnetoconductance phase using gauge/gravity duality. This hysteric phase is triggered by a spontaneous magnetization related to ℤ2 symmetry and time reversal symmetry in a 2+1 dimensional system with momentum relaxation. We derive thermoelectric conductivity formulas describing non-hysteric and hysteric phases. At low temperatures, this magnetoconductance shows similar phase transitions of topological insulator surface states. We also obtain hysteresis curves of Seebeck coefficient and Nernst signal. It turns out that our impurity parameter changes magnetic properties of the dual system. This is justified by showing increasing susceptibility and the spontaneous magnetization with increasing impurity parameter.

Generation of spin-polarized hot electrons at topological insulators surfaces by scattering from collective charge excitations

Topological insulators (TIs) are materials which exhibit topologically protected electronic surface states, acting as mass-less Dirac fermions. Beside their fascinating fundamental physics, TIs are also promising candidates for future spintronic devices. In this regard, generation of spin-polarized currents in TIs is the first and most important step towards their application in spin-based devices. Here we demonstrate that when electrons are scattered from the surface of bismuth selenide, a prototype TI, not only the elastic channel but also the inelastic channel is strongly spin dependent. In particular collective charge excitations (plasmons) excited at such surfaces show a large spin-dependent electron scattering. Electrons scattered by these excitations exhibit a high spin asymmetry, as high as 40%. The observed effect opens up new possibilities to generate spin-polarized currents at the surface of TIs or utilize the collective charge excitations to analyze the electrons’ spin. The results are also important to understand the spin polarization of the photo-excited electrons excited at TIs surfaces. Moreover, our finding will inspire new ideas for using these plasmonic excitations in the field of spin-plasmonics.

Terahertz signatures of ultrafast Dirac fermion relaxation at the surface of topological insulators

Topologically protected surface states present rich physics and promising spintronic, optoelectronic, and photonic applications that require a proper understanding of their ultrafast carrier dynamics. Here, we investigate these dynamics in topological insulators (TIs) of the bismuth and antimony chalcogenide family, where we isolate the response of Dirac fermions at the surface from the response of bulk carriers by combining photoexcitation with below-bandgap terahertz (THz) photons and TI samples with varying Fermi level, including one sample with the Fermi level located within the bandgap. We identify distinctly faster relaxation of charge carriers in the topologically protected Dirac surface states (few hundred femtoseconds), compared to bulk carriers (few picoseconds). In agreement with such fast cooling dynamics, we observe THz harmonic generation without any saturation effects for increasing incident fields, unlike graphene which exhibits strong saturation. This opens up promising avenues for increased THz nonlinear conversion efficiencies, and high-bandwidth optoelectronic and spintronic information and communication applications.

Anomalous Josephson effect modulated by magnetic misorientation in a topological unconventional superconductor hybrid structure

We study the anomalous Josephson effect induced by magnetic misorientation of asymmetric s-wave superconductor (SC)/ferromagnet insulator (FI)/normal layer/FI/d-wave SC junctions on a surface of topological insulator (TI). For the out-of-plane case, the magnetic misorientation not only leads to anomalous Josephson effects, but also realizes state transitions. However, for the in-plane case, the state transitions do not turn up any more. In particular, the plateaus phenomenon for d xy -wave SC junction emerges all the time. In addition, in the context of the in-plane case, the supercurrent rectification can be modulated by the magnetic misorientation. These unique phenomena can be employed to identify different d-wave superconductivities of three-dimensional TI and manufacture the supercurrent devices with such functions as phase storing, rectification, and quantum computation.

Quantum Oscillations in the Zeroth Landau Level: Serpentine Landau Fan and the Chiral Anomaly

We identify an unusual mechanism for quantum oscillations in nodal semimetals, driven by a single pair of Landau levels periodically closing their gap at the Fermi energy as a magnetic field is varied. These "zero Landau level" quantum oscillations (ZQOs) appear in the nodal limit where the zero-field Fermi volume vanishes and have distinctive periodicity and temperature dependence. We link the Landau spectrum of a two-dimensional (2D) nodal semimetal to the Rabi model, and show by exact solution that, across the entire Landau fan, pairs of opposite-parity Landau levels are intertwined in a "serpentine" manner. We propose 2D surfaces of topological crystalline insulators as natural settings for ZQOs. In certain 3D nodal semimetals, ZQOs lead to oscillations of anomaly physics. We propose a transport measurement capable of observing such oscillations, which we demonstrate numerically.

Topological magnetic textures in magnetic topological insulators

The surfaces of intrinsic magnetic topological insulators (TIs) host magnetic moments exchange-coupled to Dirac electrons. We study the magnetic phases arising from tuning the electron density using variational and exact diagonalization approaches. In the dilute limit, we find that magnetic skyrmions are formed, which bind to electrons, leading to a skyrmion Wigner crystal phase while at higher densities spin spirals accompanied by chiral one-dimensional channels of electrons are formed. The binding of electrons to textures raises the possibility of manipulating textures with electrostatic gating. We determine the phase diagram capturing the competition of intrinsic spin-spin interactions and carrier density and comment on the possible application to experiments in magnetic TIs and spintronic devices such as skyrmion-based memory.

Growth of topological insulator Bi2Se3 particles on GaAs via droplet epitaxy

The discovery of topological insulators (TIs) and their unique electronic properties has motivated research into a variety of applications, including quantum computing. It has been proposed that TI surface states will be energetically discretized in a quantum dot nanoparticle. These discretized states could then be used as basis states for a qubit that is more resistant to decoherence. In this work, prototypical TI Bi2Se3 nanoparticles are grown on GaAs (001) using the droplet epitaxy technique, and we demonstrate the control of nanoparticle height, area, and density by changing the duration of bismuth deposition and substrate temperature. Within the growth window studied, nanoparticles ranged from 5 to 15 nm in height with an 8–18 nm equivalent circular radius, and the density could be relatively well controlled by changing the substrate temperature and bismuth deposition time.

Anomalous Magneto-Optical Effects in an Antiferromagnet–Topological-Insulator Heterostructure

We show that large magneto-optic Kerr effects (MOKEs) emerge when an antiferromagnet (AFM) is proximately coupled to a topological insulator (TI) film---where neither the perfect collinear N\'eel ordered single-domain AFM nor the unmagnetized TI individually shows any MOKE. Because of the lack of macroscopic magnetization, the AFM only couples to the spin of one of the TI's surfaces breaking time-reversal and inversion symmetry---which leads to a small microdegree MOKE signal. This small MOKE can be easily enhanced by 5 orders of magnitude, via cavity resonance, by optimizing the AFM and TI film thicknesses on the substrate. For slightly off-resonant structures, a ${6}^{\ensuremath{\circ}}$ Kerr rotation can be electrically switched on by varying the Fermi energy. This requires less than 20 meV, which is encouraging for low-power spintronics and magneto-optic devices. We further show that this simple structure is easily resilient to 5% material growth error.