Surface Of Three-dimensional Topological Insulator Research Articles

Entanglement spectroscopy of anomalous surface states

We study the entanglement spectra of surface states of symmetry-protected topological phases. The topological bulk imprints the surface with an anomaly that does not permit it to form a trivial “vacuum” state that is gapped, unfractionalized, and symmetry preserving. Any surface wave function encodes the topology of the underlying bulk in addition to a specific surface phase. We show that the real-space entanglement spectrum of such surface wave functions are dominated by the bulk topology and do not readily permit identifying the surface phase. We thus use a modified form of entanglement spectra that incorporates the anomaly and argue that they correspond to physical edge states between different surface states. We support these arguments by explicit analytical and numerical calculations for free and interacting surfaces of three-dimensional topological insulators of electrons. Published by the American Physical Society 2024

Magnetization-induced phase transitions on the surface of three-dimensional topological insulators

Magnetization-induced phase transitions on the surface of three-dimensional topological insulators

Anisotropic angle-dependent Andreev reflection at the ferromagnet/superconductor junction on the surface of topological insulators

We theoretically demonstrate that a ferromagnetic/superconductor junction on the surface of three-dimensional topological insulators (3D TIs) has an anisotropic angle-dependent Andreev reflection when the in-plane magnetization has a component perpendicular to the junction. In the presence of in-plane magnetization, the Dirac cone’s location adjusts in the k-space, whereas its out-of-plane component induces a gap. This movement leads to the anisotropic angle-dependent Andreev reflection and creates an anomalous Hall conductance flows parallel to the interface. Also, an indirect gap induces in the junction, which removes the transport signatures of Majorana bound states. Because of the full spin-momentum locking of Dirac fermions on the surface of 3DTIs, a torque that called Andreev Transfer Torque (ATT) imposes on the junction. Moreover, we propose a setup to detect them experimentally.

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.

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.

Spectral features of magnetic domain walls on the surface of three-dimensional topological insulators

We present a theoretical investigation of electron states hosted by magnetic domain walls on the 3D topological insulator surface. The consideration includes the domain walls with distinct vectorial and spatial textures. The study is carried out on the basis of the Hamiltonian for quasi-relativistic fermions by using a continual approach and tight-binding calculations. We derive the spectral characteristics and spatial localization of the the one-dimensional low-energy states appearing at the domain walls. The antiphase domain walls are shown to generate the topologically protected chiral states with linear dispersion, the group velocity and spin-polarization direction of which depend on an easy axis orientation. In the case of an easy plane anisotropy, we predict a realization of a dispersionless state, flat band in the energy spectrum, that is spin-polarized along the surface normal. Modification of the surface states in the multi-domain case, which is approximated by a periodic set of domain walls, is described as well. We find that the magnetic domain walls with complex internal texture, such as N\'eel-like or Bloch-like walls, also host the topological states, although their spectrum and spin structure can be changed compared with the sharp wall case.

Current transfer torque and Hall conductance at the ferromagnetic topological insulators junction

In-plane magnetization on the surface of three-dimensional topological insulators (3D TIs) tunes the Dirac cone’s location in the k-space. We theoretically show that a normal/ferromagnetic junction on the surface of 3D TIs bends the propagation direction of Dirac fermions when the magnetization has a component perpendicular to the junction. This effect leads to a Hall conductance, which flows parallel to the interface. Also, it creates an indirect gap that manifests itself in the longitudinal conductance of the junction. The sign of Hall conductance is related to the in-plane magnetization direction. Based on this effect, we propose a set up to detect it experimentally. Moreover, this bending effect imposes a torque on the junction called current transfer torque (CTT). We show the z-component of CTT is non-zero in the presence of bending effect. Also, its value and direction that can be used in fabricating new devices are related to the Hall conductance.

Magnetic Proximity Effect in an Antiferromagnetic Insulator/Topological Insulator Heterostructure with Sharp InterfaceSupported by the National Key Research and Development Program of China (Grant No. 2016YFA0300600), the National Natural Science Foundation of China (Grant No. 11961141011), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000).

We report an experimental study of electron transport properties of MnSe/(Bi,Sb)2Te3 heterostructures, in which MnSe is an antiferromagnetic insulator, and (Bi,Sb)2Te3 is a three-dimensional topological insulator (TI). Strong magnetic proximity effect is manifested in the measurements of the Hall effect and longitudinal resistances. Our analysis shows that the gate voltage can substantially modify the anomalous Hall conductance, which exceeds 0.1 e 2/h at temperature T = 1.6 K and magnetic field μ 0 H = 5 T, even though only the top TI surface is in proximity to MnSe. This work suggests that heterostructures based on antiferromagnetic insulators provide a promising platform for investigating a wide range of topological spintronic phenomena.

Protected gap closing in Josephson trijunctions constructed on Bi2Te3

We carried out a phase-sensitive experiment on Josephson trijunctions constructed on the surface of three-dimensional topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$. Through local flux contol and contact resistance measurement, we observed that the minigap at the ends of the trijunctions approaches zero linearly with varying phase difference and closes completely at $\ensuremath{\pi}$ phase difference. The minigap at the center of the trijunction is protected to close over extended regions in phase space. These results agree with the theory by Fu and Kane [Phys. Rev. Lett. 100, 096407 (2008)].

Probing the minigap in topological insulator-based Josephson junctions under radio frequency irradiation**Project supported by the National Basic Research Program of China (Grant Nos. 2016YFA0300601, 2017YFA0304700, and 2015CB921402), the National Natural Science Foundation China (Grant Nos. 11527806, 91221203, 11174357, 91421303, and 11774405), and the Strategic Priority Research Program B of the Chinese Academy of Sciences (Grant Nos. XDB07010100 and XDB28000000), and

Recently, a contact-resistance-measurement method was developed to detect the minigap, hence the Andreev bound states (ABSs), in Josephson junctions constructed on the surface of three-dimensional topological insulators (3D TIs). In this work, we further generalize that method to the circumstance with radio frequency (rf) irradiation. We find that with the increase of the rf power, the measured minigap becomes broadened and extends to higher energies in a way similar to the rf power dependence of the outer border of the Shapiro step region. We show that the corresponding data of contact resistance under rf irradiation can be well interpreted by using the resistively shunted Josephson junction (RSJ) model and the Blonder–Tinkham–Klapwijk (BTK) theory. Our findings could be useful when using the contact-resistance-measurement method to study the Majorana-related physics in topological insulator-based Josephson junctions under rf irradiation.

Plasmon-Polariton from a Helical State in a Dirac Magnet

Electromagnetic field interacting with a topologically protected one-dimensional electron helical state is shown to support a one-dimensional plasmon-polariton, which is a collective electron excitation dressed with the electromagnetic field. The electronic helical state arises at the surface of three-dimensional topological insulator in the proximity of the ferromagnet and is localized at the magnetization domain wall. This opens the possibilities to manipulate quantum optical states by altering magnetic domain configurations. An exact spectral equation for such topological plasmon-polariton is derived.

Localized surfaces of three-dimensional topological insulators

We study the surface of a three-dimensional spin chiral $\mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of interaction and statistically-symmetric disorder, that confines the gapless fermionic degrees of freedom to a network of one-dimensional helical domain-walls that can be localized. We identify two distinct regimes of this gapless insulating phase, a `clogged' regime wherein the network localization is induced by its junctions between otherwise metallic helical domain-walls, and a `fully localized' regime of localized domain-walls. The experimental signatures of these regimes are also discussed.

Protected gap closing in Josephson junctions constructed on Bi2Te3 surface

On the road of searching for Majorana zero modes (MZMs) in topological insulator-based Josephson junctions, a highly sought signature is the protected full transparency of electron transport through the junctions due to the existence of the MZMs, associated with complete gap closing between the electronlike and holelike Andreev bound states (ABSs). Here we present direct experimental evidence of gap closing and full transparency in single Josephson junctions constructed on the surface of three-dimensional topological insulator (3D TI) ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$. Our results demonstrate that the two-dimensional (2D) surface of 3D TIs provides a promising platform for hosting and manipulating MZMs.

Plasmon-induced hot carrier transfer to the surface of three-dimensional topological insulators

Plasmon-induced hot carrier transfer to the surface of three-dimensional topological insulators

Nonreciprocal charge transport in two-dimensional noncentrosymmetric superconductors

Nonreciprocal charge transport phenomena are studied theoretically for two-dimensional noncentrosymmetric superconductors under an external magnetic field $B$. Rashba superconductors, surface superconductivity on the surface of three-dimensional topological insulators, and transition metal dichalcogenides (TMD) are representative systems, and the current-voltage $I$-$V$ characteristics, i.e., $V=V(I)$, for each of them is analyzed. $V(I)$ can be expanded with respect to the current $I$ as $V(I)= \sum_{j=1,\infty} a_j(B,T) I^j$, and the $(B,T)$-dependence of $a_j$ depends on the mechanism of the charge transport. Above the mean field transition temperature $T_0$, the fluctuation of the superconducting order parameter gives the additional conductivity, i.e., paraconductivity. Extending the analysis to the nonlinear response, we obtain the nonreciprocal charge transport expressed by $a_2(B,T) = a_1(T) \gamma(T) B$, where $\gamma$ converges to a finite value at $T=T_0$. Below $T_0$, the vortex motion is relevant to the voltage drop, and the dependence of $a_j$ on $B,T$ is different depending on the system and mechanisms. For the superconductors under the in-plane magnetic field, the Kosterlitz-Thouless (KT) transition occurs at $T_{\rm KT}$. In this case $\gamma$ has the characteristic temperature dependences such as $\gamma \sim (T-T_{\rm KT})^{-3/2}$ near $T_{\rm KT}$. On the other hand, for TMD with out-plane magnetic field, the KT transition is gone, and there are two possible mechanisms for the nonreciprocal response. One is the anisotropy of the damping constant for the motion of the vortex. In this case, $a_1(B) \sim B$ and $a_2(B) \sim B^2$. The other one is the ratchet potential acting on the vortex motion, which gives $a_1(B) \sim B$ and $a_2(B) \sim B$. Based on these results, we propose the experiments to identify the mechanism of the nonreciprocal charge transport.

Anomalous Fraunhofer Patterns in Gated Josephson Junctions Based on the Bulk-Insulating Topological Insulator BiSbTeSe2.

One-dimensional Majorana modes are predicated to form in Josephson junctions based on three-dimensional topological insulators (TIs). While observations of supercurrents in Josephson junctions made on bulk-insulating TI samples have been reported recently, the Fraunhofer patters observed in such TI-based Josephson junctions, which sometimes present anomalous features, are still not well-understood. Here, we report our study of highly gate-tunable TI-based Josephson junctions made of one of the most bulk-insulating TI materials, BiSbTeSe2, and Al. The Fermi level can be tuned by gating across the Dirac point, and the high transparency of the Al-BiSbTeSe2 interface is evinced by a high characteristic voltage and multiple Andreev reflections, with peak indices reaching 12. Anomalous Fraunhofer patterns with missing lobes were observed in the entire range of gate voltage. We found that, by employing an advanced fitting procedure to use the maximum entropy method in a Monte Carlo algorithm, the anomalous Fraunhofer patterns are explained as a result of inhomogeneous supercurrent distributions on the TI surface in the junction. Besides establishing a highly promising fabrication technology, this work clarifies one of the important open issues regarding TI-based Josephson junctions.

Electrical Detection of Charge-to-spin and Spin-to-Charge Conversion in a Topological Insulator Bi2Te3 Using BN/Al2O3 Hybrid Tunnel Barrier

One of the most striking properties of three-dimensional topological insulators (TIs) is spin-momentum locking, where the spin is locked at right angles to momentum and hence an unpolarized charge current creates a net spin polarization. Alternatively, if a net spin is injected into the TI surface state system, it is distinctively associated with a unique carrier momentum and hence should generate a charge accumulation, as in the so-called inverse Edelstein effect. Here using a Fe/Al2O3/BN tunnel barrier, we demonstrate both effects in a single device in Bi2Te3: the electrical detection of the spin accumulation generated by an unpolarized current flowing through the surface states, and that of the charge accumulation generated by spins injected into the surface state system. This work is the first to utilize BN as part of a hybrid tunnel barrier on TI, where we observed a high spin polarization of 93% for the TI surfaces states. The reverse spin-to-charge measurement is an independent confirmation that spin and momentum are locked in the surface states of TI, and offers additional avenues for spin manipulation. It further demonstrates the robustness and versatility of electrical access to the spin system within TI surface states, an important step towards its utilization in TI-based spintronics devices.

Modeling all-electrical detection of the inverse Edelstein effect by spin-polarized tunneling in a topological-insulator/ferromagnetic-metal heterostructure

The spin-momentum locking of the surface states in a three-dimensional topological insulator (TI) allows a charge current on the surface of the TI induced by an applied spin current onto the surface, which is known as the inverse Edelstein effect (IEE), that could be achieved either by injecting pure spin current by spin-pumping from a ferromagnetic metal (FM) layer or by injecting spin-polarized charge current by direct tunneling of electrons from the FM to the TI. Here, we present a theory of the observed IEE effect in a TI-FM heterostructure for the spin-polarized tunneling experiments. If an electrical current is passed from the FM to the surface of the TI, because of density-of-states polarization of the FM, an effective imbalance of spin-polarized electrons occurs on the surface of the TI. Due to the spin-momentum helical locking of the surface states in the TI, a difference of transverse charge accumulation appears on the TI surface in a direction orthogonal to the direction of the magnetization of the FM, which is measured as a voltage difference. Here, we derive the two-dimensional transport equations of electrons on the surface of a diffusive TI, coupled to a FM, starting from the quantum kinetic equation, and analytically solve the equations for a rectangular geometry to calculate the voltage difference.

Perfect transmission at oblique incidence by trigonal warping in graphene P-N junctions

We develop an analytical mode-matching technique for the tight-binding model to describe electron transport across graphene P-N junctions. This method shares the simplicity of the conventional mode-matching technique for the low-energy continuum model and the accuracy of the tight-binding model over a wide range of energies. It further reveals an interesting phenomenon on a sharp P-N junction: the disappearance of the well-known Klein tunneling (i.e., perfect transmission) at normal incidence and the appearance of perfect transmission at oblique incidence due to trigonal warping at energies beyond the linear Dirac regime. We show that this phenomenon arises from the conservation of a generalized pseudospin in the tight-binding model. We expect this effect to be experimentally observable in graphene and other Dirac fermions systems, such as the surface of three-dimensional topological insulators.

One-way transmission of electrons on the topological insulator surface modulated by magnetic potential

We investigate the transport properties of Dirac fermions on the surface of a three-dimensional topological insulator (TI) with magnetic modulation potentials. By using the transfer-matrix method, the transmission coefficients are obtained as a function of incident energy and incident angle. It is shown that the forward and backward propagating carriers possess different transmission coefficients at some incident energies when the charge carriers incident obliquely, which originates from the break of time reversal symmetry. Particularly, the magnetic barrier introduces asymmetric scattering; thus, the scattered angles are different for the forward and backward propagating carriers. As a consequence, the transmission in one direction is permitted while it is blocked in its reversal direction. Therefore, the unidirectional transmission of electrons is achieved on the surface of TI. Furthermore, unidirectional transmission is demonstrated by the electronic charge distributions in the system. The investigations may have potential applications in the design of TI-based one-way quantum devices.