Three-dimensional Topological Insulator Research Articles

Collective excitations in magnetic topological insulators and axion dark matter search

We investigate collective excitations in magnetic topological insulators (TIs) and their impact on axion detection. In the three-dimensional TI model with the Hubbard term, the effective action of magnons and amplitude modes is formulated by dynamical susceptibility under the antiferromagnetic and ferromagnetic states. One of the amplitude modes is identified as “axionic” quasi-particle and its effective coupling to the electromagnetic fields turns out to be enhanced by about four orders of magnitude larger than the previous estimate, which may drastically change the sensitivity of the axion search using “axion” in magnetic TIs.

Quantized Integrated Shift Effect in Multigap Topological Phases.

We show that certain three-dimensional multigap topological insulators can host quantized integrated shift photoconductivities due to bulk invariants that are defined under reality conditions imposed by additional symmetries. We recast the quantization in terms of the integrated torsion tensor and the non-Abelian Berry connection constituting Chern-Simons forms. Physically, we recognize that the topological quantization emerges purely from virtual transitions contributing to the optical response. Our findings provide another quantized electromagnetic dc response due to the nontrivial band topology, beyond the quantum anomalous Hall effect of Chern insulators and quantized circular photogalvanic effect found in Weyl semimetals.

Quantum transport of topological surface states in presence of circular n-p junctions

The surface states of topological insulators are characterized by spin-momentum locking, where the electron spin is locked perpendicular to its momentum. This property is preserved under gate potentials which can be used to manipulate spin currents without an external magnetic field enhancing the prospects for spintronic applications. Here, we investigate the scattering of the wave functions of topological surface states within the circular n-p junction positioned on the upper surface of the quintuple-layered three-dimensional topological insulator. With the analytical calculations we explain the scattering of these surface states in such systems.

Electrochemical Platform Based on the Bi2Te3 Family of Topological Insulators for the Detection of SARS-CoV-2 Pathogenic Factors.

Accurate and rapid detection of the causative agent of a disease is of great importance in controlling the spread of the disease. This work developed a biosensor with the Bi2Te3 family of topological insulators for detection of the SARS-CoV-2 virulence factor. The Bi2Te3 family is a three-dimensional topological insulator material with topologically protected surface states; the presence of these surface states facilitates charge transfer between the electrode and electrolyte interface. Compared with the detection performance of Bi2Se3, BiSbTeSe2, and a trivial insulator like Sb2Se3, Bi2Te3 exhibits superior characteristics. A Bi2Te3 electrochemical detection platform is utilized to fabricate a sensor that can detect SARS-CoV-2 DNA, RNA, and antigen for label-free target detection. The concentration range of DNA detection by the biosensor using Bi2Te3 is between 1.0 × 10-15 and 1.0 × 10-10 M, and the detection limit can reach 1.41 × 10-16 M. Furthermore, it exhibits excellent selectivity and maintains good stability even after being stored for 14 days. This study provides a new way to apply topological insulator materials in the field of biosensors and use their unique electronic structure to improve the accuracy and speed of disease detection and diagnosis.

Bosonization of 2+1 dimensional fermions on the surface of topological insulators

Three-dimensional topological insulators can be described by an effective field theory involving two ‘hydrodynamic’ Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form ℤ2 symmetry of the bosonic theory and its gauging, which originates the fermion number (−1)F, the spin sectors and the time reversal symmetry obeying T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document}2 = (−1)F. These results are detailed for the effective action and the partition function on the geometry S2 × S1.

Three-dimensional topological crystalline insulator without spin–orbit coupling in nonsymmorphic photonic metacrystal

Abstract By including certain point group symmetry in the classification of band topology, Fu proposed a class of three-dimensional topological crystalline insulators (TCIs) without spin–orbit coupling in 2011. In Fu’s model, surface states (if present) doubly degenerate at Γ ¯ and M ¯ when time-reversal and C 4 symmetries are preserved. The analogs of Fu’s model with surface states quadratically degenerate at M ¯ are widely studied, while surface states with quadratic degeneracy at Γ ¯ are rarely reported. In this study, we propose a three-dimensional TCI without spin–orbit coupling in a judiciously designed nonsymmorphic photonic metacrystal. The surface states of photonic TCIs exhibit quadratic band degeneracy in the (001) surface Brillouin zone (BZ) center ( Γ ¯ point). The gapless surface states and their quadratic dispersion are protected by C 4 and time-reversal symmetries, which correspond to the nontrivial band topology characterized by Z 2 topological invariant. Moreover, the surface states along lines from Γ ¯ to the (001) surface BZ boundary exhibit zigzag feature, which is interpreted from symmetry perspective by building composite operators constructed by the product of glide symmetries with time-reversal symmetry. The metacrystal array surrounded with air possesses high order hinge states with electric fields highly localized at the hinge that may apply to optical sensors. The gapless surface states and hinge states reside in a clean frequency bandgap. The topological surface states emerge at the boundary of the metacrystal and perfect electric conductor (PEC), which provide a pathway for topologically manipulating light propagation in photonic devices.

Influence of disorder on antidot vortex Majorana states in three-dimensional topological insulators

Influence of disorder on antidot vortex Majorana states in three-dimensional topological insulators

Atomic-Scale Characterization of Dilute Dopants in Topological Insulators via STEM-EDS Using Registration and Cell Averaging Techniques.

Magnetic dopants in three-dimensional topological insulators (TIs) offer a promising avenue for realizing the quantum anomalous Hall effect (QAHE) without the necessity for an external magnetic field. Understanding the relationship between site occupancy of magnetic dopant elements and their effect on macroscopic property is crucial for controlling the QAHE. By combining atomic-scale energy-dispersive X-ray spectroscopy (EDS) maps obtained by aberration-corrected scanning transmission electron microscopy (AC-STEM) and novel data processing methodologies, including semi-automatic lattice averaging and frame registration, we have determined the substitutional sites of Mn atoms within the 1.2% Mn-doped Sb2Te3 crystal. More importantly, the methodology developed in this study extends beyond Mn-doped Sb2Te3 to other quantum materials, traditional semiconductors, and even electron irradiation sensitive materials.

Low-energy modeling of three-dimensional topological insulator nanostructures

Low-energy modeling of three-dimensional topological insulator nanostructures

Nonlinear Hall Coefficient in Films of a Three-Dimensional Topological Insulator

The magnetoresistance and the Hall effect in transistor structures fabricated on films of the three-dimensional topological insulator (Bi,Sb)2(Te,Se)3 are studied. It is shown that the negative magnetoresistance at low magnetic field is described in terms of quantum corrections to the conductivity. The magnitude of these corrections depends on the gate voltage and increases when approaching the charge neutrality point. The Hall coefficient RH is nonlinear at low magnetic fields for any gate voltage, and the RH nonlinearity is the most pronounced at high negative gate voltages. At high fields, the slope of the magnetic field dependence of the Hall coefficient changes its sign at some gate voltage.

Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect

A delicate tension complicates the relationship between the topological magnetoelectric effect (TME) in three-dimensional (3D) Z2 topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular Z2 topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear-response theory but, according to standard symmetry arguments, simultaneously forbids a nonzero magnetoelectric coefficient in any physical finite-size system. This contrast between theories of magnetoelectric response in formal bulk models and in real finite-sized materials originates from the distinct approaches required to introduce notions of (electronic) polarization and orbital magnetization in these fundamentally different environments. In this work we argue for a modified interpretation of the bulk linear-response calculations in nonmagnetic Z2 TIs that is more plainly consistent with TRS and use this interpretation to discuss the effect's observation—still absent over a decade after its prediction. Our analysis is reinforced by microscopic bulk and thin-film calculations carried out using a simplified but still realistic effective model for the well established V2VI3 [V=(Sb,Bi) and VI=(Se,Te)] family of nonmagnetic Z2 TIs. When a uniform dc magnetic field is included in this model, the anomalous n=0 Landau levels (LLs) play the central role, both in thin films and in bulk. In the former case, only the n=0 LL eigenfunctions can support a dipole moment, which vanishes if there are no magnetic surface dopants and is quantized in the thick-film limit if magnetic dopants at the top and bottom surfaces have opposite orientation. In the latter case, the Hamiltonian projected into the n=0 LL subspace is a one-dimensional Su-Schrieffer-Heeger model with ground-state polarization that is quantized in accordance with the bulk linear-response coefficient calculated for (a lattice regularization of) the starting 3D model. Motivated by analytical results, we conjecture a type of microscopic bulk-boundary correspondence: a bulk insulator with (generalized) TRS supports a magnetoelectric coefficient that is purely itinerant (which is generically related to the geometry of the ground state) if and only if magnetic surface dopants are required for the TME to manifest in finite samples thereof. We conclude that in nonmagnetic Z2 TIs the TME is activated by magnetic surface dopants, that the charge-density response to a uniform dc magnetic field is localized at the surface and specified by the configuration of those dopants, and that the TME is qualitatively less robust against disorder than the integer quantum Hall effect. Published by the American Physical Society 2024

Crystalline finite-size topology

Topological phases stabilized by crystalline point group symmetry protection are a large class of symmetry-protected topological phases subjected to considerable experimental scrutiny. Here, we show that the canonical three-dimensional (3D) crystalline topological insulator protected by time-reversal symmetry T and fourfold rotation symmetry C4 individually or the product symmetry C4T, generically realizes finite-size crystalline topological phases in thin film geometry [a quasi-(3−1)-dimensional, or q(3−1)D, geometry]: response signatures of the 3D bulk topology coexist with topologically protected, quasi-(3−2)D, and quasi-(3−3)D boundary modes within the energy gap resulting from strong hybridization of the Dirac cone surface states of the underlying 3D crystalline topological phase. Importantly, we find qualitative distinctions between these gapless boundary modes and those of strictly 2D crystalline topological states with the same symmetry protection and develop a low-energy, analytical theory of the finite-size topological magnetoelectric response. Published by the American Physical Society 2024

Stacking model of a three-dimensional second-order topological insulator manifesting quantum anomalous Hall effect

We investigate the transport and energy spectrum properties of a three-dimensional high-order topological structure formed by stacking two-dimensional square diatomic Chern insulator lattices. Electron-hole symmetry and the energy spectrum degeneracy at individual points in the semimetallic phase are proven to be due to chiral and antiunitary symmetries in the periodic system. Additionally, we explore the influence of boundary conditions in a slab system with varying surface atom connectivity, and we demonstrate analytically the presence of zero-energy surface states in specific configurations. Moreover, we describe the emergence of two chiral hinge states driven by a perpendicular phase in the nanowire geometry. Next, the quantum Hall resistance is computed in the cross-configuration of a four-lead device. In this paper, we demonstrate that the trajectories of hinge states, determined by the number of layers in parallelepiped finite structure, give rise to fractional Hall plateaus. Published by the American Physical Society 2024

Exploring the effects of a one-dimensional periodic potential on a three-dimensional topological insulator

High mobility two-dimensional systems with superposed 1D lateral periodic potentials exhibit characteristic commensurability (Weiss) oscillations that reflect the interplay of the cyclotron radius at the Fermi level and the superlattice period. Here, we impose a one-dimensional periodic potential on strained HgTe, which is a strong 3D topological insulator. By tuning the Fermi level with top gates, the effects of the artificial potential can be studied in the bulk gap, where only Dirac surface states exist, in the conduction band, and in the valence band, where Dirac electrons and holes coexist. On the electron side, we observe clear commensurability oscillations whose period is governed by the carrier density of the top-surface Dirac electrons. Unexpectedly, weak commensurability oscillations are also observed in the valence band with a period that depends on both electron and hole density. Published by the American Physical Society 2024

Low-temperature magnetoresistance hysteresis in vanadium-doped Bi2−xTe2.4Se0.6 bulk topological insulators

Bi2−xTe2.4Se0.6 single crystals show gapless topological surface states, and doping (x) with vanadium allows to shift the chemical potential in the bulk bandgap. Accordingly, the resistivity, carrier density, and mobility are constant below 10 K, and the magnetoresistance shows weak antilocalization as expected for low-temperature transport properties dominated by gapless surface states of so-called three-dimensional topological insulators. However, the magnetoresistance also shows a hysteresis depending on the sweep rate and the magnetic field direction. Here, we provide evidence that such magnetoresistance hysteresis is enhanced if both three-dimensional bulk states and quasi-two-dimensional topological states contribute to the transport (x = 0 and 0.03), and it is mostly suppressed if the topological states govern transport (x = 0.015). It is proposed that the hysteresis in the magnetoresistance results from different spin-dependent scattering rates of the topological surface and bulk states. Generally, this observation is of relevance to the studies of topologically insulating materials in which both topological surface and bulk states exist.

Three-dimensional PT -symmetric topological phases with a Pontryagin index

We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless PT symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases host multigap topology, providing a realization of a single Z invariant in three spatial dimensions that is distinct from the Hopf index. We identify this invariant with the Pontryagin index, which describes Belavin-Polyakov-Schwartz-Tyupkin (BPST) instantons in particle physics contexts and corresponds to a three-sphere winding number. We study naturally arising multigap linked nodal rings, topologically characterized by split-biquaternion charges, which can be removed by non-Abelian braiding of nodal rings, even without closing a gap. We additionally recast the describing winding number in terms of gauge-invariant combinations of non-Abelian Berry connection elements, indicating relations to Pontryagin characteristic class in four dimensions. These topological configurations are furthermore related to fully nondegenerate multigap phases that are characterized by a pair of winding numbers relating to two isoclinic rotations in the case of four bands and can be generalized to an arbitrary number of bands. From a physical perspective, we also analyze the edge states corresponding to this Pontryagin index as well as their dissolution subject to the gap-closing disorder. Finally, we elaborate on the realization of these novel non-Abelian phases, their edge states, and linked nodal structures in acoustic metamaterials and trapped-ion experiments. Published by the American Physical Society 2024

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

Elastic three-dimensional phononic topological insulators with Dirac hierarchy

Elastic three-dimensional phononic topological insulators with Dirac hierarchy

Quasiparticle scattering in three-dimensional topological insulators near the thickness limit

Quasiparticle scattering in three-dimensional topological insulators near the thickness limit

PT -symmetric non-Hermitian Hopf metal

The Hopf insulator is a representative class of three-dimensional topological insulators beyond the standard topological classification methods based on K theory. In this Letter, we describe the metallic counterpart of the Hopf insulator in non-Hermitian systems. While the Hopf invariant is not a stable topological index due to the additional non-Hermitian degree of freedom, we show that the PT symmetry stabilizes the Hopf invariant even in the presence of the non-Hermiticity. In sharp contrast to the Hopf insulator phase in the Hermitian counterpart, we describe an interesting result that the non-Hermitian Hopf bundle exhibits topologically protected non-Hermitian degeneracy, characterized by the two-dimensional surface of exceptional points. Despite the non-Hermiticity, the Hopf metal has the quantized Zak phase, which results in bulk-boundary correspondence by showing drumheadlike surface states at the boundary. Finally, we show that, by breaking PT symmetry, the nodal surface deforms into knotted exceptional lines. Our description of the Hopf metal phase confirms the existence of the non-Hermitian topological phase outside the framework of the standard topological classifications. Published by the American Physical Society 2024