Two-dimensional Topological Insulator Research Articles

Topological nano-switches in higher-order topological insulators

Abstract We consider multi-terminal transport through a flake of rectangular shape of a two-dimensional topological insulator in the presence of an in-plane magnetic field. This system has been shown to be a second-order topological insulator, thus exhibiting corner states at its boundaries. The position of the corner states and their decay length can be controlled by the direction of the magnetic field. In the leads we assume that the magnetic field is absent and therefore we have helical one-dimensional propagating states characteristic of the spin-Hall effect. Using a low-energy effective Hamiltonian we show analytically that, in a two-terminal setup, transport can be turned on and off by a rotation of the in-plane magnetic field. Similarly, in a three terminal configuration, the in-plane magnetic field can be used to turn on and off the transmission between neighbouring contacts, thus realising a directional switch. Analytical calculations are supplemented by a numerical finite-difference method. For small values of the Fermi energy and field strength, the analytical results agree exceptionally well with the numerics. The effect of disorder is also addressed in the numerical approach. We find that the switching functionality is remarkably robust to the presence of strong disorder stemming from the topological nature of the states contributing to the electron transport.

Moiré-modulated band gap and van Hove singularities in twisted bilayer germanene

Twisting bilayers of two-dimensional topological insulators has the potential to create unique quantum states of matter. Here, we successfully synthesized a twisted bilayer of germanene on Ge2Pt(101) with a 21.8° twist angle, corresponding to a commensurate (√7×√7) structure. Using scanning tunneling microscopy and spectroscopy, we unraveled the structural and electronic properties of this configuration, revealing a moiré-modulated band gap and a well-defined edge state. This band gap opens at AB/BA stacked sites and closes at AA stacked sites, a phenomenon attributed to the electric field induced by the scanning tunneling microscopy tip. Our study further revealed two van Hove singularities at −0.8 eV and +1.04 eV, resulting in a Fermi velocity of (8 ± 1) × 105 m s−1. Our tight-binding results uncover a unique quantum state, where the topological properties could be regulated through an electric field, potentially triggering two topological phase transitions.

Two-dimensional Weyl metal and second-order topological insulator phases in the modified Kane-Mele model

Two-dimensional Weyl metal and second-order topological insulator phases in the modified Kane-Mele model

Atomic-scale magnetic doping of monolayer stanene by revealing Kondo effect from self-assembled Fe spin entities

Atomic-scale spin entity in a two-dimensional topological insulator lays the foundation to manufacture magnetic topological materials with single atomic thickness. Here, we have successfully fabricated Fe monomer, dimer and trimer doped in the monolayer stanene/Cu(111) through a low-temperature growth and systematically investigated Kondo effect by combining scanning tunneling microscopy/spectroscopy (STM/STS) with density functional theory (DFT) and numerical renormalization group (NRG) method. Given high spatial and energy resolution, tunneling conductance (dI/dU) spectra have resolved zero-bias Kondo resonance and resultant magnetic-field-dependent Zeeman splitting, yielding an effective spin Seff = 3/2 with an easy-plane magnetic anisotropy on the self-assembled Fe atomic dopants. Reduced Kondo temperature along with attenuated Kondo intensity from Fe monomer to trimer have been further identified as a manifestation of Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between Sn-separated Fe atoms. Such magnetic Fe atom assembly in turn constitutes important cornerstones for tailoring topological band structures and developing magnetic phase transition in the single-atom-layer stanene.

Magnetically tunable supercurrent in dilute magnetic topological insulator-based Josephson junctions

AbstractA superconductor, when exposed to a spin-exchange field, can exhibit spatial modulation of its order parameter, commonly referred to as the Fulde–Ferrell–Larkin–Ovchinnikov state. Such a state can be induced by controlling the spin-splitting field in Josephson junction devices, allowing access to a wide range of the phase diagram. Here we demonstrate that a Fulde–Ferrell–Larkin–Ovchinnikov state can be induced in Josephson junctions based on the two-dimensional dilute magnetic topological insulator (Hg,Mn)Te. We do this by observing the dependence of the critical current on the magnetic field and temperature. The substitution of Mn dopants induces an enhanced Zeeman effect, which can be controlled with high precision by using a small external magnetic field. We observe multiple re-entrant behaviours of the critical current as a response to an in-plane magnetic field, which we assign to transitions between ground states with a phase shifted by π. This will enable the study of the Fulde–Ferrell–Larkin–Ovchinnikov state in much more accessible experimental conditions.

Shot Noise in Helical Edge States in Presence of a Static Magnetic Defect

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Efficient Josephson diode effect on a two-dimensional topological insulator with asymmetric magnetization

Efficient Josephson diode effect on a two-dimensional topological insulator with asymmetric magnetization

In-Plane Anisotropy in the Layered Topological Insulator Ta2Ni3Te5 Investigated via TEM and Polarized Raman Spectroscopy.

Layered Ta2M3Te5 (M = Pd, Ni) has emerged as a platform to study 2D topological insulators, which have exotic properties such as spin-momentum locking and the presence of Dirac fermions for use in conventional and quantum-based electronics. In particular, Ta2Ni3Te5 has been shown to have superconductivity under pressure and is predicted to have second-order topology. Despite being an interesting material with fascinating physics, the detailed crystalline and phononic properties of this material are still unknown. In this study, we use transmission electron microscopy (TEM) and polarized Raman spectroscopy (PRS) to reveal the anisotropic properties of exfoliated few-layer Ta2Ni3Te5. An electron diffraction and TEM study reveals structural anisotropy in the material, with a preferential crystal orientation along the [010] direction. Through Raman spectroscopy, we discovered 15 vibrational modes, 3 of which are ultralow-frequency modes, which show anisotropic response with sample orientation varying with the polarization of the incident beam. Using angle-resolved PRS, we assigned the vibrational symmetries of 11 modes to Ag and two modes to B3g. We also found that linear dichroism plays a role in understanding the Raman signature of this material, which requires the use of complex elements in the Raman tensors. The anisotropy of the Raman scattering also depends on the excitation energies. Our observations reveal the anisotropic nature of Ta2Ni3Te5, establish a quick and nondestructive Raman fingerprint for determining sample orientation, and represent a significant advance in the fundamental understanding of the two-dimensional topological insulator (2DTI) Ta2Ni3Te5 material.

Phase transitions, conductance fluctuations and distributions in disordered topological insulator stanene

It is essential to understand to what extent the protected edge states of topological insulators (TIs) can survive against the degradation of the ubiquitous disorders in realistic devices. From a different perspective, disorders can also help to enrich the applications by modulation of the phases in TIs. In this work, the phases and phase transitions in stanene, a two-dimensional TI, have been investigated via the statistical approach based on the random matrix theory. Using a tight binding model with Aderson disorder term and the Landauer–Büttiker formalism, we calculated the conductance of realistic stanene ribbons of tens of nanometers long with random disorders. The calculated phase diagram presents TI in the gap, metal in high energy and ordinary insulator in large disorder region. Increasing the width of the ribbon can significantly enhance the robustness of TI phase against disorders. Due to different underlying symmetries, the metallic phase can be further categorized into unitary and orthogonal classes according to the calculated universal conductance fluctuations. The local density of states is calculated, showing characteristic patterns, which can facilitate the experimental identification of the phases. It is found that different phases have distinguishing statistical distribution of conductance. Whereas at the phase boundary the distribution exhibits intermediate features to show where the phase transition occurs. To reveal the phase evolution process, we further studied the effects of the disorders on respective transmission channels. It is found that when phase transition takes place, the major transmission channels of the old phase are fading and the new channels of the new phase are emerging.

Discovering two-dimensional magnetic topological insulators by machine learning

Discovering two-dimensional magnetic topological insulators by machine learning

From edge-state physics to entanglement spectrum: Interactions and impurities in two-dimensional topological insulators

From edge-state physics to entanglement spectrum: Interactions and impurities in two-dimensional topological insulators

Controlling the spin current around the rectangular cavities in two-dimensional topological insulators.

Controlling spin current in topological insulators (TIs) is a crucial requirement for applications in quantum computing and spintronics. Using the non-equilibrium Keldysh Green's function formalism, we demonstrate that such control can be established around rectangular cavities of two-dimensional TIs by breaking their time reversal symmetry via exchange magnetic fields and magnetic defects. In the presence of magnetic defects with xy symmetry or Ising symmetry, the density of states is localized, and the spin current forms a current loop around the rectangular cavity in TIs interfacing with two ferromagnetic stripes. We also observe that the spin direction of the traveling electrons is inverted under the reversal of bias and gate voltages. The change in the spin-polarized current around the cavities is predicted by varying the strength of Rashba spin-orbit coupling. This result allows for the creation and control of nearly fully spin-polarized currents with various spatial patterns around the cavities in TIs, and the design of tunable spin diodes for highly integrated spintronics.

Two-dimensional quadratic Weyl points, nodal loops, and spin-orbit Dirac points in PtS, PtSe, and PtTe monolayers.

Topological quasiparticles have garnered significant research attention in condensed matter physics. However, they are exceedingly rare in two-dimensional systems, particularly those hosting unconventional topological quasiparticles. In this work, employing first-principles calculations and symmetry analysis, we demonstrate that PtS, PtSe, and PtTe monolayers serve as high-quality two-dimensional topological semimetal materials. These materials exhibit multiple types of topological quasiparticles around the Fermi level in the absence of spin-orbit coupling, such as conventional linear Weyl points and unconventional quadratic Weyl points in the PtS monolayer, as well as nodal loops in PtSe and PtTe monolayers. When spin-orbit coupling (SOC) is introduced, a tiny gap opens, transforming the systems into quantum spin hall insulators. Simultaneously, three spin-orbit Dirac points, robust against SOC, appear at the X, Y, and M points. We illustrate the symmetry protection, low-energy effective model, and edge states of these topological states. Our work provides an excellent material platform for studying novel two-dimensional topological quasiparticles and topological insulators.

Finite-size effect on quantum percolation in topological insulators

We study the finite-size effect on quantum percolation in two-dimensional topological insulators. We demonstrate that the percolation threshold in topological insulators strongly depends on the localization length of the edge states in small clusters due to the finite-size effect. Also, we explain why the percolation threshold in the corresponding classical model determines the lower bound of the quantum percolation threshold in topological insulators. In addition, we extend the percolation model to a more general scenario, where the system is composed of both topological and trivial clusters. We find that the quantum percolation threshold can be less than the classical percolation threshold due to quantum tunneling of the edge states.

Non-Hermitian higher-order topological corner states on the extended kagome lattice

Exploring the interaction between topological phases and non-Hermitian potentials such as gain and loss can benefit designing robust optical devices. Recent studies have revealed topological phases can be simply from gain and loss in non-Hermitian systems. Here, we propose an extended kagome lattice model, where the non-Hermitian potentials drive the system from a trivial phase to a higher-order topological phase. Higher-order topological insulators exhibit lower-dimensional boundary states on corners or hinges. We construct two-dimensional higher-order topological insulators on different arrays of the extended kagome lattice model. Topologically protected states emerge at the corner with a 1/3 fractional charge at each corner as the strength of the gain and loss increases. The topologically protected corner states are characterized by the quantized polarization as the topological index. We find that non-Hermitian potentials provide an extra degree of freedom to switch on and off the higher-order topological corner states. The proposed system can be verified through many experimental platforms, including coupled optical resonating cavities and waveguides. Our work indicates the great prospects for constructing integrated photonics platforms and designing actively reconfigurable photonic devices.

Edge mode percolation and equilibration in the topological insulator cadmium arsenide

Two-dimensional topological insulators can feature one-dimensional charge transport via edge modes, which offer a rich ground for studying exotic quasi-particles and for quantum materials applications. In this work, we use lateral junction devices, defined by nanoscale finger gates, to study edge mode transport in the two-dimensional topological insulator Cd3As2. The finger gate can be tuned to transmit an integer number of quantum Hall edge modes and exhibits full equilibration in the bipolar regime. When the Fermi level of the channel crosses a Landau level, reflected modes percolate through the channel, resulting in an anomalous conductance peak. The device does not fully pinch off when the channel is tuned into the topological gap, which is a sign of remnant modes in the channel. These modes are expected from band inversion, while residual bulk conduction associated with the disorder potential may also play a role.

Two-dimensional topological insulators: past, present and future

Two-dimensional (2D) topological insulators (TIs) are special quantum conductors that possess an insulating bulk but metallic edge with quantized charge and spin conductance protected by electron band topology. The concept of topology and TI has not only renewed our fundamental understanding of electronic properties of solid materials, but also opened an exciting avenue towards potential applications of topological quantum devices with minimized heat dissipation and robustness against disorder. In this video article, I will first introduce and review the concept of topological insulators within the context of transport properties of solid-state materials. I will then use two examples, the organic 2D TIs and the surface-based 2D topological states, to recap the rapid theoretical and experimental developments made in this emerging field. The existence of quantized edge conductance and topological edge states of 2D TIs has been so far confirmed experimentally in several systems, such as semiconductor quantum wells, 2D transition metal dichalcogenides, metallic overlayer of bismuth on a semiconductor surface. However, discovery of high-temperature 2D TIs and construction of functional TI-based quantum devices remain largely elusive. At the end of this video article, I will offer briefly my personal perspective and possible future directions in low-dimensional topological materials.

Octastanene Halogenide: A Family of Two-dimensional Nodal Line Semimetals and Topological Insulators

With the first principle calculation and k-p model, we find that the Octastanene halogenide is a node line semimetal(NLs) without spin-orbit coupling(soc), forming a fermi ring centered on point G and protected by mirror symmetry. The band simulated by the k-p model fits well with the band calculated by GGA-PBE at point G, and the energy dispersion calculated by the Hamiltonian of the model explains well the formation of node rings. Under the SOC effect, NLs become a two dimensional Topological Insulators(TIs). With the increase of atomic number, the large band gap reaches about 0.16 ev, and the clear spiral edge state of the quantum spin hall effect is obtained. The phonon spectra of the two structures show that they are dynamically stable. These findings provide a new two dimensional material series for the future design and manufacture of NLs and TIs.

Topological band gap in intercalated epitaxial graphene

The study of functional manipulation of graphene is a critical subject, both for fundamental research and practical applications. In this study, we present that the intercalation of 5d transition metals into epitaxial graphene on SiC is a promising strategy for the realization of topologically nontrivial phases with a finite band gap in graphene. Employing first-principles calculations, grounded in density functional theory, we demonstrate that Re- and Ta-intercalated graphene evolve into two-dimensional topological insulators. These exhibit linear Dirac cones and quadratic bands with topological band gaps, respectively. The emergence of these topological states is attributed to the strong spin–orbit coupling strength of the intercalants. We show that the corresponding topological edge states persist within the finite bulk band gap, aligning with the bulk-boundary correspondence. Furthermore, we explore the spin splitting of the band structure, brought about by the inversion symmetry breaking and the spin–orbit coupling. Our study underscores that the intercalation of graphene is an effective and a feasible approach for manipulating the band gap and the topological nature of graphene. Such intercalated graphene systems hold potential utility for spintronics and low-dimensional quantum device applications.

Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation

Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation