Study Of Topological Insulators Research Articles

Recent advancements in the study of intrinsic magnetic topological insulators and magnetic Weyl semimetals

The studies of topological insulators (TI) and topological semimetals have been at frontiers of condensed matter physics and material science. Both classes of materials are characterized by robust surface states created by the topology of the bulk band structures and exhibit exotic transport properties. When magnetism is present in topological materials and breaks the time-reversal symmetry, more exotic quantum phenomena can be generated, e.g., quantum anomalous Hall effect (QAHE), axion insulator, and large intrinsic AHE. In this research update, we briefly summarize the recent research progress in magnetic topological materials, including intrinsic magnetic TI and magnetic Weyl semimetals.

AC magnetoresistance and its frequency-dependence of Fe-doped Bi2Se3 topological insulator

Bismuth selenide (Bi2Se3) is one of the most important base materials in the study of topological insulators. Doping with iron is a direct method to manipulate the magnetic order in Bi2Se3. In this paper, we first report the measurements of magnetoresistance of Fe-doped Bi2Se3 with alternating current. Unlike the DC magnetoresistance, skin effect plays an important role in AC magnetoresistance. Another interesting finding is that resonance occurs at a certain frequency, which implies an internal relaxation mechanism. The relations between resistance, magnetic field and current frequency are discussed.

Bulk defects and surface state dynamics in topological insulators: The effects of electron beam irradiation on the ultrafast relaxation of Dirac fermions in Bi2Te3

One of the most important challenges in the study of topological insulators is the realization of materials that are really insulating in the bulk, in order to emphasize quantum transport in the protected surface states. Irradiation with electron beams is a very promising approach toward this goal. By studying a series of samples of the prototype 3D topological insulator Bi2Te3, we show that while the topological properties of Dirac surface states are preserved after electron irradiation, their relaxation dynamics are very sensitive to the related modifications of the bulk properties. Using time- and angle-resolved photoelectron spectroscopy, we can reveal two distinct relaxation regimes after optical excitation for non-irradiated and irradiated samples. While the faster regime, corresponding to the first few picoseconds, presents a similar temporal evolution of the photoexcited population for all studied samples, the slower regime is strongly influenced by the controlled generation of defects in the bulk lattice. By adjusting the irradiation parameters in this class of materials, one can thus not only change the bulk transport properties but also tune the ultrafast response of the topological surface states.

Novel topological insulators from crystalline symmetries

We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions (3D), these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the appearance of these topological states in both crystals with negligible spin–orbit coupling and a fourfold rotational symmetry, as well as in mirror-symmetric crystals with sizable spin–orbit interaction characterized by the so-called mirror Chern number. Finally, we also discuss similar topological crystalline states in one-dimensional (1D) insulators, such as nanowires or atomic chains, with mirror symmetry. There, the prime physical consequence of the non-trivial topology is the presence of quantized end charges.

Gauge potential decomposition and topological current theories with applications in the study of topological insulators

The theories of gauge potential decomposition and topological currents proposed by Prof. YiShi Duan et al. have remarkable significance in the research of topological inner structures of gauge fields, with wide applications in the analysis of topological defects/excitations in various physical systems. In this paper, firstly, a brief survey for these theories is presented. Secondly, the theories are applied in the study of topological insulators in two dimensions. Topological insulators are at the cutting edge of current international research of condensed matter physics, where topological effects stem from the non-trivial topological numbers, such as the Chern numbers. In this paper different types of topological defects are investigated within one single framework, the so-called t Hooft monopole model, which acts as a $U(1)$ sub-field theory of a non-Abelian gauge field.

Topological phases in the Haldane model with spin–spin on-site interactions

Ultracold atom experiments allow the study of topological insulators, such as the non-interacting Haldane model. In this work we study a generalization of the Haldane model with spin–spin on-site interactions that can be implemented on such experiments. We focus on measuring the winding number, a topological invariant, of the ground state, which we compute using a mean-field calculation that effectively captures long-range correlations and a matrix product state computation in a lattice with 64 sites. Our main result is that we show how the topological phases present in the non-interacting model survive until the interactions are comparable to the kinetic energy. We also demonstrate the accuracy of our mean-field approach in efficiently capturing long-range correlations. Based on state-of-the-art ultracold atom experiments, we propose an implementation of our model that can give information about the topological phases.

T-Duality Simplifies Bulk–Boundary Correspondence: Some Higher Dimensional Cases

Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality trivialises the bulk-boundary correspondence in 2 dimensions. In this paper, we partially generalise these results to higher dimensions and briefly discuss the 4D quantum Hall effect.

T-Duality Simplifies Bulk-Boundary Correspondence

Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that T-duality trivializes the bulk-boundary correspondence.

Switching a normal insulator into a topological insulator via electric field with application to phosphorene.

The study of topological insulators has generally involved search of materials that have this property as an innate quality, distinct from normal insulators. Here we focus on the possibility of converting a normal insulator into a topological one by application of an external electric field that shifts different bands by different energies and induces a specific band inversion, which leads to a topological state. Phosphorene is a two-dimensional (2D) material that can be isolated through mechanical exfoliation from layered black phosphorus, but unlike graphene and silicene, single-layer phosphorene has a large band gap (1.5-2.2 eV). Thus, it was unsuspected to exhibit band inversion and the ensuing topological insulator behavior. Using first-principles calculations with applied perpendicular electric field F⊥ on few-layer phosphorene we predict a continuous transition from the normal insulator to a topological insulator and eventually to a metal as a function of F⊥. The tuning of topological behavior with electric field would lead to spin-separated, gapless edge states, that is, quantum spin Hall effect. This finding opens the possibility of converting normal insulating materials into topological ones via electric field and making a multifunctional "field effect topological transistor" that could manipulate simultaneously both spin and charge carrier. We use our results to formulate some design principles for looking for other 2D materials that could have such an electrical-induced topological transition.

Twisted Equivariant Matter

We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a corresponding 10-fold way which has appeared in condensed matter and nuclear physics. We establish a foundation for discussing continuous families of quantum systems. Having done so, topological phases of quantum systems can be defined as deformation classes of continuous families of gapped Hamiltonians. For free particles there is an additional algebraic structure on the deformation classes leading naturally to notions of twisted equivariant K-theory. In systems with a lattice of translational symmetries we show that there is a canonical twisting of the equivariant K-theory of the Brillouin torus. We give precise mathematical definitions of two invariants of the topological phases which have played an important role in the study of topological insulators. Twisted equivariant K-theory provides a finer classification of topological insulators than has been previously available.