The discovery of the three-dimensional Dirac semimetals have expanded the family of topological materials, and attracted massive attentions in recent few years. In this short review, we briefly overview the quantum transport properties of a well-studied three-dimensional Dirac semimetal, Cd3As2. These unusual transport phenomena include the unexpected ultra-high charge mobility, large linear magnetoresistivity, remarkable Shubnikov-de Hass oscillations, and the evolution of the nontrivial Berry's phase. These quantum transport properties not only reflect the novel electronic structure of Dirac semimetals, but also give the possibilities for their future device applications.
We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone, and any perturbation that preserves a certain symmetry group (generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands. The nodal line(s) is hence topologically protected by the symmetry group, and can be associated with a topological invariant. In this review, (i) we enumerate the symmetry groups that may protect a topological nodal line; (ii) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface, establishing a topological classification; (iii) for certain classes, we review the proposals for the realization of these semimetals in real materials; (iv) we discuss different scenarios that when the protecting symmetry is broken, how a topological nodal line semimetal becomes Weyl semimetals, Dirac semimetals, and other topological phases; and (v) we discuss the possible physical effects accessible to experimental probes in these materials.
The recent discovery of three-dimensional (3D) topological insulators (TIs) has provided a fertile ground for obtaining further insights into electron localization in condensed matter systems. In the past few years, a tremendous amount of research effort has been devoted to investigate electron transport properties of 3D TIs and their low dimensional structures in a wide range of disorder strength, covering transport regimes from weak antilocalization to strong localization. The knowledge gained from these studies not only offers sensitive means to probe the surface states of 3D TIs but also forms a basis for exploring novel topological phases. In this article, we briefly review the main experimental progress in the study of the localization in 3D TIs, with a focus on the latest results on ultrathin TI films. Some new transport data will also be presented in order to complement those reported previously in the literature.
Weak localization and antilocalization are quantum transport phenomena that arise from the quantum interference in disordered metals. At low temperatures, they can give distinct temperature and magnetic field dependences in conductivity, allowing the symmetry of the system to be explored. In the past few years, they have also been observed in newly emergent topological materials, including topological insulators and topological semimetals. In contrast from the conventional electrons, in these new materials the quasiparticles are described as Dirac or Weyl fermions. In this article, we review our recent efforts on the theories of weak antilocalization and interaction-induced localization for Dirac and Weyl fermions in topological insulators and topological semimetals.
The discovery of Dirac semimetal and Weyl semimetal has motivated a growing passion for investigating the unique magneto-transport properties in the topological materials. A Weyl semimetal can host Weyl fermions as its low-energy quasi-particle excitations, and therefore perform exotic features analogous to those in high-energy physics, such as the violation of the chiral charge conservation known as the chiral anomaly. One of the electrical transport signatures of the chiral anomaly is the Adler-Bell-Jackiw (ABJ) anomaly which presents as a negative magnetoresistance when the magnetic field and the current are parallel. Very recently, numerous experiments reported negative longitudinal magnetoresistance (NLMR) in topological materials, but the details of the measurement results are various. Here the materials and the corresponding experiment results are briefly reviewed. Besides the plausible explanation of the ABJ anomaly, some other origins of the NLMR are also discussed.
Under a strong magnetic field, the quantum Hall (QH) effect can be observed in two-dimensional electronic gas systems. If the quantized Hall conductivity is acquired in a system without the need of an external magnetic field, then it will give rise to a new quantum state, the quantum anomalous Hall (QAH) state. The QAH state is a novel quantum state that is insulating in the bulk but exhibits unique conducting edge states topologically protected from backscattering and holds great potential for applications in low-power-consumption electronics. The realization of the QAH effect in real materials is of great significance. In this paper, we systematically review the theoretical proposals that have been brought forward to realize the QAH effect in various real material systems or structures, including magnetically doped topological insulators, graphene-based systems, silicene-based systems, two-dimensional organometallic frameworks, quantum wells, and functionalized Sb(111) monolayers, etc. Our paper can help our readers to quickly grasp the recent developments in this field.
The recent discovery of topological insulators (TIs) offers new opportunities for the development of thermoelectrics, because many TIs (like Bi2Te3) are excellent thermoelectric (TE) materials. In this review, we will first describe the general TE properties of TIs and show that the coexistence of the bulk and boundary states in TIs introduces unusual TE properties, including strong size effects and an anomalous Seebeck effect. Importantly, the TE figure of merit zT of TIs is no longer an intrinsic property, but depends strongly on the geometric size. The geometric parameters of two-dimensional TIs can be tuned to enhance zT to be significantly greater than 1. Then a few proof-of-principle experiments on three-dimensional TIs will be discussed, which observed unconventional TE phenomena that are closely related to the topological nature of the materials. However, current experiments indicate that the metallic surface states, if their advantage of high mobility is not fully utilized, would be detrimental to TE performance. Finally, we provide an outlook for future work on topological materials, which offers great possibilities to discover exotic TE effects and may lead to significant breakthroughs in improving zT.
Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states. In this paper, we review the defects effect in these topological states and study new types of topological matters–topological hierarchy matters. We find that both topological defects (quantized vortices) and non topological defects (vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects. These topological mid-gap states have nontrivial topological properties, including the nonzero Chern number and the gapless edge states. Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters.
Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review the work completed over the last few years, including our own, regarding recent developments in several topics about disorder effects in topological states. For weak disorder, the robustness of topological states is demonstrated, especially for both quantum spin Hall states with Z2=1 and size induced nontrivial topological insulators with Z2=0. For moderate disorder, by increasing the randomness of both the impurity distribution and the impurity induced potential, the topological insulator states can be created from normal metallic or insulating states. These phenomena and their mechanisms are summarized. For strong disorder, the disorder causes a metal-insulator transition. Due to their topological nature, the phase diagrams are much richer in topological state systems. Finally, the trends in these areas of disorder research are discussed.
Two-dimensional (2D) topological insulators (TIs, or quantum spin Hall insulators) are special insulators that possess bulk 2D electronic energy gap and time-reversal symmetry protected one-dimensional (1D) edge state. Carriers in the edge state have the property of spin-momentum locking, enabling dissipation-free conduction along the 1D edge. The existence of 2D TIs was confirmed by experiments in semiconductor quantum wells. However, the 2D bulk gaps in those quantum wells are extremely small, greatly limiting potential application in future electronics and spintronics. Despite this limitation, 2D TIs with a large bulk gap attracted plenty of interest. In this paper, recent progress in searching for TIs with a large bulk gap is reviewed briefly. We start by introducing some theoretical predictions of these new materials and then discuss some recent important achievements in crystal growth and characterization.
The rise of topological insulators in recent years has broken new ground both in the conceptual cognition of condensed matter physics and the promising revolution of the electronic devices. It also stimulates the explorations of more topological states of matter. Topological crystalline insulator is a new topological phase, which combines the electronic topology and crystal symmetry together. In this article, we review the recent progress in the studies of SnTe-class topological crystalline insulator materials. Starting from the topological identifications in the aspects of the bulk topology, surface states calculations, and experimental observations, we present the electronic properties of topological crystalline insulators under various perturbations, including native defect, chemical doping, strain, and thickness-dependent confinement effects, and then discuss their unique quantum transport properties, such as valley-selective filtering and helicity-resolved functionalities for Dirac fermions. The rich properties and high tunability make SnTe-class materials promising candidates for novel quantum devices.
