Transport in two-dimensional topological materials: recent developments in experiment and theory

Abstract

We review theoretical and experimental highlights in transport in two-dimensional materials focussing on key developments over the last five years. Topological insulators are finding applications in magnetic devices, while Hall transport in doped samples and the general issue of topological protection remain controversial. In transition metal dichalcogenides valley-dependent electrical and optical phenomena continue to stimulate state-of-the-art experiments. In Weyl semimetals the properties of Fermi arcs are being actively investigated. A new field, expected to grow in the near future, focuses on the non-linear electrical and optical responses of topological materials, where fundamental questions are once more being asked about the intertwining roles of the Berry curvature and disorder scattering. In topological superconductors the quest for chiral superconductivity, Majorana fermions and topological quantum computing is continuing apace. :1907.10058v1 [cond-mat.mes-hall] arXiv

Longitudinal and anomalous Hall conductivity of a general two-band model

“…In the last decades, theoretical progress was made in identifying basic mechanisms, improving theoretical methods and revealing its deep relation to topology [12,13]. In recent years, there is an increasing interest in transport properties of systems with topological properties in material science [14][15][16], including Heusler compounds [17][18][19], Weyl semimetals [20][21][22], and graphene [23,24], and in other fields like in microcavities [25] and cold atoms [26].…”

“…The combination of both approaches, which is a systematic microscopic derivation combined with a Boltzmann-like physical interpretation, in order to find further relevant contributions is still subject of recent research [30]. The established connection between the intrinsic anomalous Hall conductivity and the Berry curvature [31][32][33][34][35] combined with ab initio band structure calculations [36,37] has become a powerful tool for combining theoretical and experimental results and is state-of-the-art in recent studies [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model

“…Even more interestingly, it has recently been shown in nanowires with Rashba spin-orbit coupling that intrinsic staggered hopping and spin-orbit coupling can induce a topological superconducting phase that completely repels the topological phase of the uniform nanowire [56]. Since these nanowires represent one of the most investigated platforms for one-dimensional topological superconductivity [57][58][59], the reported staggered-induced topological phase is within experimental reach and its fundamental understanding is, therefore, important. Generally, this can be achieved by a proper investigation of the emergent superconducting pair correlations, which has not been carried out so far; odd-ω correlations are expected to play an important role due to the topological nature of this exotic staggered phase, as has been shown for other topological systems [3,5,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”

“…MZMs appear exponentially localized at the ends and their pair amplitudes have been shown to exhibit odd-ω symmetry [3,5,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. MZMs have attracted an enormous amount of attention due to their potential use for building topological protected qubits [57][58][59]65]. Interestingly, the SC SSH model captures the main intrinsic staggered properties of systems that are under active investigation [57][58][59]65], such as in buckled quantum spin Hall insulators [55] and in nanowires with Rashba spin-orbit coupling [56].…”

“…MZMs have attracted an enormous amount of attention due to their potential use for building topological protected qubits [57][58][59]65]. Interestingly, the SC SSH model captures the main intrinsic staggered properties of systems that are under active investigation [57][58][59]65], such as in buckled quantum spin Hall insulators [55] and in nanowires with Rashba spin-orbit coupling [56]. Therefore, the study of pair correlations in the SC SSH model is expected to provide fundamental understanding of superconducting correlations in these systems.…”