Topological phases in two-dimensional materials: a review

Abstract

Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on the recent progress in the engineering of topologically nontrivial phases (such as Z2 topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc.) in two-dimensional material systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.

Tunable edge states and their robustness towards disorder

“…In the context of topologically protected edge states the term 'chiral' means that the electrons only propagate in one direction along one edge. If no magnetic field is involved this effect is called the anomalous quantum Hall effect [12][13][14] . The Kane-Mele model [15][16][17] represents a crucial extension of the Haldane model including the spin degree of freedom.…”

Strain-induced topological phase transition in phosphorene and in phosphorene nanoribbons

“…The emergence of robust edge states in twodimensional (2D) TIs that are protected by TRS, make them promising candidates for potential applications in spintronics and quantum computing [1][2][3][4][5][6]. TIs can exist intrinsically or be driven by external factors such as electrical field or by functionalization [7]. Strain engineering is a well known strategy for switching from normal insulator (NI) phase to a TI phase [7,8].…”

Tunable current partition at zero-line intersection of quantum anomalous Hall topologies

“…These ZLMs are protected from long-range scattering potential by large momentum separation and exhibit zero bend resistance in the absence of atomic defects [15,17]. Such modes are experimentally feasible [19,20] in Bernal stacked multilayer graphenes with out-of-plane electric field [21][22][23] and have attracted much attention from both theoreticians [1,17,18,[24][25][26][27][28][29][30][31][32][33][34] and experimentalists [19,20,35]. …”

“…Thus, these boundaries can be generalized to interfaces between two topologically distinct materials, like the interface between quantum anomalous Hall effect and quantum valley Hall effect [13], quantum spin-Hall effect and quantum valley Hall effect [14], or the graphene nanoroad between two structurally different boron-nitride sheets [15]. One widely explored system is the zero-line modes (ZLMs) occurred at the interface, across which the valley Chern numbers varies [1,16]. These ZLMs are protected from long-range scattering potential by large momentum separation and exhibit zero bend resistance in the absence of atomic defects [15,17].…”