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

Abstract

At the interface between two-dimensional materials with different topologies, topologically protected one-dimensional states (also named as zero-line modes) arise. Here, we focus on the quantum anomalous Hall effect based zero-line modes formed at the interface between regimes with different Chern numbers. We find that, these zero-line modes are chiral and unilaterally conductive due to the breaking of time-reversal invariance. For a beam splitter consisting of two intersecting zero lines, the chirality ensures that current can only be injected from two of the four terminals. Our numerical results further show that, in the absence of contact resistance, the (anti-)clockwise partitions of currents from these two terminals are the same owing to the current conservation, which effectively simplifies the partition laws. We find that the partition is robust against relative shift of Fermi energy, but can be effectively adjusted by tuning the relative magnetization strengths at different regimes or relative angles between zero lines. PACS numbers:Introduction-. The presence of edge states that are topologically protected from backscattering is one of the striking hall-marks of topologically nontrivial insulators [1][2][3][4][5]. According to the rigorous bulk-edge correspondence rule [6,7], edge states appear at the boundary of two-dimensional topological systems, like quantum Hall effect [8], quantum anomalous Hall effect [9,10], and quantum spin-Hall effect (or two-dimensional topological insulators) [11,12]. These edge states are localized at the boundaries that are interfaces between topological materials and topologically trivial vacuum. 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]. 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].

Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

“…2 b, an intersection between two surface steps can easily evolve via a pinch-off event into a configuration in which an isthmus of constant surface height separates the steps; indeed, the width of such an isthmus will tend to grow due to the line tensions of the steps, and the quantum junction will be removed. A similar mechanism affects the intersection of two domain walls 31 . In fact, setups like those depicted in the inset of Fig.…”

Transport induced dimer state from topological corner states

“…Two-dimensional insulators with nontrivial band topology have been widely studied in the past decades [1][2][3][4], which include quantum anomalous Hall effect [5][6][7][8][9][10], quantum spin Hall effect [11][12][13][14], quantum valley Hall effect [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], and topological crystalline insulators [32][33][34]. These topological phases are characterized by nontrivial band topological in-dices as well as gapless edge states, which are robust against disorders and exhibit quantized conductivity [5-9, 13, 35-40].…”

Transport features of topological corner states in honeycomb lattice with multihollow structure

“…Honeycomb lattice materials, such as graphene and MoS 2 , are ideal platforms for exploring topological phases 2,[23][24][25][26][27][28] . The famous Kane-Mele model of quantum spin Hall effect is first theoretically proposed on grapehe 29 , which is later demonstrated to have an extremely small band gap 30 .…”