Finite-size effects in the quantum anomalous Hall system

Abstract

We theoretically investigate the finite size effect in quantum anomalous Hall (QAH) system. Using Mn-doped HgTe quantum well as an example, we demonstrate that the coupling between the edge states is spin dependent, and is related not only to the distance between the edges but also to the doping concentration. Thus, with proper tuning of the two, we can get four kinds of transport regimes: quantum spin Hall regime, QAH regime, edge conducting regime, and normal insulator regime. These transport regimes have distinguishing edge conducting properties while the bulk is insulting. Our results give a general picture of the finite size effect in QAH system, and are important for the transport experiments in QAH nanomaterials as well as future device applications.PACS numbers: 72.25.Dc, 75.50.Pp Quantum anomalous Hall (QAH) state is a new state of matter of two dimensional (2D) insulator, which has a quantized Hall conductivity without Landau level. 1-4Energy band of the QAH state is topological nontrivial and can be characterized by the first Chern number, similar to the quantum Hall state. 5,6 Different from the normal quantum hall state, the QAH state does not need an external magnetic field to break the time reversal symmetry (TRS). 10 This has led to its recent experimental observation in magnetic TI of Cr-doped (Bi, Sb) 2 Te 3 . 16Numerous exotic properties of the QAH state are yet to be explored, which are not only of fundamental importance but also have potential applications.In this work, we theoretically investigate the QAH system in a finite stripe geometry, where the finite size effect can influence its transport property. The same effect in quantum spin Hall (QSH) system, 17 as well as in the 3D topological insulators, 18,19 has been studied in details in last few years. A key finding is that, when the sample is narrow enough, the coupling of edge states will open an energy gap, and the quantized conductance of the edge states disappears. Thus, there exists a critical width in QSH system, below which the gapless edge states are destroyed. The finite size effect is crucial for the device application, since it determines the transport property of small device . Here, we illustrate that the finite size effect in the QAH system is more complex than that in QSH system. Due to the magnetic doping, the coupling between edge states becomes spin dependent, and is also related to the doping concentration. Given the width of ribbon and the doping concentration, we can distinguish four kinds of transport regimes in a QAH ribbon. While the bulk is insulating in all these transport regimes, they have different edge conducting behaviors. Because that the edge conducting channel is the key feature of topological nontrivial system and is the base of many novel quantum electronic devices, our results may be important for the QAH state in nanomaterials as well as the device application of the QAH system.The system we study is a Mn-doped HgTe quantum well (QW). Without Mn doping, its electronic states can be described by ...

Light-induced phase crossovers in a quantum spin Hall system

“…Since then, there have been intensive studies to investigate the exotic properties in QSH systems [7]. They include topological field theory [8][9][10], finite-size crossovers in topological insulators [11,12], magnetic doping in QSH system (Mndoped HgTe quantum well) [13], disorder induced topological Anderson insulator in QSH systems [14][15][16][17][18][19], Floquet topological insulator states in QSH systems [20][21][22][23], as well as QSH effects in three-dimensional topological insulators [24][25][26][27][28].…”

“…The QAH effect was first experimentally observed in Ref. [30]; in another work on finite-size effects in QAH systems [13], they adopted the magnetic doping (Mn doping) to break the time-reversal symmetry and introduce the QAH phase in the HgTe quantum well. By appropriate tuning of the doping concentration and the system size, they have obtained a variety of topological phases [13].…”

“…Yet, this experimental success [13] in realizing QAH states proved difficult to follow up upon, since the doping concentration is difficult to tune continuously in experiments. Therefore, departing from previous works [13], we shall provide a more experimentally accessible alternative to realizing QAH states, using circularly polarized light instead of magnetic doping to break the time-reversal symmetry in HgTe quantum well.…”

“…Yet, this experimental success [13] in realizing QAH states proved difficult to follow up upon, since the doping concentration is difficult to tune continuously in experiments. Therefore, departing from previous works [13], we shall provide a more experimentally accessible alternative to realizing QAH states, using circularly polarized light instead of magnetic doping to break the time-reversal symmetry in HgTe quantum well. This hinges on the fact that the intensity of circularly polarized light can be easily tuned continuously in experiments, and that Floquet driving can induce a host of exotic phases in various media, such as disorder-induced Floquet topological insulators [36], quenched topological boundary modes induced by Floquet engineering [37], Floquet semimetal with exotic topological linkages [38], Floquet mechanism for non-Abelian fractional quantum Hall states [39], photoinduced half-integer quantized conductance plateaus in topological insulators [40].…”

Pure spin current and perfect valley filter by designed separation of the chiral states in two-dimensional honeycomb lattices

“…When a system hosts two or more spatially separated chiral states, the influence of finite size effect on the chiral states may be significant [17][18][19] . The size effect can induce a undesired gap if the two chiral states with same momentum have overlap in the real space.…”