Topological Anderson insulator phenomena

We present a microscopic theory to give a physical picture of the formation of quantum anomalous Hall (QAH) effect in magnetized graphene coupled with Rashba spin-orbit coupling. Based on a continuum model at valley K or K ′ , we show that there exist two distinct physical origins of QAH effect at two different limits. For large exchange field M , the quantization of Hall conductance in the absence of Landau-level quantization can be regarded as a summation of the topological charges carried by Skyrmions from real spin textures and Merons from AB sublattice pseudo-spin textures; while for strong Rashba spin-orbit coupling λR, the four-band low-energy model Hamiltonian is reduced to a two-band extended Haldane's model, giving rise to a nonzero Chern number C = 1 at either K or K ′ . In the presence of staggered AB sublattice potential U , a topological phase transition occurs at U = M from a QAH phase to a quantum valley-Hall phase. We further find that the band gap responses at K and K ′ are different when λR, M , and U are simultaneously considered. We also show that the QAH phase is robust against weak intrinsic spin-orbit coupling λSO, and it transitions a trivial phase when λSO > ( M 2 + λ 2 R + M )/2. Moreover, we use a tight-binding model to reproduce the ab-initio method obtained band structures through doping magnetic atoms on 3 × 3 and 4 × 4 supercells of graphene, and explain the physical mechanisms of opening a nontrivial bulk gap to realize the QAH effect in different supercells of graphene.

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“…The different bulk band gap responses at K and K ′ are consistent with the tightbinding result discussed in Ref. [18].…”

Section: Robustness Of Quantum Anomalous Hall Effect a Staggeredsupporting

confidence: 90%

Microscopic theory of quantum anomalous Hall effect in graphene

et al. 2012

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“…25,26 TAI has been investigated in more related models, such as Haldane model, KaneMele model and 3DTI model. [27][28][29][30][31][32] It is indicated that TAI is dependent on the type of disorder, for example, TAI phase is absent for the magnetic disorder and spatially correlated disorder. 33,34 On the other hand, gapped and gapless topological phases and transport characteristics in layered structures and thin films have been studied recently in the presence and absence of disorder.…”

Section: Introductionmentioning

confidence: 99%

Topological Anderson insulator phase in a Dirac-semimetal thin film

Chen

Zhou

2017

Phys. Rev. B

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The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either normal insulator or quantum spin Hall insulator depending on the thin film thickness. We present the study of disorder effects in thin film of Dirac semimetals. It is found that moderate Anderson disorder strength can drive a topological phase transition from normal band insulator to topological Anderson insulator in Dirac semimetal thin film. The numerical calculation based on the model parameters of Dirac semimetal Na3Bi shows that in the topological Anderson insulator phase a quantized conductance plateau occurs in the bulk gap of band insulator, and the distributions of local currents further confirm that the quantized conductance plateau arises from the helical edge states induced by disorder. Finally, an effective medium theory based on Born approximation fits the numerical data.

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“…For numerical calculation, the tight-binding representation of the four-band Hamiltonian on square lattice is used. [24][25][26] To realize the QAH phase, magnetic doping is needed to break the TRS between the two spin blocks. When one spin block is in normal insulting regime, but the other is topological nontrivial, QAH state appears, resulting in nonzero net Hall conductance.…”

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confidence: 99%

Finite-size effects in the quantum anomalous Hall system

Lü

Gao

2014

Phys. Rev. B

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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 ...

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Topological Anderson insulator phenomena

Cited by 87 publications

References 46 publications

Microscopic theory of quantum anomalous Hall effect in graphene

Microscopic theory of quantum anomalous Hall effect in graphene

Topological Anderson insulator phase in a Dirac-semimetal thin film

Finite-size effects in the quantum anomalous Hall system

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