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Register a new userSurvival of the quantum anomalous Hall effect in orbital magnetic fields as a consequence of the parity anomaly
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Recent experimental progress in condensed matter physics enables the observation of signatures of the parity anomaly in two-dimensional Dirac-like materials. Using effective field theories and analyzing band structures in external out-of-plane magnetic fields (orbital fields), we show that topological properties of quantum anomalous Hall (QAH) insulators are related to the parity anomaly. We demonstrate that the QAH phase survives in orbital fields, violates the Onsager relation, and can be therefore distinguished from a quantum Hall (QH) phase. As a fingerprint of the QAH phase in increasing orbital fields, we predict a transition from a quantized Hall plateau with $sigma_mathrm{xy}= -mathrm{e}^2/mathrm{h}$ to a not perfectly quantized plateau, caused by scattering processes between counterpropagating QH and QAH edge states. This transition can be especially important in paramagnetic QAH insulators, such as (Hg,Mn)Te/CdTe quantum wells, in which exchange interaction and orbital fields compete.
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The low-energy physics of two-dimensional Quantum Anomalous Hall insulators like (Hg,Mn)Te quantum wells or magnetically doped (Bi,Sb)Te thin films can be effectively described by two Chern insulators, including a Dirac, as well as a momentum-dependent mass term. Each of those Chern insulators is directly related to the parity anomaly of planar quantum electrodynamics. In this work, we analyze the finite temperature Hall conductivity of a single Chern insulator in 2+1 space-time dimensions under the influence of a chemical potential and an out-of-plane magnetic field. At zero magnetic field, this non-dissipative transport coefficient originates from the parity anomaly of planar quantum electrodynamics. We show that the parity anomaly itself is not renormalized by finite temperature effects. However, it induces two terms of different physical origin in the effective action of a Chern insulator, which is proportional to the Hall conductivity. The first term is temperature and chemical potential independent, and solely encodes the intrinsic topological response. The second term specifies the non-topological thermal response of conduction and valence band states. In particular, we show that the relativistic mass of a Chern insulator counteracts finite temperature effects, whereas its non-relativistic mass enhances these corrections. Moreover, we extend our analysis to finite magnetic fields and relate the thermal response of a Chern insulator therein to the spectral asymmetry, which is a measure of the parity anomaly in orbital fields.
We study the electronic structures and topological properties of $(M+N)$-layer twisted graphene systems. We consider the generic situation that $N$-layer graphene is placed on top of the other $M$-layer graphene, and is twisted with respect to each other by an angle $theta$. In such twisted multilayer graphene (TMG) systems, we find that there exists two low-energy flat bands for each valley emerging from the interface between the $M$ layers and the $N$ layers. These two low-energy bands in the TMG system possess valley Chern numbers that are dependent on both the number of layers and the stacking chiralities. In particular, when the stacking chiralities of the $M$ layers and $N$ layers are opposite, the total Chern number of the two low-energy bands for each valley equals to $pm(M+N-2)$ (per spin). If the stacking chiralities of the $M$ layers and the $N$ layers are the same, then the total Chern number of the two low-energy bands for each valley is $pm(M-N)$ (per spin). The valley Chern numbers of the low-energy bands are associated with large, valley-contrasting orbital magnetizations, suggesting the possible existence of orbital ferromagnetism and anomalous Hall effect once the valley degeneracy is lifted either externally by a weak magnetic field or internally by Coulomb interaction through spontaneous symmetry breaking.
We report on the scaling behavior of V-doped (Bi,Sb)$_2$Te$_3$ samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a two-dimensional integer quantum Hall state, we observe a dimensional crossover to three spatial dimensions as a function of layer thickness. In the limit of a sufficiently thick layer, we find scaling behavior matching the flow diagram of two parallel conducting topological surface states of a three-dimensional topological insulator each featuring a fractional shift of $frac{1}{2} e^2/h$ in the flow diagram Hall conductivity, while we recover the expected integer quantum Hall behavior for thinner layers. This constitutes the observation of a distinct type of quantum anomalous Hall effect, resulting from $frac{1}{2} e^2/h$ Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.
The quantum anomalous Hall (QAH) state is a two-dimensional bulk insulator with a non-zero Chern number in absence of external magnetic fields. Protected gapless chiral edge states enable dissipationless current transport in electronic devices. Doping topological insulators with random magnetic impurities could realize the QAH state, but magnetic order is difficult to establish experimentally in the bulk insulating limit. Here we predict that the single quintuple layer of GdBiTe3 film could be a stoichiometric QAH insulator based on ab-initio calculations, which explicitly demonstrate ferromagnetic order and chiral edge states inside the bulk gap. We further investigate the topological quantum phase transition by tuning the lattice constant and interactions. A simple low-energy effective model is presented to capture the salient physical feature of this topological material.
The recent prediction, and subsequent discovery, of the quantum anomalous Hall (QAH) effect in thin films of the three-dimensional ferromagnetic topological insulator (MTI) (Cr$_y$Bi$_x$Sb$_{1-x-y}$)$_2$Te$_3$ has opened new possibilities for chiral-edge-state-based devices in zero external magnetic field. Like the $ u=1$ quantum Hall system, the QAH system is predicted to have a single chiral edge mode circulating along the boundary of the film. Backscattering of the chiral edge mode should be suppressed, as recently verified by the observation of well-quantized Hall resistivities $rho_{yx} = pm h/e^2$, along with longitudinal resistivities as low as a few ohms. Dissipationless 1D conduction is also expected along magnetic domain walls. Here, we intentionally create a magnetic domain wall in a MTI and study electrical transport along the domain wall. We present the first observation of chiral transport along domain walls, in agreement with theoretical predictions. We present further evidence that two modes equilibrate and co-propagate along the length of the domain wall.
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