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Register a new userTemperature and Chemical Potential Dependence of the Parity Anomaly in Quantum Anomalous Hall Insulators
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Added by
Christian Tutschku MSc
Publication date
2020
fields
Physics
and research's language is
English
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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.
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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.
Quantum transport in magnetic topological insulators reveals the strong interplay between the magnetism and topology of electronic band structures. A recent experiment on magnetically doped topological insulator Bi2Se3 thin films showed the anomalous temperature dependence of the magnetoconductivity while their field dependence presents a clear signature of weak anti-localization [Tkac et al., Phys. Rev. Lett. 123, 036406(2019)]. Here we demonstrate that the tiny mass of the surface electrons induced by the bulk magnetization leads to a temperature-dependent correction to the pi Berry phase, and generates a decoherence mechanism to the phase coherence length of the surface electrons. As a consequence, the quantum correction to the conductivity can exhibit non-monotonic behavior by decreasing the temperature. This effect is attributed to the close relation of the Berry phase and quantum interference of the topological surface electrons in quantum topological materials.
The quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has quantized Hall resistance of h/Ce2 and vanishing longitudinal resistance under zero magnetic field, where C is called the Chern number. The QAH effect has been realized in magnetic topological insulators (TIs) and magic-angle twisted bilayer graphene. Despite considerable experimental efforts, the zero magnetic field QAH effect has so far been realized only for C = 1. Here we used molecular beam epitaxy to fabricate magnetic TI multilayers and realized the QAH effect with tunable Chern number C up to 5. The Chern number of these QAH insulators is tuned by varying the magnetic doping concentration or the thickness of the interior magnetic TI layers in the multilayer samples. A theoretical model is developed to understand our experimental observations and establish phase diagrams for QAH insulators with tunable Chern numbers. The realization of QAH insulators with high tunable Chern numbers facilitates the potential applications of dissipationless chiral edge currents in energy-efficient electronic devices and opens opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects.
We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and integer values when the superconducting phase difference across the junction advances by $2pi$. This leads to characteristic differences in the splittings of the spin multiplets by exchange coupling and single-ion anisotropy at phase differences, for which time-reserval symmetry is preserved. We discuss the resulting $8pi$-periodic (or $mathbb{Z}_4$) fractional Josephson effect in the context of recent experiments.
We show that in the presence of $n$-fold rotation symmetries and time-reversal symmetry, the number of fermion flavors must be a multiple of $2n$ ($n=2,3,4,6$) on two-dimensional lattices, a stronger version of the well-known fermion doubling theorem in the presence of only time-reversal symmetry. The violation of the multiplication theorems indicates anomalies, and may only occur on the surface of new classes of topological crystalline insulators. Put on a cylinder, these states have $n$ Dirac cones on the top and on the bottom surfaces, connected by $n$ helical edge modes on the side surface.
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