Momentum-dependent mass and AC Hall conductivity of quantum anomalous Hall insulators and their relation to the parity anomaly

Tutschku, Christian; Böttcher, J.; Meyer, René; Hankiewicz, Ewelina M.

doi:10.1103/physrevresearch.2.033193

Cited by 11 publications

(8 citation statements)

References 60 publications

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“…the holographic computations in [179,180]). 55 Hydrodynamic behavior has been measured most reliably or has been the- oretically argued for in (2+1)-dimensional materials [182][183][184] where the parity anomaly leads to anomalous transport effects [93,[185][186][187][188]. Our discussion of (2+1)-dimensional hydrodynamics in section 2.5.2 will help relating our (3+1)-dimensional hydrodynamic transport effects to these lower dimensional experiments and theoretical descriptions.…”

Section: Jhep04(2021)078mentioning

confidence: 95%

Chiral hydrodynamics in strong external magnetic fields

Ammon

Grieninger

Hernandez

et al. 2021

J. High Energ. Phys.

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We construct the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods. We determine the constitutive equations for the energy-momentum tensor and the axial charge current, in part from a generating functional. Furthermore, we derive the Kubo formulas which relate two-point functions of the energy-momentum tensor and charge current to 27 transport coefficients: 8 independent thermodynamic, 4 independent non-dissipative hydrodynamic, and 10 independent dissipative hydrodynamic transport coefficients. Five Onsager relations render 5 more transport coefficients dependent. We uncover four novel transport effects, which are encoded in what we call the shear-induced conductivity, the two expansion-induced longitudinal conductivities and the shear-induced Hall conductivity. Remarkably, the shear-induced Hall conductivity constitutes a novel non-dissipative transport effect. As a demonstration, we compute all transport coefficients explicitly in a strongly coupled quantum fluid via holography.

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Section: Jhep04(2021)078mentioning

confidence: 95%

Chiral hydrodynamics in strong external magnetic fields

Ammon

Grieninger

Hernandez

et al. 2021

J. High Energ. Phys.

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“…In this context, the corresponding chiral magnetic effect gives rise to quantized electric currents upon applying an external magnetic field. Another well studied anomaly is the parity anomaly [18][19][20][21][22][23][24][25], which gives rise to topological effects in two-dimensional gapless (Dirac) phases [26,27] related to the emergence of Chern-Simons theories.…”

Section: Introductionmentioning

confidence: 99%

“…However, the regularization explicitly breaks certain symmetries of the original action, hence giving rise to anomalies as we now show. We use the standard Pauli-Villars method [24] to obtain the topological action in the low-energy regime, which consists in introducing a mass termmψψ withm = m − αk 2 . To reveal the "parity" anomaly [62], we first consider the Dirac case (a = 0); we determine the effective Chern-Simons action, by calculating a one-loop triangle diagram [55,63], and we obtain…”

Section: Introductionmentioning

confidence: 99%

Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

2020

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Quantum anomalies offer a useful guide for the exploration of transport phenomena in topological semimetals. In this work, we introduce a model describing a semimetal in four spatial dimensions, whose nodal points act like tensor monopoles in momentum space. This system is shown to exhibit monopole-to-monopole phase transitions, as signaled by a change in the value of the topological Dixmier-Douady invariant as well as by the associated surface states on its boundary. We use this model to reveal an intriguing "4D parity magnetic effect," which stems from a parity-type anomaly. In this effect, topological currents are induced upon time modulating the separation between the fictitious monopoles in the presence of a magnetic perturbation. Besides its theoretical implications in both condensed matter and quantum field theory, the peculiar four-dimensional (4D) magnetic effect revealed by our model could be measured by simulating higher-dimensional semimetals in synthetic matter.

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“…The vielbein variations naturally include nonisotropic and nonsymmetric viscous responses. Therefore our formulation is analogous to related frameworks that introduce a nonzero torsion [49,[56][57][58][59][60][61]. Before extracting the coefficients we note that the timereversal odd viscosity tensor in a PT -invariant theory can be decomposed as follows:…”

Section: Hall Transportmentioning

confidence: 99%

Quantum Hall effective action for the anisotropic Dirac semimetal

et al. 2020

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We present a study of Hall transport in semi-Dirac critical phases. The construction is based on a covariant formulation of relativistic systems with spatial anisotropy. Geometric data together with external electromagnetic fields is used to devise an expansion procedure that leads to a low-energy effective action consistent with the discrete PT symmetry that we impose. We use the action to discuss terms contributing to the Hall transport and extract the coefficients. We also discuss the associated scaling symmetry.

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Momentum-dependent mass and AC Hall conductivity of quantum anomalous Hall insulators and their relation to the parity anomaly

Cited by 11 publications

References 60 publications

Chiral hydrodynamics in strong external magnetic fields

Chiral hydrodynamics in strong external magnetic fields

Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

Quantum Hall effective action for the anisotropic Dirac semimetal

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