Hall Viscosity in Quantum Systems with Discrete Symmetry: Point Group and Lattice Anisotropy

Rao, Pranav; Bradlyn, Barry

doi:10.1103/physrevx.10.021005

Cited by 48 publications

(40 citation statements)

References 79 publications

(100 reference statements)

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“…Many interesting avenues remain in the geometric description of emergent gapless fermions with background fields, including also nodal line systems [37,119]. It would be interesting to study the gravitational anomalies in Weyl and Dirac systems with many nodes, taking fully into account the relevant space-group symmetries and defects [16,42,[120][121][122]. More generally, the appearance of low-energy quasirelativistic fermions with exotic geometric backgrounds within feasible experimental reach is expected to give more insight also to the physics of gravity with torsion, although the symmetries and status of the background fields are dramatically different.…”

Section: Discussionmentioning

confidence: 99%

Torsional Landau levels and geometric anomalies in condensed matter Weyl systems

Laurila

Nissinen

2020

Phys. Rev. B

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We consider the role of coordinate-dependent Fermi velocities, equivalent to effective tetrad (or vierbein) frame fields characterizing momentum space geometry, and torsional Landau levels (LLs) in condensed matter systems with low-energy Weyl quasiparticles. In contrast to their relativistic counterparts, they arise at finite momenta and with an explicit cutoff to the linear spectrum. Via the universal coupling of tetrads to momentum, they experience geometric chiral and axial anomalies with gravitational character. More precisely, at low energy, the fermions experience background fields corresponding to emergent anisotropic Riemann-Cartan and Newton-Cartan space-times, depending on the form of the low-energy dispersion. On these backgrounds, we show how torsion and the Nieh-Yan (NY) anomaly appear in condensed matter Weyl systems with an ultraviolet (UV) parameter with dimensions of momentum. The torsional NY anomaly arises from the spectral flow of torsional LLs and the linear Weyl description with a cutoff. We carefully review the torsional anomaly and spectral flow for relativistic fermions at zero momentum and contrast this with the spectral flow, nonzero torsional anomaly, and the appearance of the dimensionful UV-cutoff parameter in condensed matter systems at finite momentum. We apply this to chiral transport anomalies sensitive to the emergent tetrads in nonhomogeneous chiral superconductors, superfluids, and Weyl semimetals under elastic strain. This leads to previously overlooked suppression of anomalous density at nodes from momentum space geometry, as compared to (pseudo)gauge fields. We also briefly discuss torsion in anomalous thermal transport for nonrelativistic Weyl fermions, which arises via Luttinger's fictitious gravitational field corresponding to thermal gradients.

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Section: Discussionmentioning

confidence: 99%

Torsional Landau levels and geometric anomalies in condensed matter Weyl systems

Laurila

Nissinen

2020

Phys. Rev. B

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“…Tensor α describes dissipative behavior respecting both stress symmetry and objectivity, i.e., α ijkl = α jikl = α klij . Tensor β on the other hand, describes nondissipative Hall viscosity 7,[23][24][25][26][27] , i.e., β ijkl = −β klij , and is nonzero only when time-reversal symmetry is broken. Finally, γ breaks stress objectivity, i.e., γ ijkl = −γ ijlk , coupling fluid stress to the vorticity.…”

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confidence: 99%

Electron hydrodynamics in anisotropic materials

et al. 2020

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Rotational invariance strongly constrains the viscosity tensor of classical fluids. When this symmetry is broken in anisotropic materials a wide array of novel phenomena become possible. We explore electron fluid behaviors arising from the most general viscosity tensors in two and three dimensions, constrained only thermodynamics and crystal symmetries. We find nontrivial behaviors in both two- and three-dimensional materials, including imprints of the crystal symmetry on the large-scale flow pattern. Breaking time-reversal symmetry introduces a non-dissipative Hall component to the viscosity tensor, and while this vanishes for 3D isotropic systems we show it need not for anisotropic materials. Further, for such systems we find that the electronic fluid stress can couple to the vorticity without breaking time-reversal symmetry. Our work demonstrates the anomalous landscape for electron hydrodynamics in systems beyond graphene, and presents experimental geometries to quantify the effects of electronic viscosity.

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“…Inspired by recent work on viscoelastic linear response of anisotropic systems [60,61], it would be interesting and straightforward to extend this work to anisotropic chiral superconductors.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Hall viscosity and conductivity of two-dimensional chiral superconductors

2020

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We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chiral superconductors, where fermions pair due to a short-range attractive potential, e.g. \boldsymbol{p+\mathrm{i}p}𝐩+i𝐩 pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chiral superconductors, where the Coulomb potential decays as inverse distance, we find an intermediate behavior between intrinsic two-dimensional superconductors and superfluids. These results are obtained by means of both effective and microscopic field theory.

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Hall Viscosity in Quantum Systems with Discrete Symmetry: Point Group and Lattice Anisotropy

Cited by 48 publications

References 79 publications

Torsional Landau levels and geometric anomalies in condensed matter Weyl systems

Torsional Landau levels and geometric anomalies in condensed matter Weyl systems

Electron hydrodynamics in anisotropic materials

Hall viscosity and conductivity of two-dimensional chiral superconductors

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