Rotational strain in Weyl semimetals: A continuum approach

Arjona, Vicente; Vozmediano, María A. H.

doi:10.1103/physrevb.97.201404

Cited by 57 publications

(54 citation statements)

References 40 publications

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“…Ref. [130] listed the richer structure that u ij and its antisymmetric counterpart w ij = 1 2 (∂ i u j − ∂ j u i ) can induce in the low energy theory. For example, u ij induces an anisotropic Fermi velocity [47] and its trace a deformation potential [39] and the vector A i = w ij b j is responsible for a linear dispersion tilt and a pseudo-Zeeman term [39].…”

Section: Discussionmentioning

confidence: 99%

Pseudo-electromagnetic fields in 3D topological semimetals

2019

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Dirac and Weyl semimetals, materials where electrons behave as relativistic fermions, react to position-and time-dependent perturbations, such as strain, as if emergent electromagnetic fields were applied. Since they differ from external electromagnetic fields in their symmetries and phenomenology they are called pseudo-electromagnetic fields, and enable a simple and unified description of a variety of inhomogeneous systems involving topological semimetals. We review the different physical ways to create effective pseudo-fields, their observable consequences as well as their similarities and differences compared to electromagnetic fields. Among these difference is their effect on quantum anomalies, the absence of a classical symmetry in the quantum theory, which we revisit from a quantum field theory and a semiclassical viewpoint. We conclude with predicted observable signatures of the pseudo-fields and the nascent experimental status. * All authors contributed equally to the preparation of this review arXiv:1903.11088v1 [cond-mat.mes-hall]

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Section: Discussionmentioning

confidence: 99%

Pseudo-electromagnetic fields in 3D topological semimetals

2019

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“…(52) suggests that the displacement of Fermi surface pockets away from zero momentum (as in graphene) may have a significant effect on viscous response functions. Another interesting direction for future work is to extend our formalism to systems with an external magnetic field, and to three dimensional systems such as topological semimetals 50,51 .…”

Section: Discussionmentioning

confidence: 99%

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

Rao

Bradlyn

2020

Phys. Rev. X

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Inspired by recent experiments on graphene, we examine the non-dissipative viscoelastic response of anisotropic two-dimensional quantum systems. We pay particular attention to electron fluids with point group symmetries, and those with discrete translational symmetry. We start by extending the Kubo formalism for viscosity to systems with internal degrees of freedom and discrete translational symmetry, highlighting the importance of properly considering the role of internal angular momentum. We analyze the Hall components of the viscoelastic response tensor in systems with discrete point group symmetry, focusing on the hydrodynamic implications of the resulting forces. We show that though there are generally six Hall viscosities, there are only three independent contributions to the viscous force density. To compute these coefficients, we develop a framework to consistently write down the long-wavelength stress tensor and viscosity for multi-component lattice systems. We apply our formalism to lattice and continuum models, including a lattice Chern insulator and anisotropic superfluid. arXiv:1910.10727v1 [cond-mat.mes-hall]

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“…Finally, for completeness we also include the leading order behavior of the out-of-plane components of the Hall viscosity in Appendix A. Three-dimensional contributions to the Hall viscosity analogous to these have recently appeared in the study of topological semimetals. 62,63 V. EFFECTIVE ANISOTROPY OF THE TILTED FIELD SYSTEM Now that we have computed the current and stress response functions for the tilted field system, we will attempt to view the system, in the limit of small tilt and strong confinement, as a two-dimensional fluid. The natural question arises, is there an intrinsically twodimensional system that recreates the behavior of the strongly confined tilted field system?…”

Section: Hall Viscositymentioning

confidence: 99%

Viscoelastic response of quantum Hall fluids in a tilted field

Offertaler

Bradlyn

2019

Phys. Rev. B

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In this paper, we examine the viscoelastic properties of integer quantum Hall (IQH) states in a tilted magnetic field. In particular, we explore to what extent the tilted-field system behaves like a two-dimensional electron gas with anisotropic mass in the presence of strain deformations. We first review the Kubo formalism for viscosity in an external magnetic field, paying particular attention to the role of rotational symmetry and contact terms. Next, we compute the conductivity, stress, and viscosity tensors for IQH states in the presence of a tilted field and vertical confining potential. By comparing our results with the recently developed bimetric formalism, we show that, at the level of the contracted Hall viscosity tensor, the mapping between tilted field and effective mass anisotropy holds only if we simultaneously modify the background perpendicular magnetic field; in other words, a simultaneous measurement of the density, contracted Hall viscosity, and Hall conductivity at fixed particle number can distinguish between tilted field and effective mass anisotropy. Additionally, we show that in the presence of a tilted magnetic field, the stress tensor acquires an unusual anisotropic ground state average, leading to anomalous elastic response functions. We develop a formalism for projecting a three-dimensional Hamiltonian with confining potential and magnetic field to a two-dimensional Hamiltonian in order to further address the phenomenology of the tilted-field IQH fluid. We find that the projected fluid couples non-minimally to geometric deformations, indicating the presence of internal geometric degrees of freedom.Let us begin by reviewing the most pertinent results from linear response theory in the context of a timereversal asymmetric fluid. We write down the general Kubo formula, with an eye towards features relevant to topological phases of matter. In particular, we will review the Kubo formula for the (Hall) conductivity, and re-derive the Kubo formulas for the (Hall) viscosity. We will focus especially on the role of rotational symmetry and the interpretation of "contact" (diamagnetic) terms in the response functions. Further background can be found in Refs. 5, 39-41. A. Review of linear response theoryThe typical linear response set-up 42 starts with a system described by an unperturbed (time-independent) Hamiltonian H 0 , an unperturbed density matrix ρ 0 that

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Rotational strain in Weyl semimetals: A continuum approach

Cited by 57 publications

References 40 publications

Pseudo-electromagnetic fields in 3D topological semimetals

Pseudo-electromagnetic fields in 3D topological semimetals

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

Viscoelastic response of quantum Hall fluids in a tilted field

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