[Paper Review] Strain in Weyl semimetals. A continuum approach

Vicente Arjona, María A. H. Vozmediano|arXiv (Cornell University)|Sep 7, 2017

Topological Materials and Phenomena3 citations

TL;DR

This paper introduces a continuum field theory approach to strain in Weyl semimetals, revealing that the antisymmetric part of the deformation gradient tensor—previously absent in 2D Dirac materials—gives rise to novel electron-phonon couplings. These include new elastic gauge fields, cone tilting, and pseudo-Zeeman effects, fundamentally altering the low-energy electronic response beyond conventional deformation potential theory.

ABSTRACT

The coupling of lattice deformations to the low energy electronic excitations of Dirac matter involve novel types of electron--phonon couplings as the celebrated elastic gauge fields first analyzed in graphene. In the continuum low energy approach, lattice deformations coupling to the electronic degrees of freedom are characterized by the (symmetric) strain tensor defined in elasticity theory. We review these couplings in Weyl semimetals and examine the coupling of electronic excitations to the antisymmetric part of the deformation gradient tensor associated to rotational strain. The new couplings, absent in the two dimensional materials, have important physical implications: they give rise to new elastic gauge fields, contribute to the deformation potential, tilt the cones and generate new pseudo--Zeeman couplings.

Motivation & Objective

• To extend the continuum description of strain in Dirac and Weyl semimetals beyond symmetric strain tensors.
• To identify and characterize the physical effects arising from the antisymmetric part of the deformation gradient tensor in three-dimensional Weyl semimetals.
• To establish how rotational strain—previously irrelevant in 2D systems—generates new electronic couplings and modifies band structure.
• To clarify the role of elastic gauge fields and pseudo-Zeeman terms in the low-energy effective Hamiltonian under strain.

Proposed method

• Formalism is developed using the continuum limit of the lattice Hamiltonian, incorporating the strain tensor from elasticity theory.
• The deformation gradient tensor is decomposed into symmetric (strain) and antisymmetric (rotation) parts, with the latter treated as a gauge field.
• Effective low-energy Hamiltonians are derived that include couplings to both symmetric and antisymmetric strain components.
• The electronic spectrum is analyzed under strain to identify cone tilting and new pseudo-spin-orbit-like couplings.
• Symmetry and gauge invariance principles are applied to classify the new couplings and distinguish them from conventional deformation potential effects.
• Theoretical predictions are derived using continuum field theory, with no microscopic lattice details required.

Experimental results

Research questions

• RQ1 How does the antisymmetric part of the deformation gradient tensor influence electronic excitations in Weyl semimetals?
• RQ2 What novel elastic gauge fields emerge from rotational strain in three-dimensional Dirac and Weyl systems?
• RQ3 How does strain-induced cone tilting modify the electronic band structure in Weyl semimetals?
• RQ4 In what way do these new couplings contribute to the deformation potential beyond the standard scalar term?
• RQ5 What is the origin and physical significance of the pseudo-Zeeman coupling in strained Weyl semimetals?

Key findings

• The antisymmetric part of the deformation gradient tensor generates new elastic gauge fields not present in two-dimensional Dirac materials like graphene.
• Rotational strain induces a novel pseudo-Zeeman coupling that lifts spin degeneracy in the electronic spectrum of Weyl semimetals.
• Strain causes a tilt in the Weyl cones, modifying the Fermi velocity and breaking Lorentz invariance in the low-energy theory.
• The new couplings contribute to the deformation potential, altering the response of electronic states to mechanical stress.
• These effects arise from the intrinsic chiral nature of Weyl fermions and are absent in systems with time-reversal symmetry.
• The continuum approach reveals that rotational strain couples to electronic degrees of freedom via a gauge-like interaction, distinct from scalar strain.