Electron-phonon interactions and instabilities in Weyl semimetals under magnetic fields and torsional strain

We study the presence of an external magnetic field, in combination with torsional strain, over the electron-phonon interactions in a type I Weyl semimetal. This particular superposition of field and strain, modeled in the continuum approximation by an effective gauge field, leads to an asymmetric pseudo-magnetic field at each Weyl node of opposite chirality. Therefore, we also studied the role of nodal asymmetry in the properties of the system by means of the Kadanoff-Wilson renormalization group and the corresponding flow equations. By solving those, we discuss the evolution of the coupling parameters of the theory, and analyze possible fixed points and lattice (Peierls) instabilities emerging from interactions between phonons with the chiral Landau level in the very strong pseudo-magnetic field regime.

💡 Research Summary

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This paper investigates how the simultaneous presence of an external magnetic field and torsional strain influences electron‑phonon interactions and possible instabilities in a type‑I Weyl semimetal (WSM). The authors begin by showing that torsional strain can be described, within a continuum approximation, by an effective gauge field A_S that generates a uniform pseudo‑magnetic field B_S. When combined with a real magnetic field B_0 (taken along the crystal’s z‑axis), each Weyl node of chirality ξ = ± experiences a different total magnetic field B_ξ = B_0 + ξ B_S. This node‑dependent field breaks the symmetry between the two nodes and can be tuned to very large values because the strain‑induced component can far exceed realistic laboratory magnetic fields.

The single‑particle Hamiltonian is written as
H_ξ = ξ b_0 σ_0 + ξ v_ξ σ·