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

TL;DR

This work develops a field-theoretic renormalization group framework to study electron-phonon interactions in a two-node type-I Weyl semimetal under a combination of external magnetic field and torsional strain, which generates node-dependent pseudo-magnetic fields $B_{\xi}=B_0+\xi B_S$. By projecting to the very strong pseudo-magnetic field regime and focusing on the lowest Landau level, the authors derive one-loop RG flow equations for the electron-electron and electron-phonon couplings, including both Peierls and Cooper channels, and analyze fixed points and the adiabatic Peierls instability (CDW) across symmetric ($\Delta=0$) and symmetry-broken ($\Delta>0$) cases. The critical temperatures $T_c$ and, when applicable, the characteristic temperatures $T_0^*$, are expressed in terms of exponents $\gamma_{\varepsilon}$ and $\gamma_{Δ,ε}$, which depend on the nodal asymmetry parameter $ε=|B_0/B_S|$ and the velocity asymmetry, showing that strain can enhance or suppress the Peierls instability depending on symmetry. Overall, the work reveals magneto-strain engineering of CDW instabilities in Weyl semimetals and extends prior RG analyses to include nodal asymmetry effects induced by torsional strain. The findings underscore the crucial role of Cooper-channel processes in determining the instability and provide a roadmap for tuning electronic phases via combined magnetic and mechanical controls.

Abstract

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.

Figures (9)

• Figure 1: Non-interacting energy dispersion in Eq. \ref{['eq:eigenvalues_2']}, illustrated for the choice of parameters $b_0 = 0.2 \hbar v_+/\ell_+$, $v_- = 1.5 v_+$, $\ell_- = \ell_+/\sqrt{0.7}$, and $k_{\pm} = \pm\, 5/\ell_+$. The corresponding Fermi energy is $0.5 \hbar v_+ / \ell_+$ above $k_+$.
• Figure 2: Bare values of $g_1$ (top panel) and $g_2$ (bottom panel) as functions of $B_0/B_S$. For $g_2$, we display the curves for different values of $\delta v / v_F$.
• Figure 3: Plots of $\lambda_P(\nu_m=0,l)$ and $\lambda_C(\nu_m=0,l)$ as functions of $\beta \Lambda(l)$ for different values of $\gamma$ and $\Delta/\Lambda(l)$. The black dots corresponds to intersections between the two functions.
• Figure 4: Plots of $\lambda_P - \lambda_C$ as a function of $\beta \Lambda(l)$ for different values of $\gamma$ and $\Delta /\Lambda(l)$.
• Figure 5: First order corrections to the effective action, corresponding to: (a) First term in Eq. \ref{['C_1ord-See-4bar']}, (b) Second term in Eq. \ref{['C_1ord-See-4bar']}, and (c) Eq. \ref{['C_1ord-Sep']}.