Non-Fermi-liquid behaviour of electrons coupled to gauge phonons

Abstract

We identify overdamped gauge phonons as a new microscopic route to non-Fermi-liquid behaviour in Dirac materials. These phonons couple to electronic currents rather than densities, thereby realising a lattice analogue of transverse gauge-field mechanisms without requiring proximity to a quantum critical point. By computing the electronic self-energy with a phonon propagator dressed by electron-phonon interactions, we show that the low-energy behaviour is controlled by the orbital susceptibility chi and a dimensionless damping parameter alpha. In the overdamped regime, alpha >> 1, quasiparticles display strong deviations from Fermi-liquid theory. For chi > 0, Fermi-liquid behaviour persists only in a parametrically narrow infrared window before crossing over to non-Fermi-liquid scaling. For chi < 0, the Fermi-liquid regime is replaced by marginal-Fermi-liquid behaviour at the lowest energies, followed by a crossover to non-Fermi-liquid scaling. These results establish strain- induced gauge phonons as a promising source of anomalous metallic behaviour in systems such as twisted bilayer graphene.

Figures (3)

• Figure 1: One-loop electron-phonon contribution to the self-energy $\Sigma_\lambda(\bm{k}, i\varepsilon_n)$.
• Figure 2: Imaginary part of the retarded self-energy, $\Im m\,\Sigma^{R}_{+}$, as a function of the dimensionless energy $\bar{\varepsilon}$. The insets show the corresponding local scaling exponent $\zeta(\bar{\varepsilon})$. (a) and (d) correspond to $\bar{\chi}=10^{-6}$,$\bar{\alpha}=10^{2}$, and $c_{\rm ph}/v_{\rm F}=10^{-1}$, and shows predominantly Fermi-liquid like behaviour (as $\bar{\varepsilon}_{\ast} =10^{-2}$). (b) and (e) correspond to $\bar{\chi}=10^{1}$, $\bar{\alpha}=10^{2}$, and $c_{\rm ph}/v_{\rm F}=10^{-1}$, and show a crossover from Fermi-liquid like scaling toward non-Fermi-liquid behaviour, at $\bar{\varepsilon}_{\ast} \simeq10^{-5}$ (denoted by the purple dashed vertical line), with an effective exponent close to $2/3$. (c) and (f) corresponds to $\bar{\chi}=-10^{1}$$\bar{\alpha}=10^{2}$, and $c_{\rm ph}/v_{\rm F}=10^{-1}$. The crossover from a marginal-Fermi-liquid like regime to a non-Fermi-liquid regime occurs at the same energy, $\bar{\varepsilon}_{\ast} \simeq10^{-5}$.
• Figure 3: Imaginary part of the retarded self-energy $\Im m\Sigma^{R}_{+}(k_F,\bar{\varepsilon})$ for monolayer graphene and MATBG, evaluated using the material parameters discussed in the text. The dashed line shows the Fermi-liquid scaling $\bar{\varepsilon}^2$. For monolayer graphene (blue), the self-energy follows the expected Fermi-liquid behaviour over the accessible energy window. In contrast, for MATBG (purple), the enhanced electronic response leads to an observable departure from Fermi-liquid behaviour. The inset shows the local logarithmic slope $\zeta(\bar{\varepsilon}) = d\ln \Im m \Sigma^{R}_{+}(k_F,\bar{\varepsilon}) / d\ln \bar{\varepsilon}$, showing $\zeta \rightarrow 2$ for graphene and a steady departure of $\zeta \rightarrow 2$ for MATBG.