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

Non-Fermi-Liquid Behaviour of Electrons Coupled to Gauge Phonons

Overview

This work studies the electronic self-energy generated by the coupling of electronic currents to "gauge phonons" - phonon modes that couple to electronic currents rather than densities. The authors show that when these phonons become strongly damped, they can induce non-Fermi-liquid (NFL) behaviour in Dirac materials like twisted bilayer graphene.

Problem & Context

• Landau's Fermi-liquid theory provides the canonical low-energy description of interacting metals, but many correlated metals exhibit robust non-Fermi-liquid (NFL) behaviour, such as linear-in-temperature electrical resistivity.
• One route to NFL behaviour is the coupling of electrons to gapless bosonic collective fluctuations, like overdamped order parameter fluctuations near a quantum critical point.
• Another mechanism is the coupling of electrons to overdamped transverse gauge fluctuations, which can produce a fermion decay rate scaling as ε^(2/3), signaling the breakdown of the quasiparticle description.

Methodology

• The authors consider a model of electrons coupled to "gauge phonons" - phonon modes that couple to electronic currents rather than densities. This coupling arises naturally in crystals with non-orthogonal lattice vectors, like oblique, triangular, or strained square/rectangular lattices.
• They compute the electronic self-energy at one-loop order, with the transverse phonon propagator dressed by the electron-phonon interaction.
• The low-energy physics is controlled by two key parameters: the orbital magnetic susceptibility χ and a dimensionless damping parameter ᾱ.

Results

• When the phonons become strongly damped (ᾱ ≫ 1), the system exhibits robust NFL behaviour:
  • For χ > 0, the low-energy regime remains Fermi-liquid-like, but rapidly crosses over to a non-Fermi-liquid regime at higher energies.
  • For χ < 0, the Fermi-liquid infrared behaviour is replaced by a marginal-Fermi-liquid regime at the lowest energies, followed by a crossover to non-Fermi-liquid scaling at higher energies.
• The crossover scale between regimes is controlled by the competition between the bare phonon dispersion and the orbital susceptibility correction.

Interpretation

• Strain-induced gauge phonons provide a new microscopic route to non-Fermi-liquid physics in Dirac materials, with twisted bilayer graphene as a particularly promising platform.
• The mechanism does not require proximity to a quantum critical point, in contrast to conventional order-parameter criticality scenarios for NFL behaviour.
• The results establish that any bosonic mode coupling predominantly to electronic currents, rather than densities, may provide an alternative route to NFL behaviour.

Limitations & Uncertainties

• The material parameter estimates suggest the non-Fermi-liquid regime may not be readily accessible in monolayer graphene, but could be observable in twisted bilayer graphene due to the stronger electronic response.
• The model assumptions, such as the single-mode approximation for the phonon dispersion, may affect the quantitative details but not the qualitative conclusions.

What Comes Next

• Exploring the possible relevance of this mechanism to other correlated systems, such as the cuprates, where linear-in-temperature transport remains a central open problem.
• Investigating the interplay between the gauge-phonon-induced non-Fermi-liquid physics and other interaction effects in twisted bilayer graphene.