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arXiv:2603.11176 · SciPost Physics

Can electronic quantum criticality drive phonon-induced linear-in-temperature resistivity?

Haoyu Guo, Debanjan Chowdhury

Published Aug 21, 2026• 0 citations
arXivHTMLPDF

Abstract

Optical phonons naturally generate linear-in-temperature ( T T ) resistivity in the equipartition regime, but their finite gap prevents this mechanism from surviving to asymptotically low temperatures. Here we analyze whether proximity to an electronic quantum critical point can remove this obstruction by strongly softening an optical phonon. We first derive a model-independent criterion for such softened phonons to control low-temperature transport. In addition to reducing the renormalized optical gap, the Landau-damped phonon must acquire a dynamical exponent z_p;gt d z p > d , where d d is the spatial dimension of the phonon, so that a sufficiently large thermally occupied phase space survives as T\to 0 T → 0 . We then analyze a concrete mechanism in which the phonon couples nonlinearly to long-wavelength electronic collective modes near a quantum critical point associated with an order parameter carrying zero center-of-mass momentum, and apply it to the Ising-nematic problem. Within a large- N N field theoretic formulation, the phonon softening is enhanced near criticality, but in the clean theory the resulting dynamics lies at or near the boundary for asymptotic T T -linear scattering. Including feedback from the softened phonon back onto the electronic critical sector further weakens the tendency toward robust low-temperature T T -linear transport. Our results sharpen both the promise and the limitations of phonon-based explanations of strange-metal transport near electronic criticality.

DOI
10.21468/scipostphys.21.2.047

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Optical phonons naturally generate linear-in-temperature ( T T ) resistivity in the equipartition regime, but their finite gap prevents this mechanism from surviving to asymptotically low temperatures. Here we analyze whether proximity to an electronic quantum critical point can remove this obstruction by strongly softening an optical phonon. We first derive a model-independent criterion for such softened phonons to control low-temperature transport. In addition to reducing the renormalized optical gap, the Landau-damped phonon must acquire a dynamical exponent z_p;gt d z p > d , where d d is the spatial dimension of the phonon, so that a sufficiently large thermally occupied phase space survives as T\to 0 T → 0 . We then analyze a concrete mechanism in which the phonon couples nonlinearly to long-wavelength electronic collective modes near a quantum critical point associated with an order parameter carrying zero center-of-mass momentum, and apply it to the Ising-nematic problem. Within a large- N N field theoretic formulation, the phonon softening is enhanced near criticality, but in the clean theory the resulting dynamics lies at or near the boundary for asymptotic T T -linear scattering. Including feedback from the softened phonon back onto the electronic critical sector further weakens the tendency toward robust low-temperature T T -linear transport. Our results sharpen both the promise and the limitations of phonon-based explanations of strange-metal transport near electronic criticality.
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The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. Usually it is associated with the proximity to a quantum critical point (a second order transition at temperature T = 0) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes, while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electronic diffusive modes, that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio C_V/T ~ log(1/T), down to low temperatures.
The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, leading to a broken symmetry phase) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electron density diffusive modes that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio CV/T∼log(1/T), down to low temperatures.
We consider the transport properties of a model of fermions scattered by a critical bosonic mode. The mode is overdamped and scattering is mainly in the forward direction. Such a mode appears at the quantum critical point for an electronic nematic phase transition and in gauge theories for a U(1) spin liquid. It leads to a short fermion lifetime, violating Landau's criterion for a Fermi liquid. In spite of this, transport can be described by a Boltzmann equation. We include momentum relaxation by umklapp scattering, supplemented by weak impurity scattering. We find that above a very low temperature which scales with ${\mathrm{\ensuremath{\Delta}}}_{q}^{3}$, where ${\mathrm{\ensuremath{\Delta}}}_{q}$ is the minimum umklapp scattering vector, the resistivity is linear in TTT with a coefficient which is independent of the amount of disorder. This picture holds until the temperature dependent part of the resistivity exceeds that due to impurity scattering. We compare the relaxation time approximation with an exact numerical solution of the Boltzmann equation. Surprisingly we find that, unlike the resistivity, the Hall coefficient strongly deviates from the relaxation time approximation and shows a strong reduction with increasing temperature. We comment on possible comparisons with experiments on high Tc{T}_{c}Tc​ cuprates.
Metals at the brink of electronic quantum phase transitions display high-temperature superconductivity, competing orders, and unconventional charge transport, revealing strong departures from conventional Fermi liquid behavior. Investigation of these fascinating intertwined phenomena has been at the center of research across a variety of correlated materials over the past many decades. A ubiquitous experimental observation is the emergence of a universal timescale that governs electrical transport and momentum relaxation. In this Letter, we analyze an equally important theoretical question of how the energy contained in the electronic degrees of freedom near a quantum phase transition relaxes to the environment via their coupling to acoustic phonons. Assuming that the bottleneck for energy dissipation is controlled by the coupling between electronic degrees of freedom and acoustic phonons, we present a universal theory of the temperature dependence of the energy relaxation rate in a marginal Fermi liquid. We find that the energy relaxation rate exhibits a complex set of temperature-dependent crossovers controlled by emergent energy scales in the problem. We place these results in the context of recent measurements of the energy relaxation rate via nonlinear optical spectroscopy in the normal state of hole-doped cuprates.
We study the optical conductivity $\ensuremath{\sigma}(\ensuremath{\Omega})$ of an electron system near a quantum-critical point with finite-wavelength ordering. $\ensuremath{\sigma}(\ensuremath{\Omega})$ vanishes in clean Galilean-invariant systems, unless electrons are coupled to dynamical collective modes, which dissipate the current. This coupling introduces a nonuniversal energy scale. Depending on the parameters of each specific system, a variety of responses arise near criticality: scaling peaks at a temperature- and doping-dependent frequency, peaks at a fixed frequency, or no peaks to be associated with criticality. Therefore the lack of scaling in the far-infrared conductivity in cuprates does not necessarily call for new concepts of quantum criticality.