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arXiv:2112.06966

A stability bound on the $T$-linear resistivity of conventional metals

Chaitanya Murthy, Akshat Pandey, Ilya Esterlis, Steven Allan Kivelson

Published Dec 13, 2021• 0 citations
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Abstract

Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is $1/τ_\text{tr} = 2πλT$, where $λ$ is a dimensionless strength of the electron-phonon coupling. The fact that measured values satisfy $λ\lesssim 1$ has been noted in the context of a possible "Planckian" bound on transport. However, since the electron-phonon scattering is quasi-elastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a "stability" bound on $λ$ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.

DOI
10.48550/arxiv.2112.06966

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A stability bound on the TTT-linear resistivity of conventional metals
Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is 1/τtr=2πλT1/τ_\text{tr} = 2πλT1/τtr​=2πλT, where λλλ is a dimensionless strength of the electron-phonon coupling. The fact that measured values satisfy λ≲1λ\lesssim 1λ≲1 has been noted in the context of a possible "Planckian" bound on transport. However, since the electron-phonon scattering is quasi-elastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a "stability" bound on λλλ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.
Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is 1/ τ tr = 2 π λ T , where λ is a dimensionless strength of the electron–phonon coupling. The fact that measured values satisfy λ ≲ 1 has been noted in the context of a possible “Planckian” bound on transport. However, since the electron–phonon scattering is quasielastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a “stability” bound on λ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.
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Phonons have long been thought to be incapable of explaining key phenomena in strange metals, including linear-in-\textit{T} Planckian resistivity from high to very low temperatures. We argue that these conclusions were based on static, perturbative approaches that overlooked essential time-dependent and nonperturbative electron-lattice physics. In fact ``phonons'' are not the best target for discussion, just like ``photons'' are not the best way to think about Maxwell's equations. Quantum optics connects photons and electromagnetism, as developed 60 years ago by Glauber and others. We have been developing the parallel world of quantum acoustics. Far from being only of academic interest, the new tools are rapidly exposing the secrets of the strange metals, revealing strong vibronic (vibration-electronic) interactions playing a crucial role forming polarons and charge density waves, linear-in-TTT resistivity at the Planckian rate over thousands of degrees, resolution of the Drude peak infrared anomaly, and the absence of a T4T^4T4 low-temperature resistivity rise in 2D systems, and of a Mott-Ioffe-Regel resistivity saturation. We derive Planckian transport, polarons, CDWs, and pseudogaps from the Fröhlich model. The ``new physics'' has been hiding in this model all along, in the right parameter regime, if it is treated nonperturbatively. In the course of this work we have uncovered the generalization of Anderson localization to dynamic media: a universal Planckian diffusion emerges, a ``ghost'' of Anderson localization. Planckian diffusion is clearly defined and is more fundamental than the popular but elusive, model dependent concept of ``Planckian speed limit''.
We present a lattice model of fermions with N flavors and random interactions that describes a Planckian metal at low temperatures T→0 in the solvable limit of large N. We begin with quasiparticles around a Fermi surface with effective mass m^{*} and then include random interactions that lead to fermion spectral functions with frequency scaling with k_{B}T/ℏ. The resistivity ρ obeys the Drude formula ρ=m^{*}/(ne^{2}τ_{tr}), where n is the density of fermions, and the transport scattering rate is 1/τ_{tr}=fk_{B}T/ℏ; we find f of order unity and essentially independent of the strength and form of the interactions. The random interactions are a generalization of the Sachdev-Ye-Kitaev models; it is assumed that processes nonresonant in the bare quasiparticle energies only renormalize m^{*}, while resonant processes are shown to produce the Planckian behavior.
Relaxational processes for conduction electrons in metals come with characteristic temperature dependences; classic examples at low temperatures are the 1/T21/{T}^{2}1/T2 law for the relaxation time in a Fermi liquid, and the Bloch 1/T51/{T}^{5}1/T5 law for electron-phonon scattering. The strange metal phase of cuprate superconductors is governed instead by the Planckian time, which is given in terms of fundamental constants only. This Colloquium discusses the concept of such a fundamental timescale and the degree to which it provides a lower bound for relaxation times, and illustrates these ideas with examples from conventional and unconventional metals.