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arXiv:2305.02336 · Physical Review Research

Theory of shot noise in strange metals

Alexander Nikolaenko, Subir Sachdev A, Aavishkar A. Patel

Published Nov 13, 2023• 22 citations
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Abstract

We extend the theory of shot noise in coherent metals to shot noise in strange metals without quasiparticle excitations. This requires a generalization of the Boltzmann equation with a noise source to distribution functions which depend independently on the excitation momentum and energy. We apply this theory to a model of a strange metal with linear in temperature ($T$) resistivity, describing a Fermi surface with a spatially random Yukawa coupling to a critical boson. We find a suppression of the Fano factor in the strange metal, and describe the dependence of the shot noise on temperature and applied voltage. At low temperatures, we obtain a Fano factor equal to $1/6$, in contrast to the $1/3$ Fano factor in diffusive metals with quasiparticles. Our results are in general agreement with recent observations by Chen et al. (arXiv:2206.00673). We further compare the random Yukawa model to quasi-elastic electron-phonon scattering that also generates $T$-linear resistivity, and argue that shot noise observations offer a useful diagnostic to distinguish between them.

DOI
10.1103/physrevresearch.5.043143

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We extend the theory of shot noise in coherent metals to shot noise in strange metals without quasiparticle excitations. This requires a generalization of the Boltzmann equation with a noise source to distribution functions which depend independently on the excitation momentum and energy. We apply this theory to a model of a strange metal with linear in temperature (TTT) resistivity, describing a Fermi surface with a spatially random Yukawa coupling to a critical boson. We find a suppression of the Fano factor in the strange metal, and describe the dependence of the shot noise on temperature and applied voltage. At low temperatures, we obtain a Fano factor equal to 1/61/61/6, in contrast to the 1/31/31/3 Fano factor in diffusive metals with quasiparticles. Our results are in general agreement with recent observations by Chen et al. (arXiv:2206.00673). We further compare the random Yukawa model to quasi-elastic electron-phonon scattering that also generates TTT-linear resistivity, and argue that shot noise observations offer a useful diagnostic to distinguish between them.
The strange metal is a mysterious non-Fermi liquid which shows linear-in-TTT resistivity behavior at finite temperatures, and, as found in recent experiments, vanishingly small shot noise in the linear-in-TTT regime. Here, we investigate the shot noise of a strange metal based on a phenomenological model of marginal Fermi liquid (MFL), where fermions couple to some collective boson mode, leading to TTT-linear scattering rate at finite TTT. It is found that in the diffusive regime where the MFL scattering length is small compared to the system size, the shot noise vanishes, and the thermal noise becomes a temperature- and voltage-independent constant. Introducing additional impurity scattering increases the shot noise, and is probably consistent with the current experiment.
Strange metals—ubiquitous in correlated quantum materials—transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures ( T ), such metals generically exhibit strange metal behavior with a T -linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/ T ) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.
The strange metal phase of correlated electrons materials was described in a recent theory by a model of a Fermi surface coupled a two-dimensional quantum critical bosonic field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained for a wide range of intermediate temperatures, including the linear in temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at lower temperatures. For an [Formula: see text]-component boson with [Formula: see text], we use multiple graphics processing units (GPUs) to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to the emergence of the physics of the random transverse-field Ising model at low temperatures, as has been proposed by Hoyos, Kotabage, and Vojta. This regime is controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a "quantum critical phase" away from the quantum critical point, as observed in several cuprates. For the [Formula: see text] Ising scalar, the mean-field treatment is not applicable, and so we use Hybrid Monte Carlo simulations running on multiple GPUs; we find a rounded transition and localization physics, with strange metal behavior in an extended region around the transition.
Recent studies have shown that a spatially random Yukawa-type interaction between a Fermi surface and critical bosons can produce linear-in-temperature resistivity, the defining signature of strange metals. In this article, we systematically classify all scalar couplings of the form (ψ†ψ)nϕm(ψ^{\dagger}ψ)^nϕ^m(ψ†ψ)nϕm in arbitrary dimensions to identify possible candidates for strange-metal behaviour within this disordered framework. We find that only spatially random Yukawa-type interaction in (2+1)(2+1)(2+1) dimensions can yield linear resistivity. This indicates that linear resistivity is not a universal property of all spatially random scalar coupling, and strange-metal property replies on both dimensions and interaction type.
Strange metal behavior has been observed in an expanding list of quantum materials, with heavy fermion metals serving as a prototype setting. Among the intriguing questions is the nature of charge carriers; there is an increasing recognition that the quasiparticles are lost, as captured by Kondo destruction quantum criticality. Among the recent experimental advances is the measurement of shot noise in a heavy-fermion strange metal. We are thus motivated to study current fluctuations by advancing a minimal Bose-Fermi Kondo lattice model, which admits a well-defined large-NNN limit. Showing that the model in equilibrium captures the essential physics of Kondo destruction, we proceed to derive quantum kinetic equations and compute shot noise to the leading nontrivial order in 1/N1/N1/N. Our results reveal a strong suppression of the shot noise at the Kondo destruction quantum critical point, thereby providing the understanding of the striking experiment. Broader implications of our results are discussed.
A recent theory is reviewed for the shot noise of coherent radiation propagating through a random medium. The Fano factor [Formula: see text] (the ratio of the noise power and the mean transmitted current) is related to the scattering matrix of the medium. This is the optical analogue of Büttiker's formula for electronic shot noise. Scattering by itself has no effect on the Fano factor, which remains equal to 1 (as for a Poisson process). Absorption and amplification both increase the Fano factor above the Poisson value. For strong absorption [Formula: see text] has the universal limit [Formula: see text], with f the Bose–Einstein function at the frequency of the incident radiation. This is the optical analogue of the one-third reduction factor of electronic shot noise in diffusive conductors. In the amplifying case the Fano factor diverges at the laser threshold, while the signal-to-noise ratio [Formula: see text] reaches a finite, universal limit.