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arXiv:2409.16398 · Physical review. B./Physical review. B

Shot noise in a phenomenological model of a marginal Fermi liquid

Yiming Wu, Josephine J. Yu, S. Raghu

Published Dec 27, 2024• 1 citation
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Abstract

The strange metal is a mysterious non-Fermi liquid which shows linear-in-$T$ resistivity behavior at finite temperatures, and, as found in recent experiments, vanishingly small shot noise in the linear-in-$T$ 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 $T$-linear scattering rate at finite $T$. 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.

DOI
10.1103/physrevb.110.235157

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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.
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.
Despite much theoretical effort, there is no complete theory of the "strange" metal state of the high temperature superconductors, and its linear-in-temperature T resistivity.Recent experiments showing an unexpected linear-in-field B magnetoresistivity have deepened the puzzle.We propose a simple model of itinerant electrons, interacting via random couplings, with electrons localized on a lattice of "quantum dots" or "islands."This model is solvable in a particular large-N limit and can reproduce observed behavior.The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations.For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-T resistivity and a T ln T specific heat as T → 0. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-T crossover to a fully incoherent regime that also has a linear-in-T resistivity.We describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function of B=T; however, the magnetoresistance saturates at large B. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands.Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic field B applied perpendicular to the plane of the sample, at large B. The resistance also scales linearly in T at small B, and as TfðB=TÞ at intermediate B. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.
We revisit a phenomenological model of fermions coupled to fluctuating bosons that emerges from finite-momentum particle-particle pairs for describing the strange metal phase in the cuprates. The incoherent bosons dominate the transport properties for the resistivity and optical conductivity in the non-Fermi-liquid phase. Within the Kubo formalism, the resistivity is approximately linear in temperature with a Drude form for the optical conductivity, such that the Drude lifetime is inversely proportional to the temperature. Here, we compute the transport properties of such bosons within the memory-matrix approach that successfully captures the hydrodynamic regime. This technique emerges as the appropriate framework for describing the transport coefficients of the strange metal phase. Our analysis confirms the TTT-linear resistivity due to the umklapp scattering that we obtained for this effective model. Finally, we provide new predictions regarding the variation of the thermal conductivity with temperature and examine the validity of the Wiedemann-Franz law.
"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.
We construct a model that exhibits resistivity going as a power law in temperature TTT, as ${T}^{\ensuremath{\alpha}}$ down to the lowest temperature. There is no residual resistivity because we assume the absence of disorder and momentum relaxation is due to umklapp scattering. Our model consists of a quantum spin liquid state with a spinon Fermi surface and a hole Fermi surface made out of doped holes. The key ingredient is a set of singular 2kF2{k}_{F}2kF​ modes living on a ring in momentum space. Depending on parameters, $\ensuremath{\alpha}$ may be unity (strange metal) or even smaller. The model may be applicable to a doped organic compound, which has been found to exhibit linear TTT resistivity. We conclude that it is possible to obtain strange metal behavior starting with a model that is not so strange.
The breakdown of the celebrated Fermi liquid theory in the strange metal phase is the central enigma of correlated quantum matter. Motivated by recent experiments reporting short-lived carriers, along with the ubiquitous observations of modulated excitations in the phase diagram of cuprates, we propose a phenomenological boson-fermion model for this phase. Along with the fermions, we consider fluctuating bosons emerging from the remnants of a pair density wave as additional current carriers in the strange metal phase. These bosonic excitations are finite-momentum Cooper pairs and thus carry twice the electronic charge, and their net spin can either be zero or one arising from the two spin-1/21/21/2 electrons. We show in a perturbative calculation within Kubo formalism that such a model displays a TlogTTlogTTlogT dependence of the resistivity with temperature and manifests the Drude form of the ac conductivity. Furthermore, such bosons are incoherent and hence do not contribute to the Hall conductivity. Finally, the bosons emerging from finite-momentum pairs of spin-triplet symmetry also reproduce the recently observed linear-in-field magnetoresistance in the optimally doped and overdoped cuprates [P. Giraldo-Gallo et al., Science 361, 479 (2018); J. Ayres et al., Nature 595, 661 (2021)].