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arXiv:2512.21763 · Physical review. B./Physical review. B

High-temperature quantum oscillations of a nonequilibrium non-Fermi liquid

Anonymous, Li-kun Shi, Inti Sodemann

Published Jul 1, 2026• 0 citations
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Abstract

A periodically driven Fermi gas coupled to a simple boson bath reaches a non-equilibrium steady-state occupation with sharp non-analyticities at certain momenta. Here, we demonstrate that these non-analyticities behave as emergent Fermi surfaces by showing that they give rise to quantum oscillations of observables with a period controlled by the effective Fermi surface area enclosed by these non-analyticities. However, these oscillations have several striking differences with standard equilibrium quantum oscillations. For example, they remain non-analytic at finite temperatures, their amplitude can survive up to extremely high temperatures comparable to the frequency of the drive, and they can display non-monotonic temperature dependence completely at odds with standard Lifshits-Kosevich behavior.

DOI
10.1103/pmsn-5jtp

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A periodically driven Fermi gas coupled to a simple boson bath reaches a non-equilibrium steady-state occupation with sharp non-analyticities at certain momenta. Here, we demonstrate that these non-analyticities behave as emergent Fermi surfaces by showing that they give rise to quantum oscillations of observables with a period controlled by the effective Fermi surface area enclosed by these non-analyticities. However, these oscillations have several striking differences with standard equilibrium quantum oscillations. For example, they remain non-analytic at finite temperatures, their amplitude can survive up to extremely high temperatures comparable to the frequency of the drive, and they can display non-monotonic temperature dependence completely at odds with standard Lifshits-Kosevich behavior.
We demonstrate that periodically driven Fermions coupled to simple bosonic baths have steady state occupations of Floquet Bloch bands that generically display nonanalyticities at certain momenta that resemble the Fermi surfaces of equilibrium non-Fermi liquids. Remarkably these nonequilibrium Fermi surfaces remain sharp even when the bath is at finite temperature, leading to critical power-law decaying correlations at finite temperature, a phenomenon with no analog in equilibrium. We also show that generically there is in-gap current rectification for clean metals lacking inversion symmetry, and explain why this occurs universally regardless of the details of collisions.
We show that the steady state of a periodically driven Bose gas coupled to a thermal bath features emergent Fermi surfaces both in its high temperature and Bose-Einstein-condensate (BEC) states. These emergent Fermi surfaces are non-analyticities in the occupation function as a function of momentum arising from the lack of detailed balance of collisions away from equilibrium. They are stronger in the BEC than in the normal gas, and can be more robust against finite temperature smearing than the usual equilibrium Fermi surfaces of Fermi gases. We also show that they give rise to analogous rich phenomena, such as Friedel oscillations in the density correlations and quantum oscillations in response to applied magnetic fields controlled by their areas, albeit with marked quantitative differences. Our results establish non-equilibrium conditions as a promising alternative pathway to achieve the long-sought-after emergence of Fermi surfaces in bosonic system. We outline strategies to experimentally discover these exotic states in ultra-cold atomic clouds.
We investigate nonequilibrium steady states of driven-dissipative ideal quantum gases of both bosons and fermions. We focus on systems of sharp particle number that are driven out of equilibrium either by the coupling to several heat baths of different temperature or by time-periodic driving in combination with the coupling to a heat bath. Within the framework of (Floquet-)Born-Markov theory, several analytical and numerical methods are described in detail. This includes a mean-field theory in terms of occupation numbers, an augmented mean-field theory taking into account also nontrivial two-particle correlations, and quantum-jump-type Monte Carlo simulations. For the case of the ideal Fermi gas, these methods are applied to simple lattice models and the possibility of achieving exotic states via bath engineering is pointed out. The largest part of this work is devoted to bosonic quantum gases and the phenomenon of Bose selection, a nonequilibrium generalization of Bose condensation, where multiple single-particle states are selected to acquire a large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among others, we provide a theory for transitions where the set of selected states changes, describe an efficient algorithm for finding the set of selected states, investigate beyond-mean-field effects, and identify the dominant mechanisms for heat transport in the Bose-selected state.
We demonstrate the existence of a nonequilibrium "Floquet Fermi liquid" state arising in partially filled Floquet Bloch bands weakly coupled to ideal fermionic baths, which possess a collection of "Floquet Fermi surfaces" enclosed inside each other, resembling matryoshka dolls. We elucidate several properties of these states, including their quantum oscillations under magnetic fields which feature slow beating patterns of their amplitude reflecting the different areas of the Floquet Fermi surfaces, consistent with those observed in microwave induced resistance oscillation experiments. We also investigate their specific heat and thermodynamic density of states and demonstrate how by controlling properties of the drive, such as its frequency, one can tune some of the Floquet Fermi surfaces toward nonequilibrium Van Hove singularities without changing the electron density.
In this paper we investigate magneto-oscillations in the specific heat and the magnetization of nonrelativistic fermions coupled to a fluctuating U(1)U(1)U(1) gauge field. This model obtains as an effective model for the underdoped cuprates realizing a so-called ``algebraic charge liquid,'' which is a true non-Fermi-liquid state. Our study is driven by very recent observations of quantum oscillations in the underdoped cuprates. We calculate corrections to the standard Lifshitz-Kosevich expression due to the internal gauge degree of freedom for the oscillation amplitude. We perform this calculation in the dirty limit in a model with N\mathcal{N}N species of fermions. The $\mathcal{N}\ensuremath{\rightarrow}\ensuremath{\infty}$ result corresponds to the well-known Fermi-liquid result reproducing the Lifshitz-Kosevich result. We capture the effect of the gauge field on the oscillation amplitude to Gaussian accuracy controlled in the small parameter 1/N1/\mathcal{N}1/N. Our main finding is the presence of qualitative and quantitative differences compared to standard Fermi-liquid theory.
We construct examples of translationally invariant solvable models of strongly correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi-liquid behavior. In the marginal-Fermi-liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi surfaces. The self-energy has a singular frequency dependence but lacks momentum dependence, reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞. In the low-temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi surface in the non-Fermi-liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse-grained descriptions of a class of intermediate-scale non-Fermi-liquid behavior in generic correlated metals.