High-Temperature Quantum Oscillations of a Non-equilibrium Non-Fermi Liquid

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.

Figures (7)

• Figure 1: (a) Electrons driven by light of frequency $\Omega$ and coupled to an ohmic boson bath, have an occupation of states (b) with a discontinuous second derivative at momentum $k_F^2/2m= \hbar \Omega$. Here we chosen $\bar{n}_e =n_e h/(m\Omega)= 0.8$, $\kappa^2=e^2|\mathcal{E}|^2/(m\hbar\Omega^3)=0.04$.
• Figure 2: Jump of the second derivative of the occupation for $\bar{n}_e =0.8$, and various driving amplitudes $\kappa$: (a) low-temperature regime, (b) high-temperature regime (note difference in x-axis), (c) log-log plot of full temperature dependence and fits. Amplitude of the resulting quantum oscillations in the interval $\Omega/\omega_c \in [40, 43]$ in the (d) low-temperature and (e) high-temperature regimes. (f) Jump of second derivative and oscillation amplitude as a function of driving amplitude. (g) Low-temperature oscillations for different magnetic fields showing that the full width at half maximum (FWHM) scales approximately linearly with $\omega_c$.
• Figure 3: (a) Quantum oscillations at small driving amplitudes, $\kappa$ and low bath temperature. At $\kappa\rightarrow0$ we see only the equilibrium quantum oscillations with a period controlled by the density, which decrease rapidly as the driving amplitude $\kappa$ increases, while the new oscillations of the emergent Floquet Fermi surface with period controlled by $\Omega$ emerge. (b) At higher bath temperatures the equilibrium oscillations are exponentially suppressed and essentially invisible, and the Floquet oscillations are clearly visible and non-analytic as a function of field. At larger drive amplitudes only the Floquet quantum oscillations are visible both at (c) small and (b) large bath temperatures.
• Figure B-4: a) Non-perturbative Free energy oscillations at $k_BT_{\rm bath} = 0.2\hbar \Omega$ for $d = 1$. b) Amplitude of the oscillations at $\Omega=30.5\omega_c$ for ${\bar{n}_e }=0.8~ (\rm red),1.8 ~(\rm yellow)$.
• Figure C-5: a) Full free energy variations as in Eq.(\ref{['F_full']}) of the main text. b) Isolated oscillatory component.