We extend the kinetic operator formalism developed in the companion paper [H.Guo,arXiv:2311.03455] to study the general eigenvalues of the fluctuation normal modes. We apply the formalism to calculate the optical conductivity of a critical Fermi surface near the Ising-Nematic quantum critical point. We find that the conductivity is the sum of multiple conduction channels including both the soft and non-soft eigenvectors of the kinetic operator, and therefore it is not appropriate to interpret the optical conductivity using extended Drude formula for momentum conserved systems. We also show that the propagation of the FS soft modes is governed by a Boltzmann equation from which hydrodynamics emerges. We calculate the viscosity and it shows clear signature of the non-Fermi liquid physics.We extend the kinetic operator formalism developed in the companion paper [H.Guo,arXiv:2311.03455] to study the general eigenvalues of the fluctuation normal modes. We apply the formalism to calculate the optical conductivity of a critical Fermi surface near the Ising-Nematic quantum critical point. We find that the conductivity is the sum of multiple conduction channels including both the soft and non-soft eigenvectors of the kinetic operator, and therefore it is not appropriate to interpret the optical conductivity using extended Drude formula for momentum conserved systems. We also show that the propagation of the FS soft modes is governed by a Boltzmann equation from which hydrodynamics emerges. We calculate the viscosity and it shows clear signature of the non-Fermi liquid physics.

arXiv:2311.03458Nov 6, 20230 citations

Transport signatures of transient superfluids

Yonah Lemonik, Aditi Mitra

Recent advances in ultra-fast measurement in cold atoms, as well as pump-probe spectroscopy of K $_3$ C $_{60}$ films, have opened the possibility of rapidly quenching systems of interacting fermions to, and across, a finite temperature superfluid transition. However determining that a transient state has approached a second-order critical point is difficult, as standard equilibrium techniques are inapplicable. We show that the approach to the superfluid critical point in a transient state may be detected via time-resolved transport measurements, such as the optical conductivity. We leverage the fact that quenching to the vicinity of the critical point produces a highly time dependent density of superfluid fluctuations, which affect the conductivity in two ways. Firstly by inelastic scattering between the fermions and the fluctuations, and secondly by direct conduction through the fluctuations. The competition between these two effects leads to non-monotonic behavior in the time-resolved optical conductivity, providing a signature of the critical transient state.Recent advances in ultra-fast measurement in cold atoms, as well as pump-probe spectroscopy of K$_3$C$_{60}$ films, have opened the possibility of rapidly quenching systems of interacting fermions to, and across, a finite temperature superfluid transition. However determining that a transient state has approached a second-order critical point is difficult, as standard equilibrium techniques are inapplicable. We show that the approach to the superfluid critical point in a transient state may be detected via time-resolved transport measurements, such as the optical conductivity. We leverage the fact that quenching to the vicinity of the critical point produces a highly time dependent density of superfluid fluctuations, which affect the conductivity in two ways. Firstly by inelastic scattering between the fermions and the fluctuations, and secondly by direct conduction through the fluctuations. The competition between these two effects leads to non-monotonic behavior in the time-resolved optical conductivity, providing a signature of the critical transient state.

Nov 27, 20170 citations

Quantum criticality and optical conductivity in a two-valley system

Yasha Gindikin, Songci Li, Alex Levchenko +3 more

We demonstrate that the optical conductivity of a Fermi liquid (FL) in the absence of umklapp scattering is dramatically affected by the topology of the Fermi surface (FS). Specifically, electron-electron ( $\mathit{ee}$ ) scattering leads to rapid current relaxation in systems with multiple, or multiply connected, FSs, provided that the valleys have different effective masses. This effect results from intervalley drag. We microscopically derive the optical conductivity of a two-valley system, both within the FL regime and near a quantum critical point (QCP) of the Ising-nematic type. In the FL regime, intervalley drag restores the Gurzhi-like scaling of the conductivity, $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{0}$. This dependence contrasts sharply with the previously identified subleading contribution to the conductivity of a two-dimensional FL with a single convex FS, where $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{2}ln|\ensuremath{\omega}|$. The vanishing of the leading term in the optical conductivity is a signature of geometric constraints on $\mathit{ee}$ scattering channels, which are lifted for a multiply connected FS. A large differential response, $d\mathrm{Re}\ensuremath{\sigma}/d\ensuremath{\mu}$ with $\ensuremath{\mu}$ being the chemical potential, is predicted at the Lifshitz transition from a single-valley to a multivalley FS, which should be observable within the experimentally accessible frequency range. Near a QCP, intervalley drag leads to a ${|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$ scaling of $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ in two dimensions, thus providing a specific current-relaxing process for this long-standing conjecture.We demonstrate that the optical conductivity of a Fermi liquid (FL) in the absence of umklapp scattering is dramatically affected by the topology of the Fermi surface (FS). Specifically, electron-electron ($\mathit{ee}$) scattering leads to rapid current relaxation in systems with multiple, or multiply connected, FSs, provided that the valleys have different effective masses. This effect results from intervalley drag. We microscopically derive the optical conductivity of a two-valley system, both within the FL regime and near a quantum critical point (QCP) of the Ising-nematic type. In the FL regime, intervalley drag restores the Gurzhi-like scaling of the conductivity, $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{0}$. This dependence contrasts sharply with the previously identified subleading contribution to the conductivity of a two-dimensional FL with a single convex FS, where $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{2}ln|\ensuremath{\omega}|$. The vanishing of the leading term in the optical conductivity is a signature of geometric constraints on $\mathit{ee}$ scattering channels, which are lifted for a multiply connected FS. A large differential response, $d\mathrm{Re}\ensuremath{\sigma}/d\ensuremath{\mu}$ with $\ensuremath{\mu}$ being the chemical potential, is predicted at the Lifshitz transition from a single-valley to a multivalley FS, which should be observable within the experimentally accessible frequency range. Near a QCP, intervalley drag leads to a ${|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$ scaling of $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ in two dimensions, thus providing a specific current-relaxing process for this long-standing conjecture.

arXiv:2406.10503Physical review. B./Physical review. BAug 20, 20243 citations

Recent advances in ultra-fast measurement in cold atoms, as well as pump-probe spectroscopy of K

_3

_{60}

films, have opened the possibility of rapidly quenching systems of interacting fermions to, and across, a finite temperature superfluid transition. However determining that a transient state has approached a second-order critical point is difficult, as standard equilibrium techniques are inapplicable. We show that the approach to the superfluid critical point in a transient state may be detected via time-resolved transport measurements, such as the optical conductivity. We leverage the fact that quenching to the vicinity of the critical point produces a highly time dependent density of superfluid fluctuations, which affect the conductivity in two ways. Firstly by inelastic scattering between the fermions and the fluctuations, and secondly by direct conduction through the fluctuations. The competition between these two effects leads to non-monotonic behavior in the time-resolved optical conductivity, providing a signature of the critical transient state.

\mathit{ee}

) scattering leads to rapid current relaxation in systems with multiple, or multiply connected, FSs, provided that the valleys have different effective masses. This effect results from intervalley drag. We microscopically derive the optical conductivity of a two-valley system, both within the FL regime and near a quantum critical point (QCP) of the Ising-nematic type. In the FL regime, intervalley drag restores the Gurzhi-like scaling of the conductivity, $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{0}$. This dependence contrasts sharply with the previously identified subleading contribution to the conductivity of a two-dimensional FL with a single convex FS, where $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{2}ln|\ensuremath{\omega}|$. The vanishing of the leading term in the optical conductivity is a signature of geometric constraints on

\mathit{ee}

scattering channels, which are lifted for a multiply connected FS. A large differential response, $d\mathrm{Re}\ensuremath{\sigma}/d\ensuremath{\mu}$ with $\ensuremath{\mu}$ being the chemical potential, is predicted at the Lifshitz transition from a single-valley to a multivalley FS, which should be observable within the experimentally accessible frequency range. Near a QCP, intervalley drag leads to a ${|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$ scaling of $\mathrm{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ in two dimensions, thus providing a specific current-relaxing process for this long-standing conjecture.