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Transport signatures of transient superfluids

Yonah Lemonik, Aditi Mitra

Published Nov 27, 2017• 0 citations
OpenAlex

Abstract

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.

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Recent advances in ultra-fast measurement in cold atoms, as well as pump-probe spectroscopy of K3_33​C60_{60}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 ultrafast 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. First, by inelastic scattering between the fermions and the fluctuations, and second by direct conduction through the fluctuations, with the latter providing a lower resistance current carrying channel. The competition between these two effects leads to nonmonotonic behavior in the time-resolved optical conductivity, providing a signature of the critical transient state.
Results are presented for the quench dynamics of a clean and interacting electron system, where the quench involves varying the strength of the attractive interaction along arbitrary quench trajectories. The initial state before the quench is assumed to be a normal electron gas, and the dynamics is studied in a regime where long-range order is absent, but nonequilibrium superconducting fluctuations need to be accounted for. A quantum kinetic equation using a two-particle irreducible formalism is derived. Conservation of energy, particle number, and momentum emerge naturally, with the conserved currents depending on both the electron Green's functions and the Green's functions for the superconducting fluctuations. The quantum kinetic equation is employed to derive a kinetic equation for the current, and the transient optical conductivity relevant to pump-probe spectroscopy is studied. The general structure of the kinetic equation for the current is also justified by a phenomenological approach that assumes model F in the Halperin-Hohenberg classification, corresponding to a nonconserved order parameter coupled to a conserved density. Linear response conductivity and the diffusion coefficients in thermal equilibrium are also derived, and connections with Aslamazov-Larkin fluctuation corrections are highlighted. Results are also presented for the time evolution of the local density of states. It is shown that Andreev scattering processes result in an enhanced density of states at low frequencies. For a quench trajectory corresponding to a sudden quench to the critical point, the density of states is shown to grow in a manner where the time after the quench plays the role of the inverse detuning from the critical point.
Recent pump-probe experiments on underdoped cuprates and similar systems suggest the existence of a transient superconducting state above Tc{T}_{c}Tc​. This poses the question of how to reliably identify the emergence of long-range order, in particular superconductivity, out of equilibrium. We investigate this point by studying a quantum quench in an extended Hubbard model and by computing various observables, which are used to identify (quasi-)long-range order in equilibrium. Our findings imply that, in contrast to current experimental studies, it does not suffice to study the time evolution of the optical conductivity to identify superconductivity. In turn, we suggest to utilize time-resolved angle-resolved photoemission spectroscopy experiments to probe for the formation of a condensate in the two-particle channel.
There has been significant interest in the generation of very short-lived superconducting states in solid-state films. Here, we consider the role of nonequilibrium superconducting fluctuations in such systems, generated by an interaction quench, considering the limit of large static disorder. In particular, we argue that because of critical slowing down, the regime of the fluctuation dominated normal state is more important than might be naively thought. We show how such a state might appear in the optical conductivity, and give the appropriate nonequilibrium generalization of the Azlamazov-Larkin and Maki-Thompson fluctuation corrections to the optical conductivity. For a quench to the superconducting critical point, we show that the fluctuation corrections lead to power-law aging behavior in the optical conductivity. The power-law aging from Azlamazov-Larkin and Maki-Thompson terms are qualitatively different, despite the effect of the two being similar in dc measurements in thermal equilibrium. These signatures provide a road map for experiments to identify the role of superconducting fluctuations in a transient state.
Results are presented for the time evolution of fermions initially in a nonzero temperature normal phase, following the switch on of an attractive interaction. The dynamics are studied in the disordered phase close to the critical point, where the superfluid fluctuations are large. The analysis is conducted within a two-particle irreducible, large NNN approximation. The system is considered from the perspective of critical quenches where it is shown that the fluctuations follow universal model A dynamics. A signature of this universality is found in a singular correction to the fermion lifetime, given by a scaling form ${t}^{(3\ensuremath{-}d)/2}{S}_{d}({\ensuremath{\varepsilon}}^{2}t)$, where ddd is the spatial dimension, ttt is the time since the quench, and $\ensuremath{\varepsilon}$ is the fermion energy. The singular behavior of the spectral density is interpreted as arising due to incoherent Andreev reflections off superfluid fluctuations.
The photoexcited state associated with superconducting fluctuations above the superconducting critical temperature Tc{T}_{c}Tc​ is studied based on the time-dependent Ginzburg-Landau approach. The excited state is created by an electric-field pulse and is probed by a weak secondary external field, which is treated by the linear response theory mimicking pump-probe spectroscopy experiments. The behavior is basically controlled by two relaxation rates: one is ${\ensuremath{\gamma}}_{1}$ proportional to the temperature measured from the critical point $T\ensuremath{-}{T}_{c}$, and the other is ${\ensuremath{\gamma}}_{2}$ proportional to the excitation intensity of the pump pulse. The excited state approaches the equilibrium state exponentially in a long time $t\ensuremath{\gg}{\ensuremath{\gamma}}_{1}^{\ensuremath{-}1}$, while in the intermediate-time domain we find a power-law or logarithmic decay with different exponents for $t\ensuremath{\ll}{\ensuremath{\gamma}}_{2}^{\ensuremath{-}1}$ and ${\ensuremath{\gamma}}_{2}^{\ensuremath{-}1}\ensuremath{\ll}t\ensuremath{\ll}{\ensuremath{\gamma}}_{1}^{\ensuremath{-}1}$, even though the system is located away from the critical point. This is interpreted as the critical point in equilibrium being extended to a finite region in the excited situation. The parameter dependences on both the pump and probe currents are also systematically studied in all dimensions.