Shear viscosity and imperfect fluidity in bosonic and fermionic superfluids

In this paper we address the ratio of the shear viscosity to entropy density $\eta/s$ in bosonic and fermionic superfluids. A small $\eta/s$ is associated with nearly perfect fluidity, and more general measures of the fluidity perfection/imperfection are of wide interest to a number of communities. We use a Kubo approach to concretely address this ratio via low temperature transport associated with the quasi-particles. Our analysis for bosonic superfluids utilizes the framework of the one-loop Bogoliubov approximation, whereas for fermionic superfluids we apply BCS theory and its BCS-BEC extension. Interestingly, we find that the transport properties of strict BCS and Bogoliubov superfluids have very similar structures, albeit with different quasi-particle dispersion relations. While there is a dramatic contrast between the power law and exponential temperature dependence for $\eta$ alone, the ratio $\eta/s$ for both systems is more similar. Specifically we find the same linear dependence (on the ratio of temperature $T$ to inverse lifetime $\gamma(T)$) with $\eta/s \propto T/\gamma(T)$, corresponding to imperfect fluidity. By contrast, near the unitary limit of BCS-BEC superfluids a very different behavior results, which is more consistent with near-perfect fluidity.Comment: v2: 8 pages, 3 figure

Combined effects of pairing fluctuations and a pseudogap in the Cuprate Hall effect

The normal-state behavior of the temperature-dependent Hall coefficient in cuprate superconductors is investigated using linear response theory. The Hall conductivity is of paramount importance in that its sign and magnitude directly reflect the sign of the charge carriers and the size of particle-hole asymmetry effects. Here we apply a strong-pairing fluctuation theory that incorporates pseudogap effects known to be important in cuprate transport. As a result, in the vicinity of the transition temperature our theoretical approach goes beyond the conventional superconducting fluctuation formalism. In this regime, pseudogap effects are evident in both the transverse and longitudinal conductivities and the bosonic response is explicitly gauge invariant. The presence of a gap in the excitation spectrum is also apparent at higher temperatures, where the gapped fermionic quasiparticles are the dominant contribution to the Hall coefficient. The observed non-monotonic temperature dependence of the Hall coefficient therefore results from a delicate interplay between the fermionic quasiparticles and the bosonic fluctuations. An important feature of our work is that the sign of the Hall conductivity from the Cooper pair fluctuations is the same as that of their fermionic constituents. Thus, we find no sign change in the Hall coefficient above the transition temperature. This prediction is corroborated by experiments, away from special charge ordering stoichiometries. The theoretical results presented in this paper provide crucial signatures that can be experimentally verified, enabling validation of the present theory.Comment: 14 pages, 8 figure

Cuprate diamagnetism in the presence of a pseudogap: Beyond the standard fluctuation formalism

It is often claimed that among the strongest evidence for preformed-pair physics in the cuprates are the experimentally observed large values for the diamagnetic susceptibility and Nernst coefficient. These findings are most apparent in the underdoped regime, where a pseudogap is also evident. While the conventional (Gaussian) fluctuation picture has been applied to address these results, this preformed-pair approach omits the crucial effects of a pseudogap. In this paper we remedy this omission by computing the diamagnetic susceptibility and Nernst coefficient in the presence of a normal state gap. We find a large diamagnetic response for a range of temperatures much higher than the transition temperature. In particular, we report semi-quantitative agreement with the measured diamagnetic susceptibility onset temperatures, over the entire range of hole dopings. Notable is the fact that at the lower critical doping of the superconducting dome, where the transition temperature vanishes and the pseudogap onset temperature remains large, the onset temperature for both diamagnetic and transverse thermoelectric transport coefficients tends to zero. Due to the importance attributed to the cuprate diamagnetic susceptibility and Nernst coefficient, this work helps to clarify the extent to which pairing fluctuations are a component of the cuprate pseudogap

Quasi-condensation in two-dimensional Fermi gases

In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. We find that quasi-condensation mirrors Berezinskii-Kosterlitz-Thouless behavior in many ways, including the emergence of a strong zero momentum peak in the pair momentum distribution. Importantly, the disappearance of this quasi-condensate occurs at a reasonably well defined crossover temperature. The resulting phase diagram, pair momentum distribution, and algebraic power law decay are compatible with recent experiments throughout the continuum from BEC to BCS

Correcting inconsistencies in the conventional superfluid path integral scheme

In this paper we show how to redress a shortcoming of the path integral scheme for fermionic superfluids and superconductors. This approach is built around a simultaneous calculation of electrodynamics and thermodynamics. An important sum rule, the compressibility sum rule, fails to be satisfied in the usual calculation of the electromagnetic and thermodynamic response at the Gaussian fluctuation level. Here we present a path integral scheme to address this inconsistency. Specifically, at the leading order we argue that the superconducting gap should be calculated using a different saddle point condition modified by the presence of an external vector potential. This leads to the well known gauge-invariant BCS electrodynamic response and is associated with the usual (mean field) expression for thermodynamics. In this way the compressibility sum rule is satisfied at the BCS level. Moreover, this scheme can be readily extended to address arbitrary higher order fluctuation theories. At any level this approach will lead to a gauge invariant and compressibility sum rule consistent treatment of electrodynamics and thermodynamics.Comment: Comments welcome. Submitted directly to Phys. Rev. B Rapid Communication

Two-dimensional spin-imbalanced Fermi gases at non-zero temperature: Phase separation of a non-condensate

We study a trapped two-dimensional spin-imbalanced Fermi gas over a range of temperatures. In the moderate temperature regime, associated with current experiments, we find reasonable semi-quantitative agreement with the measured density profiles as functions of varying spin imbalance and interaction strength. Our calculations show that, in contrast to the three-dimensional case, the phase separation which appears as a spin balanced core, can be associated with non-condensed fermion pairs. We present predictions at lower temperatures where a quasi-condensate will first appear, based on the pair momentum distribution and following the protocols of Jochim and collaborators. While these profiles also indicate phase separation, they exhibit distinctive features which may aid in identifying the condensation regime.Comment: 4 pages, 4 figur

Signatures of pairing and spin-orbit coupling in correlation functions of Fermi gases

We derive expressions for spin and density correlation functions in the (greatly enhanced) pseudogap phase of spin-orbit coupled Fermi superfluids. Density-density correlation functions are found to be relatively insensitive to the presence of these Rashba effects. To arrive at spin-spin correlation functions we derive new $f$-sum rules, valid even in the absence of a spin conservation law. Our spin-spin correlation functions are shown to be fully consistent with these $f$-sum rules. Importantly, they provide a clear signature of the Rashba band-structure and separately help to establish the presence of a pseudogap.Comment: 5 pages, 2 figures, with 5 page supplemen

Topological effects on transition temperatures and response functions in three-dimensional Fermi superfluids

We investigate the effects of topological order on the transition temperature, $T_c$, and response functions in fermionic superfluids with Rashba spin-orbit coupling and a transverse Zeeman field in three dimensions. Our calculations, relevant to the ultracold atomic Fermi gases, include fluctuations beyond mean-field theory and are compatible with $f$-sum rules. Reminiscent of the $p_x + i p_y$ superfluid, the topological phase is stabilized when driven away from the Bose-Einstein condensation and towards the BCS limit. Accordingly, while experimentally accessible, $T_c$ is significantly suppressed in a topological superfluid. Above $T_c$, the spin and density response functions provide signatures of topological phases via the recombination or amplification of frequency dependent peaks

Unified approach to electrical and thermal transports in high-TcT_c superconductors

In this paper we present a consolidated equation for all low-field transport coefficients, based on a reservoir approach developed for non-interacting quasiparticles. This formalism allows us to treat the two distinct types of charged (fermionic and bosonic) quasiparticles that can be simultaneously present, as for example in superconductors. Indeed, in the underdoped cuprate superconductors these two types of carriers result in two onset temperatures with distinct features in transport: $T^*$, where the fermions first experience an excitation (pseudo)gap, and $T_c$, where bosonic conduction processes are dominant and often divergent. This provides the central goal of this paper, which is to address the challenges in thermoelectric transport that stem from having two characteristic temperatures as well as two types of charge carriers whose contributions can in some instances enhance each other and in others compete. We show how essential features of the cuprates (their "bad-metal" character and the presence of Fermi arcs) provide an explanation for the classic pseudogap onset signatures at $T^*$ in the longitudinal resistivity, $\rho_{xx}$. Based on the fits to the temperature-dependent $\rho_{xx}$, we present the implications for all of the other thermoelectric transport properties

Exact correlation functions in the cuprate pseudogap phase: combined effects of charge order and pairing

There is a multiplicity of charge ordered, pairing-based or pair density wave theories of the cuprate pseudogap, albeit arising from different microscopic mechanisms. For mean field schemes (of which there are many) we demonstrate here that they have precise implications for two body physics in the same way that they are able to address the one body physics of photoemission spectroscopy. This follows because the full vertex can be obtained exactly from the Ward-Takahashi identity. As an illustration, we present the spin response functions, finding that a recently proposed pair density wave (Amperean pairing) scheme is readily distinguishable from other related scenarios.Comment: Corrects an error in Eq. (1). Numerical results and conclusions remain unchanged. Supplemental Material update