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Observing the amplitude-Higgs mode in superconductors has been a central challenge in condensed matter physics. Unlike the phase mode in the electromagnetic (EM) response, the amplitude mode is not needed to satisfy gauge invariance. Indeed, it couples to linear EM response properties only in special superconductors that are associated with a pairing vector $\mathbf{Q} \neq 0$. In this paper we characterize the amplitude-mode contribution within a gauge-invariant treatment of the linear optical conductivity for these non-uniform superconductors, noting that they are by their very nature particularly vulnerable to pair-breaking from non-magnetic impurities. This leads to inevitable damping of the Higgs mode. Our gauge-invariant formulation provides an in-depth understanding of two sets of $f$-sum rules which must be obeyed. We illustrate how difficult it is to disentangle the neutral amplitude mode contributions from those of the charged quasi-particles. These observations are presented in the context of an applied supercurrent, where we observe a new low-frequency feature that reflects the superfluid density and appears consistent with recent experiments., Comment: 9 pages, 5 figures

Quench experiments on a unitary Bose gas around a broad Feshbach resonance have led to the discovery of universal dynamics. This universality is manifested in the measured atomic momentum distributions where, asymptotically, a quasi-equilibrated metastable state is found in which both the momentum distribution and the time scales are determined by the particle density. In this paper we present counterpart studies but for the case of a very narrow Feshbach resonance of $^{133}$Cs atoms having a width of 8.3 mG. In dramatic contrast to the behavior reported earlier, a rapid quench of an atomic condensate to unitarity is observed to ultimately lead to coherent oscillations involving dynamically produced condensed and non-condensed molecules and atoms. The same characteristic frequency, determined by the Feshbach coupling, is observed in all types of particles. To understand these quench dynamics and how these different particle species are created, we develop a beyond Hartree-Fock-Bogoliubov dynamical framework including a new type of cross correlation between atoms and molecules. This leads to a quantitative consistency with the measured frequency. Our results, which can be applied to the general class of bosonic superfluids associated with narrow Feshbach resonances, establish a new paradigm for universal dynamics dominated by quantum many-body interactions., Comment: 11 pages, 7 figures

The recent observations of a stable molecular condensate emerging from a condensate of bosonic atoms and related "super-chemical" dynamics have raised an intriguing set of questions. Here we provide a microscopic understanding of this unexpected stability and dynamics in atom-molecule superfluids; we show one essential element behind these phenomena is an extremely narrow Feshbach resonance in $^{133}$Cs at 19.849G. Comparing theory and experiment we demonstrate how this narrow resonance enables the dynamical creation of a large closed-channel molecular fraction superfluid, appearing in the vicinity of unitarity. Theoretically the observed superchemistry (\textit{i.e.}, Bose enhanced reactions of atoms and molecules), is found to be assisted by the formation of Cooper-like pairs of bosonic atoms that have opposite momenta. Importantly, this narrow resonance opens the possibility to explore the quantum critical point of a molecular Bose superfluid and related phenomena which would not be possible near a more typically broad Feshbach resonance., Comment: 14 pages, 8 figures; close to the published version

In this paper we address the question of whether high-temperature superconductors have anything in common with BCS-BEC crossover theory. Towards this goal, we present a proposal and related predictions which provide a concrete test for the applicability of this theoretical framework. These predictions characterize the behavior of the Ginzburg-Landau coherence length, $\xi_0^{\text{coh}}$, near the transition temperature $T_{\text{c}}$, and across the entire superconducting $T_{\text{c}}$ dome in the phase diagram. That we are lacking a systematic characterization of $\xi_0^{\text{coh}}$ in the entire class of cuprate superconductors is perhaps surprising, as it is one of the most fundamental properties of any superconductor. This paper is written to motivate further experiments and, thus, address this shortcoming. Here we show how measurements of $\xi_0^{\text{coh}}$ contain direct indications for whether or not the cuprates are associated with BCS-BEC crossover and, if so, where within the crossover spectrum a particular superconductor lies., Comment: 9 pages, 3 figures; published version

In cosmological evolution, it is the homogeneous scalar field (inflaton) that drives the universe to expand isotropically and to generate standard model particles. However, to simulate cosmology, atomic gas research has focused on the dynamics of Bose-Einstein condensates (BEC) with continuously applied forces. In this paper we argue a complementary approach needs also to be pursued; we, thus, consider the analogue BEC experiments in a non-driven, closed atomic system. We implement this using a BEC in an optical lattice which, after a quench, freely transitions from an unstable to a stable state. This dynamical evolution displays the counterpart "preheating", "reheating" and "thermalization" phases of cosmology. Importantly, our studies of these analogue processes yield tractable analytic models. Of great utility to the cold atom community, such understanding elucidates the dynamics of non-adiabatic condensate preparation., Comment: 14 pages, 7 figures

New developments in superconductivity, particularly through unexpected and often astonishing forms of superconducting materials, continue to excite the community and stimulate theory. It is now becoming clear that there are two distinct platforms for superconductivity: natural and synthetic materials. The study of these artificial materials has greatly expanded in the last decade or so, with the discoveries of new forms of superfluidity in artificial heterostructures and the exploitation of proximitization. Natural superconductors continue to surprise through the Fe-based pnictides and chalcogenides, and nickelates as well as others. It is the goal of this review to present this two-pronged investigation into superconductors, with a focus on those that we have come to understand belong somewhere between the Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) regimes. We characterize in detail the nature of this "crossover" superconductivity, which is to be distinguished from crossover superfluidity in atomic Fermi gases. In the process, we address the multiple ways of promoting a system out of the BCS and into the BCS-BEC crossover regime within the context of concrete experimental realizations. These involve natural materials, such as organic conductors, as well as artificial, mostly two-dimensional materials, such as magic-angle twisted bilayer and trilayer graphene, or gate-controlled devices, as well as one-layer and interfacial superconducting films. This work should be viewed as a celebration of BCS theory by showing that even though this theory was initially implemented with the special case of weak correlations in mind, it can in a very natural way be extended to treat the case of these more exotic strongly correlated superconductors., Comment: v5, close to the published version. 54 pages, 40 figures

We present results for the entire set of anomalous charge and heat transport coefficients for metallic systems in the presence of a finite-temperature heat bath. In realistic physical systems this necessitates the inclusion of inelastic dissipation mechanisms; relatively little is known theoretically about their effects on anomalous transport. Here we demonstrate how these dissipative processes are strongly intertwined with Berry-curvature physics. Our calculations are made possible by the introduction of a Caldeira-Leggett reservoir which allows us to avoid the sometimes-problematic device of the pseudogravitational potential. Using our formulas, we focus on the finite-temperature behavior of the important anomalous Wiedemann-Franz ratio. Despite previous expectations, this ratio is found to be non-universal as it can exhibit either an upturn or a downturn as temperature increases away from zero. We emphasize that this derives from a \textit{competition} between Berry curvatures having different signs in different regions of the Brillouin zone. We point to experimental support for these observations and for the behavior of an alternative ratio involving a thermoelectric response which, by contrast, appears to be more universal at low temperatures. Our work paves the way for future theory and experiment, demonstrating how inelastic scattering at non-zero temperature affects the behavior of all anomalous transport coefficients., Comment: 19 pages, 7 figures; published version

The creation of a Hamiltonian in the quantum regime which has non-trivial topological features is a central goal of the cold-atom community, enabling widespread exploration of novel phases of quantum matter. A general scheme to synthesize such Hamiltonians is based on dynamical modulation of optical lattices which thereby generate vector potentials. At the same time the modulation can lead to heating and serious difficulties with equilibration. Here we show that these challenges can be overcome by demonstrating how a Hofstadter Bose-Einstein condensate (BEC) can be dynamically realized, using experimental protocols. From Gross-Pitaevskii simulations our study reveals a complex, multistage evolution; this includes a chaotic intermediate "heating" stage followed by a spontaneous reentrance to the BEC. The observed behavior is reminiscent of evolution in cosmological models.

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., Comment: Published version

We study quantum geometric contributions to the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, $T_{\mathrm{BKT}}$, in the presence of fluctuations beyond BCS theory. Because quantum geometric effects become progressively more important with stronger pairing attraction, a full understanding of 2D multi-orbital superconductivity requires the incorporation of preformed pairs. We find it is through the effective mass of these pairs that quantum geometry enters the theory and this suggests that the quantum geometric effects are present in the non-superconducting pseudogap phase as well. Increasing these geometric contributions tends to raise $T_{\mathrm{BKT}}$ which then competes with fluctuation effects that generally depress it. We argue that a way to physically quantify the magnitude of these geometric terms is in terms of the ratio of the pairing onset temperature $T^*$ to $T_{\mathrm{BKT}}$. Our paper calls attention to an experimental study demonstrating how both temperatures and, thus, their ratio may be currently accessible. They can be extracted from the same voltage-current measurements which are generally used to establish BKT physics. We use these observations to provide rough preliminary estimates of the magnitude of the geometric contributions in, for example, magic angle twisted bilayer graphene., Comment: 15 pages, 7 figures; published version

We show that jet emission from a Bose condensate with periodically driven interactions, a.k.a. "Bose fireworks", contains essential information on the condensate wavefunction, which is difficult to obtain using standard detection methods. We illustrate the underlying physics with two examples. When condensates acquire phase patterns from external potentials or from vortices, the jets display novel sub-structure, such as oscillations or spirals, in their correlations. Through a comparison of theory, numerical simulations and experiments, we show how one can quantitatively extract the phase and the helicity of a condensate from the emission pattern. Our work demonstrating the strong link between jet emission and the underlying quantum system, bears on the recent emphasis on jet sub-structure in particle physics.

This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii-Kosterlitz-Thouless (BKT) temperature $T_{\text{BKT}}$ as a function of \emph{attractive} pairing strength by associating it with the onset of "quasi-condensation" in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established Quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS-BEC crossover theory for fermions, leads to non-monotonic behavior for $T_{\text{BKT}}$ as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that $T_{\text{BKT}}$ has an absolute maximum of the order of $0.1 E_F$. We discuss how our results compare with those derived from the Nelson Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in $T_\text{BKT}$ followed by an often dramatic decrease before the system enters the BEC regime., Comment: 11 pages + 6 figures; updated version

Atomic Fermi gases provide an ideal platform for studying the pairing and superfluid physics, using a Feshbach resonance between closed channel molecular states and open channel scattering states. Of particular interest is the strongly interacting regime. We show that the closed-channel fraction $Z_{cc}$ provides an effective probe for the important many-body interacting effects, especially through its density dependence, which is absent from two-body theoretical predictions. Here we measure $Z_{cc}$ as a function of interaction strength and the Fermi temperature $T_\text{F}$ in a trapped $^6$Li superfluid throughout the entire BCS--BEC crossover, in quantitative agreement with theory when important thermal contributions outside the superfluid core are taken into account. Away from the deep BEC regime, the fraction $Z_{cc}$ is sensitive to $T_\text{F}$. In particular, our data show $Z_{cc} \propto T_\text{F}^{\alpha}$ with $\alpha=1/2$ at unitarity, in quantitative agreement with calculations of a two-channel pairing fluctuation theory, and $\alpha$ increases rapidly into the BCS regime, reflecting many-body interaction effects as predicted., Comment: Updated with the final version. This submission contains supplementary information as an ancillary file

Experiments on planar Josephson junction architectures have recently been shown to provide an alternative way of creating topological superconductors hosting accessible Majorana modes. These zero-energy modes can be found at the ends of a one-dimensional channel in the junction of a two-dimensional electron gas (2DEG) proximitized by two spatially separated superconductors. The channel, which is below the break between the superconductors, is not in direct contact with the superconducting leads, so that proximity coupling is expected to be weaker and less well-controlled than in the simple nanowire configuration widely discussed in the literature. This provides a strong incentive for this paper which investigates the nature of proximitization in these Josephson architectures. At a microscopic level we demonstrate how and when it can lead to topological phases. We do so by going beyond simple tunneling models through solving self-consistently the Bogoliubov-de Gennes equations of a heterostructure multicomponent system involving two spatially separated $s$-wave superconductors in contact with a normal Rashba spin-orbit-coupled 2DEG. Importantly, within our self-consistent theory we present ways of maximizing the proximity-induced superconducting gap by studying the effect of the Rashba spin-orbit coupling, chemical potential mismatch between the superconductor and 2DEG, and sample geometry on the gap. Finally, we note (as in experiment) a Fulde-Ferrell-Larkin-Ovchinnikov phase is also found to appear in the 2DEG channel, albeit under circumstances which are not ideal for topological superconducting phase., Comment: 19 pages, 14 figures

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 figures

A Bose condensate subject to a periodic modulation of the two-body interactions was recently observed to emit matter-wave jets resembling "fireworks" [Nature 551, 356(2017)]. In this paper, combining experiment with numerical simulation, we demonstrate that these "Bose fireworks" represent a late stage in a complex time evolution of the driven condensate. We identify a "density wave" stage which precedes jet emission and results from interference of matterwaves. The density waves self-organize and self-amplify without the breaking of long range translational symmetry. Importantly, this density wave structure deterministically establishes the template for the subsequent patterns of the emitted jets. Our simulations, in good agreement with experiment, also address the apparent asymmetry in the jet pattern and show it is fully consistent with momentum conservation.

We study fermion-parity-changing quantum phase transitions (QPTs) in platform Josephson junctions. These QPTs, associated with zero-energy bound states, are rather widely observed experimentally. They emerge from numerical calculations frequently without detailed microscopic insight. Importantly, they may incorrectly lend support to claims for the observations of Majorana zero modes. In this paper we present a fully consistent solution of the Bogoliubov-de Gennes equations for a multi-component Josephson junction. This provides insights into the origin of the QPTs. It also makes it possible to assess the standard self energy approximations which are widely used to understand proximity coupling in topological systems. The junctions we consider are complex and chosen to mirror experiments. Our full proximity calculations associate the mechanism behind the QPT as deriving from a spatially extended, proximity-induced magnetic "defect". This defect arises because of the insulating region which effects a local reorganization of the bulk magnetization in the proximitized superconductor. Our results suggest more generally that QPTs in Josephson junctions generally do not require the existence of spin-orbit coupling and should not be confused with, nor are they indicators of, Majorana physics., Comment: 15 pages, 8 figures

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.

In this paper we demonstrate the necessity of including the generally omitted collective mode contributions in calculations of the Meissner effect for non-uniform superconductors. We consider superconducting pairing with non-zero center of mass momentum, as is relevant to high transition temperature cuprates, cold atoms, and quantum chromodynamic superconductors. For the concrete example of the Fulde-Ferrell phase we present a quantitative calculation of the superfluid density, showing the collective mode contributions are not only appreciable but that they derive from the amplitude mode of the order parameter. This latter mode (related to the Higgs mode in a charged system) is generally viewed as being invisible in conventional superconductors. However, our analysis shows that it is extremely important in pair-density wave type superconductors, where it destroys superfluidity well before the mean-field order parameter vanishes.

Optical control and manipulation of cold atoms has become an important topic in condensed matter. Widely employed are optical lattice shaking experiments which allow the introduction of artificial gauge fields, the design of topological bandstructures, and more general probing of quantum critical phenomena. Here we develop new numerical methods to simulate these periodically driven systems by implementing lattice shaking directly. As a result we avoid the usual assumptions associated with a simplified picture based on Floquet dynamics. A demonstrable success of our approach is that it yields quantitative agreement with experiment, including Kibble-Zurek scaling. Importantly, we argue that because their dynamics corresponds to an effective non-linear Schr\"{o}dinger equation, these particular superfluid studies present a unique opportunity to address how general Floquet band engineering is affected by interactions. In particular, interactions cause instabilities at which the behavior of the system changes dramatically.

We show that topological phases should be realizable in readily available and well studied heterostructures. In particular we identify a new class of topological materials which are well known in spintronics: helical ferromagnet-superconducting junctions. We note that almost all previous work on topological heterostructures has focused on creating Majorana modes at the proximity interface in effectively two-dimensional or one-dimensional systems. The particular heterostructures we address exhibit finite range proximity effects leading to nodal superconductors with Majorana modes localized well away from this interface. To show this, we implement a Bogoliubov-de Gennes (BdG) proximity numerical scheme, which importantly, involves two finite dimensions in a three dimensional junction. Incorporating this level of numerical complexity serves to distinguish ours from alternative numerical BdG approaches which are limited by generally assuming translational invariance or periodic boundary conditions along multiple directions. With this access to the edges, we are then able to illustrate in a concrete fashion the wavefunctions of Majorana zero modes, and, moreover, address finite size effects. In the process we establish consistency with a simple analytical model.

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 figure

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 Communications

We present a general diagrammatic theory for determining consistent electromagnetic response functions in strongly correlated fermionic superfluids. The general treatment of correlations beyond BCS theory requires a new theoretical formalism not contained in the current literature. Among concrete examples are a rather extensive class of theoretical models which incorporate BCS-BEC crossover as applied to the ultra cold Fermi gases, along with theories specifically associated with the high-$T_c$ cuprates. The challenge is to maintain gauge invariance, while simultaneously incorporating additional self-energy terms arising from strong correlation effects. Central to our approach is the application of the Ward-Takahashi identity, which introduces collective mode contributions in the response functions and guarantees that the $f$-sum rule is satisfied. We outline a powerful and very general method to determine these collective modes in a manner compatible with gauge invariance. Finally, as an alternative approach, we contrast with the path integral formalism. Here, the calculation of gauge invariant response appears more straightforward. However, the collective modes introduced are essentially those of strict BCS theory, with no modification from correlation effects. Since the path integral scheme simultaneously addresses electrodynamics and thermodynamics, we emphasize that it should be subjected to a consistency test beyond gauge invariance, namely that of the compressibility sum-rule. We show how this sum-rule fails in the conventional path integral approach., Comment: 10 pages + 7 pages Supplementary Material

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.

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.

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 supplement

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 updated

We report the crystal structure, magnetization and neutron scattering measurements on the double perovskite Ba$_2$YOsO$_6$. The $Fm\overline{3}m$ space group is found both at 290~K and 3.5~K with cell constants $a_0 = 8.3541(4)$~{\AA} and $8.3435(4)$~\AA, respectively. Os$^{5+}$ ($5d^3$) ions occupy a non-distorted, geometrically frustrated face-centered-cubic (FCC) lattice. A Curie-Weiss temperature $\theta = -772$~K suggests the presence of a large antiferromagnetic interaction and a high degree of magnetic frustration. A magnetic transition to long range antiferromagnetic order, consistent with a Type I FCC state below $T_{\rm N} \sim 69$~K, is revealed by magnetization, Fisher heat capacity and elastic neutron scattering, with an ordered moment of 1.65(6)~$\mu_B$ on Os$^{5+}$. The ordered moment is much reduced from either the expected spin only value of $\sim 3 \mu_B$ or the value appropriate to $4d^3$ Ru$^{5+}$ in isostructural Ba$_2$YRuO$_6$ of 2.2(1)~$\mu_B$, suggesting a role for spin orbit coupling (SOC). Triple axis neutron scattering measurements of the order parameter suggest an additional first-order transition at $T = 67.45$~K, and the existence of a second ordered state. % Time-of-flight inelastic neutron results reveal a large spin gap $\Delta \sim 17$~meV, unexpected for an orbitally quenched, $d^3$ electronic configuration. We discuss this in the context of the $\sim 5$~meV spin gap observed in the related Ru$^{5+}$, $4d^3$ cubic double perovskite Ba$_2$YRuO$_6$, and attribute the $\sim 3$ times larger gap to stronger SOC present in this heavier, $5d$, osmate system., Comment: 10 pages, 9 figures

We investigate equilibration processes shortly after sudden perturbations are applied to ultracold trapped superfluids. We show the similarity of phase imprinting and localized density depletion perturbations, both of which initially are found to produce "phase walls". These planar defects are associated with a sharp gradient in the phase. Importantly they relax following a quite general sequence. Our studies, based on simulations of the complex time-dependent Ginzburg-Landau equation, address the challenge posed by these experiments: how a superfluid eventually eliminates a spatially extended planar defect. The processes involved are necessarily more complex than equilibration involving simpler line vortices. An essential mechanism for relaxation involves repeated formation and loss of vortex rings near the trap edge., Comment: Expanded version: 11 pages, 12 figures

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 figures

Essential to understanding the cuprate pseudogap phase is a study of the charge (and spin) response functions, which we address here via a consistent approach to the Fermi arcs and the Fermi pockets scenario of Yang, Rice and Zhang (YRZ). The two schemes are demonstrated to be formally similar, and to share a common physics platform; we use this consolidation to address the inclusion of vertex corrections which have been omitted in YRZ applications. We show vertex corrections can be easily implemented in a fashion analytically consistent with sum rules and that they yield important contributions to most observables. A study of the charge ordering susceptibility of the YRZ scenario makes their simple physics evident: they represent the inclusion of charged bosonic, spin singlet degrees of freedom, and are found to lead to a double peak structure., Comment: 5 pages, 1 figure, with included 4-page Supplementary Material

We address the physics of equilibration in ultracold atomic gases following a quench of the interaction parameter. We focus on the momentum distribution of the excitations, $n_{\mathbf k}$, and observe that larger ${\mathbf k}$ modes will equilibrate faster, as has been claimed in recent experimental work. We identify three time regimes. At short times $n_{\mathbf k}$ exhibits oscillations; these are damped out at intermediate times where the system appears to be in a false-equilibrium. Finally, at longer times, full equilibration occurs. This false-equilibrium is associated with the necessarily slower relaxation of the condensate which sufficiently high ${\mathbf k}$-states (of the excitation response) will then quasi-adiabatically follow. Our work bears on the recent literature focus on interaction quench experiments. We take issue with the fact that theories to date assume that the oscillatory regime is adequate for addressing experiments., Comment: v2: major rewriting, 6 pages, 3 figures

We present numerical simulations of phase imprinting experiments in ultracold trapped Fermi gases which are in good agreement with recent, independent experimental results. Our focus is on the sequence and evolution of defects using the fermionic time-dependent Ginzburg-Landau equation, which contains dissipation necessary for equilibration. In contrast to other simulations we introduce small, experimentally unavoidable symmetry breaking, particularly that associated with thermal fluctuations and with the phase imprinting tilt angle, and illustrate their dramatic effects. The former causes vortex rings in confined geometries to move to the trap surface and rapidly decay into more stable vortex lines, as appears consistent with recent experimental claims. The latter aligns the precessing and relatively long-lived vortex filaments, rendering them difficult to distinguish from solitons., Comment: 5 pages, 2 figures, with included supplementary material

In this paper we compare Bose transport in normal phase atomic gases with its counterpart in Fermi gases, illustrating the non-universality of two dimensional bosonic transport associated with different dissipation mechanisms. Near the superfluid transition temperature $T_c$, a striking similarity between the fermionic and bosonic transport emerges because super-conducting(fluid) fluctuation transport for Fermi gases is dominated by the bosonic, Cooper pair component. As in fluctuation theory, one finds that the Seebeck coefficient changes sign at $T_c$ and the Lorenz number approaches zero at $T_c$. Our findings appear semi-quantitatively consistent with recent Bose gas experiments., Comment: v3: longer version 8 pages, 3 figures

We address quantum oscillation experiments in high Tc superconductors and the evidence from these experiments for a pseudogap versus a Fermi liquid phase at high magnetic fields. As a concrete alternative to a Fermi liquid phase, the pseudogap state we consider derives from earlier work within a Gor'kov-based Landau level approach. Here the normal state pairing gap in the presence of high fields is spatially non-uniform, incorporating small gap values. These, in addition to d-wave gap nodes, are responsible for the persistence of quantum oscillations. Important here are methodologies for distinguishing different scenarios. To this end we examine the temperature dependence of the oscillations. Detailed quantitative analysis of this temperature dependence demonstrates that a high field pseudogap state in the cuprates may well "masquerade" as a Fermi liquid., Comment: 5 pages, 3 figures

We address conservation laws associated with current, momentum and energy and show how they can be satisfied within many body theories which focus on pair correlations. Of interest are two well known t-matrix theories which represent many body theories which incorporate pairing in the normal state. The first of these is associated with Nozieres Schmitt-Rink theory, while the second involves the t-matrix of a BCS-Leggett like state as identified by Kadanoff and Martin. T-matrix theories begin with an ansatz for the single particle self energy and are to be distinguished from $\Phi$-derivable theories which introduce an ansatz for a particular contribution to the thermodynamical potential. Conservation laws are equivalent to Ward identities which we address in some detail here. Although $\Phi$-derivable theories are often referred to as "conserving theories", a consequence of this work is the demonstration that these two t-matrix approaches similarly can be made to obey all conservation laws. Moreover, simplifying approximations in $\Phi$-derivable theories, frequently lead to results which are incompatible with conservation., Comment: 12 pages, 1 figure

We present a theoretical study of the compressibility, $\kappa$, in a Fermi gas with attractive contact interactions, providing predictions for the strongly-attractive regime and the superfluid phase. Our work emphasizes the compressibility sum rule and gauge invariance as constraints on $\kappa$ and we show how within a particular $t$-matrix approach, these can be satisfied in the normal phase when no approximations are made. For tractability, approximations must be introduced, and it is believed that thermodynamical approaches to $\kappa$ are more reliable, than correlation function based schemes. Contrasting with other studies in the literature, we present thermodynamic calculations of $\kappa$; these yield semi-quantitative agreement with experiment and provide physical insight into similar results obtained via quantum Monte Carlo simulations., Comment: 5 pages, 1 figure

We study the static and dynamic behavior of charge ordering within a d-wave pair pseudogap (pg) scenario. This is addressed using a density-density correlation function derived from the standard pg self energy, $\Sigma$ and compatible with the longitudinal and transverse sum rules. The broadening factor $\gamma$ in $\Sigma$ reflects the breaking of pairs into constituent fermions. We apply this form for $\Sigma$ (derived elsewhere for high fields) to demonstrate the existence of quantum oscillations in a non-Fermi liquid pg state. Our conclusion is that the pseudogap-induced pairbreaking, via $\gamma$, allows the underlying fermiology to be revealed; in YBCO, finite $\omega$ and $\gamma$ enable antinodal fluctuations, despite the competition with a d-wave gap in the static and superconducting limits., Comment: 5 pages, 3 figures

In this paper we study the transient dynamics of a Bose superfluid subsequent to an interaction quench. Essential for equilibration is a source of dissipation which we include following the approach of Caldeira and Leggett. Here we solve the equations of motion exactly by integrating out an environmental bath. We thereby derive precisely the time dependent density correlation functions with the appropriate analytic and asymptotic properties. The resulting structure factor exhibits the expected damping and thereby differs from that of strict Bogoliubov theory. These damped sound modes, which reflect the physics beyond mean field approaches, are characterized and the structure factors are found to compare favorably with experiment., Comment: 5 pages, 2 figures

In this paper we deduce transport properties in the presence of a pseudogap associated with precursor superconductivity. Our theoretical analysis is based on the widely adopted self energy expression reflecting this normal state gap, which has appeared in interpretations of photoemission and in other experiments. Thus, it should be generally applicable. Here we address THz conductivity $\sigma (\omega) = \sigma_1(\omega) + i \sigma_2(\omega)$ measurements in the underdoped high temperature superconductors and arrive at reasonable agreement between theory and recent experiment for both $\sigma_1$ and $\sigma_2$ above and below $T_c$., Comment: 8 pages, 2 figures

In this paper we apply the emerging- consensus understanding of the fermionic self energy deduced from angle resolved photoemisssion spectroscopy (ARPES) experiments to deduce the implications for orbital diamagnetism in the underdoped cuprates. Many theories using many different starting points have arrived at a broadened BCS-like form for the normal state self energy associated with a d-wave excitation gap, as is compatible with ARPES data. Establishing compatibility with the f-sum rules, we show how this self energy, along with the constraint that there is no Meissner effect in the normal phase are sufficient to deduce the orbital susceptibility. We conclude, moreover, that diamagnetism is large for a d-wave pseudogap. Our results should apply rather widely to many theories of the pseudogap, independent of the microscopic details., Comment: 15 pages, 8 figures