Charged Superfluids Research Articles

Electrodynamics of Superconductors: From Lorentz to Galilei at Zero Temperature.

We discuss the derivation of the electrodynamics of superconductors coupled to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper pairs. Our results are obtained at zero temperature where, according to the third law of thermodynamics, the entropy of the system is zero. In the nonrelativistic limit, we obtain a Galilei-invariant superconducting system, which differs with respect to the familiar Schrödinger-like one. From this point of view, there are similarities with the Pauli equation of fermions, which is derived from the Dirac equation in the nonrelativistic limit and has a spin-magnetic field term in contrast with the Schrödinger equation. One of the peculiar effects of our model is the decay of a static electric field inside a superconductor exactly with the London penetration length. In addition, our theory predicts a modified D'Alembert equation for the massive electromagnetic field also in the case of nonrelativistic superconducting matter. We emphasize the role of the Nambu-Goldstone phase field, which is crucial to obtain the collective modes of the superconducting matter field. In the special case of a nonrelativistic neutral superfluid, we find a gapless Bogoliubov-like spectrum, while for the charged superfluid we obtain a dispersion relation that is gapped by the plasma frequency.

Electromagnetic fluctuation and collective modes in relativistic bosonic superfluid in mixed dimensions

In Gaussian approximation, we investigate the marginal electromagnetic fluctuation in models of charged relativistic bosonic superfluids in three and two spatial dimensions at zero temperature. The electromagnetism is modeled by the ordinary Maxwell term and the non-local pseudo-electrodynamics action in these dimensions respectively. We explore the collective excitations in these systems by integrating the superfluid velocity fields. We unveil that different collectives mode dispersions are results of the competition between different characteristic scales of speed and that between short-ranged and long-ranged interactions. In (3+1) dimensions, we derive the roton mode reminiscent of what was discovered in the context of the free relativistic Bose–Einstein condensate as a generalization of the Higgs mode and determine the necessary and sufficient condition for the roton to exist. In (2+1) dimensions, besides solving the dispersion relation for the surface plasmon, we prove there cannot be roton-like excitation in this model as opposed to its (3+1) dimensional counterpart, and additionally derive the asymptotic lines of the dispersion in the limits of long wavelength and short distance. These asymptotic dispersions are supplied with alternative perspective using duality.

Collective excitations of a charged Fermi superfluid in the BCS-BEC crossover

We consider collective excitations in the superfluid state of Fermi condensed charged gases. The dispersion and damping of collective excitations at nonzero temperatures are examined, and the coexistence and interaction of different branches of collective excitations: plasma oscillations, pair-breaking Higgs modes, and Carlson–Goldman phonon-like excitations are taken into account. The path integral methods for superfluid Fermi gases and for Coulomb gas are combined into a unified formalism that extends the Gaussian fluctuation approximation to account for plasmonic modes. This approximation of Gaussian pair and density fluctuations is able to describe all branches of collective excitations existing in a charged superfluid. The spectra of collective excitations are determined in two ways: from the spectral functions and from the complex poles of the fluctuation propagator. A resonant avoided crossing of different modes is shown. It is accompanied by resonant enhancement of the response provided by the pair-breaking modes due to their interaction with plasma oscillations. This may facilitate the experimental observation of the pair-breaking modes.

Low-Lying Collective Excitations of Superconductors and Charged Superfluids

We investigate theoretically the momentum-dependent frequency and damping of low-lying collective excitations of superconductors and charged superfluids in the BCS–BEC crossover regime. The study is based on the Gaussian pair-and-density fluctuation method for the propagator of Gaussian fluctuations of the pair and density fields. Eigenfrequencies and damping rates are determined in a mutually consistent nonperturbative way as complex poles of the fluctuation propagator. Particular attention is paid to new features with respect to preceding theoretical studies, which were devoted to collective excitations of superconductors in the far BCS regime. We find that at a sufficiently strong coupling, new branches of collective excitations appear, which manifest different behavior as functions of the momentum and the temperature.

Spectrum of a supersymmetric color superconductor

We have recently shown that the ground state of mathcal{N} = 4, SU(Nc) super Yang- Mills coupled to Nf ≪ Nc flavors, in the presence of non-zero isospin and R-symmetry charges, is a supersymmetric, superfluid, color superconductor. The holographic description consists of Nf D7-brane probes in AdS5×S5 with electric and instantonic fields on their worldvolume. These correspond to fundamental strings and D3-branes dissolved on the D7-branes, respectively. Here we use this description to determine the spectrum of mesonic excitations. As expected for a charged superfluid we find non-relativistic, massless Goldstone modes. We also find extra ungapped modes that are not associated to the breaking of any global symmetries but to the supersymmetric nature of the ground state. If the quark mass is much smaller than the scale of spontaneous symmetry breaking a pseudo-Goldstone boson is also present. We highlight some new features that appear only for Nf> 2. We show that, in the generic case of unequal R-symmetry charges, the dissolved strings and D3-branes blow up into a D5-brane supertube stretched between the D7-branes.

Mixture of two unequally charged superfluids in a magnetic field

The artificial magnetic fields engineered for ultracold gases depend on the internal structure of the neutral atoms. Therefore the components of a mixture composed of two atomic gases can exhibit a different response to an artificial magnetic field. Such a mixture can be interpreted as a mixture of two atomic gases, carrying different synthetic charges. We consider such mixtures of two superfluids with unequal synthetic charges in a ring trap subject to a uniform artificial magnetic field. The charge imbalance in such a mixture changes the distribution of excited particles over angular momentum states compared to that of an equally charged mixture. This microscopic difference exhibits macroscopic consequences, such as the occurrence of an angular momentum transfer between two unequally charged components. Due to the interfluid atomic interactions in a ring, the angular momentum transfer can create a counterflowing persistent current in the weakly charged superfluid. Even in the limiting case of a charged and an uncharged superfluid mixture, a persistent current can be induced in the uncharged superfluid, despite the fact that it is not directly coupled to the magnetic field. The stability analysis shows that the induction depends on the interplay between the interfluid interaction and the applied magnetic field. We obtain instability boundaries of the system and construct phase diagrams as a function of the interfluid interaction and the magnetic field. We investigate these properties employing the Bogoliubov approximation.

Glitches as probes of neutron star internal structure and dynamics: Effects of the superfluid-superconducting core

Glitches, sudden spin-up of pulsars with subsequent recovery, provide us with a unique opportunity to investigate various physical processes, including the crust-core coupling, distribution of reservoir angular momentum within different internal layers, spin-up in neutral and charged superfluids and constraining the equation of state of the neutron star (NS) matter. In this work, depending on the dynamic interaction between the vortex lines and the nuclei in the inner crust, and between the vortex lines and the magnetic flux tubes in the outer core, various types of relaxation behavior are obtained and confronted with the observations. It is shown that the glitches have strong potential to deduce information about the cooling behavior and interior magnetic field configuration of NSs. Some implications of the relative importance of the external spin-down torques and the superfluid internal torques for recently observed unusual glitches are also discussed.

Effective theory of vortices in two-dimensional spinless chiralp-wave superfluids

We propose a $\mathbb{U}(1) \times \mathbb{Z}_2$ effective gauge theory for vortices in a $p_x+ip_y$ superfluid in two dimensions. The combined gauge transformation binds $\mathbb{U}(1)$ and $\mathbb{Z}_2$ defects so that the total transformation remains single-valued and manifestly preserves the the particle-hole symmetry of the action. The $\mathbb{Z}_2$ gauge field introduces a complete Chern-Simons term in addition to a partial one associated with the $\mathbb{U}(1)$ gauge field. The theory reproduces the known physics of vortex dynamics such as a Magnus force proportional to the superfluid density. More importantly, it predicts a universal Abelian phase, $\exp(i\pi/8)$, upon the exchange of two vortices. This phase is modified by non-universal corrections due to the partial Chern-Simon term, which are nevertheless screened in a charged superfluid at distances that are larger than the penetration depth.

Skyrmions in a density wave state: A mechanism for chiral superconductivity

Broken symmetry states characterizing density waves of higher angular momentum in correlated electronic systems are intriguing objects. In the scheme of characterization by angular momentum, conventional charge and spin density waves correspond to zero angular momentum. Here, we explore a class of exotic density wave states that have topological properties observed in recently discovered topological insulators. These rich topological density wave states deserve closer attention in not only high temperature superconductors but in other correlated electron states, as in heavy fermions, of which an explicit example will be discussed. The state discussed has nontrivial charge [Formula: see text] skyrmionic spin texture. These skyrmions can condense into a charged superfluid. Alternately, they can fractionalize into merons and anti-merons. The fractionalized particles that are confined in skyrmions in the insulating phase, can emerge at a deconfined quantum critical point, which separates the insulating and the superconducting phases. These fractional particles form a two-component spin-singlet chiral [Formula: see text] wave superconducting state that breaks time reversal symmetry. Possible connections of this exotic order to the superconducting state in the heavy-fermion material [Formula: see text] are suggested. The direct evidence of such a chiral superconducting state is polar Kerr effect that was observed recently.

Experimental consequences of predicted charge rigidity of superconductors

The theory of hole superconductivity predicts that in superconductors the charged superfluid is about a million times more rigid than the normal electron fluid. We point out that this physics should give rise to large changes in the bulk and surface plasmon dispersion relations of metals entering the superconducting state, that have not yet been experimentally detected and would be in stark contradiction with the expected behavior within conventional BCS-London theory. We also propose that this explains the puzzling experimental observations of Avramenko et al. [1] on electron sound propagation in superconductors and the puzzling experiments of de Heer et al. [2] detecting large electric dipole moments in small metal clusters, as well as the Tao effect [3] on aggregation of superconducting microparticles in an electric field. Associated with the enhanced charge rigidity is a large increase in the electric screening length of superconductors at low temperatures that has not yet been experimentally detected. The physical origin of the enhanced charge rigidity and its relation to other aspects of the theory of hole superconductivity is discussed.

Ultracold fermions in real or fictitious magnetic fields: BCS-BEC evolution and type-I–type-II transition

We study ultracold neutral fermion superfluids in the presence of fictitious magnetic fields, as well as charged fermion superfluids in the presence of real magnetic fields. Charged fermion superfluids undergo a phase transition from type-I to type-II superfluidity, where the magnetic properties of the superfluid change from being a perfect diamagnet without vortices to a partial diamagnet with the emergence of the Abrikosov vortex lattice. The transition from type-I to type-II superfluidity is tuned by changing the scattering parameter (interaction) for fixed density. We also find that neutral fermion superfluids such as $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ are extreme type-II superfluids and are more robust to the penetration of a fictitious magnetic field in the BCS-BEC crossover region near unitarity, where the critical fictitious magnetic field reaches a maximum as a function of the scattering parameter (interaction).

Universal Mechanism for Breaking thehc/2ePeriodicity of Flux-Induced Oscillations in Small Superconducting Rings

A universal mechanism of restoration of minimal hc/e periodicity in the response of small superconducting rings or cylinders to the magnetic flux is proposed. The mechanism is based on the dependence of the Cooper pair's internal energy on its motion as a whole and does not rely on the presence of quasiparticles in the system. The thermal equilibrium hc/2e periodicity is broken by an offset of the transition between different current-carrying states. The magnitude of the offset is calculated for an s-wave superconducting cylinder of radius R in the limit R>>xi_{0}, where xi_{0} is the BCS coherence length and turns out to be exponentially small. A possible enhancement of the effect for nodal superconductors is suggested. Similar conclusions should also apply to the response of charged or neutral superfluids to rotation.

The interface between quantum mechanics and general relativity

The generation, as well as the detection, of gravitational radiation by means of charged superfluids is considered. One example of such a “charged superfluid” consists of a pair of Planck-mass-scale, ultracold “Millikan oil drops”, each with a single electron on its surface in a strong magnetic field, in which the oil of the drop is replaced by superfluid helium. When levitated in a magnetic trap, and subjected to microwave-frequency electromagnetic radiation, a pair of such “Millikan oil drops” separated by a microwave wavelength can become an efficient quantum transducer between quadrupolar electromagnetic and gravitational radiation. This leads to the possibility of a Hertz-like experiment, in which the source of microwave-frequency gravitational radiation consists of one pair of “Millikan oil drops” driven by microwaves, and the receiver of such radiation consists of another pair of “Millikan oil drops” in the far field driven by the gravitational radiation generated by the first pair. The second pair then back-converts the gravitational radiation into detectable microwaves. The enormous enhancement of the conversion efficiency for these quantum transducers over that for electrons arises from the fact that there exists macroscopic quantum phase coherence in these charged superfluid systems.

Critical Behavior of High Temperature Superconductors

We consider the scaling behavior in the critical domain of superconductors at zero external magnetic field. The Josephson's relation for a charged superfluid is proved without assuming the hyperscaling relation. On the other hand we discuss the dual Ginzburg-Landau model. In this dual model, due to the presence of two mass scales, a continuous family of non equivalent scalings can be defined. The relevant critical regimes are identified, and the corresponding critical exponents are predicted.

Scaling critical behavior of superconductors at zero magnetic field

We consider the scaling behavior in the critical domain of superconductors at zero external magnetic field. The first part of the paper is concerned with the Ginzburg-Landau model in the zero-magnetic-field Meissner phase. We discuss the scaling behavior of the superfluid density and we give an alternative proof of Josephson's relation for a charged superfluid. This proof is obtained as a consequence of an exact renormalization group equation for the photon mass. We obtain Josephson's relation directly in the form ${\ensuremath{\rho}}_{s}\ensuremath{\sim}{t}^{\ensuremath{\nu}};$ that is, we do not need to assume that the hyperscaling relation holds. Next, we give an interpretation of a recent experiment performed in thin films of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ We argue that the measured mean-field-like behavior of the penetration depth exponent ${\ensuremath{\nu}}^{\ensuremath{'}}$ is possibly associated with a nontrivial critical behavior and we predict the exponents $\ensuremath{\nu}=1$ and $\ensuremath{\alpha}=\ensuremath{-}1$ for the correlation length and specific heat, respectively. In the second part of the paper we discuss the scaling behavior in the continuum dual Ginzburg-Landau model. After reviewing lattice duality in the Ginzburg-Landau model, we discuss the continuum dual version by considering a family of scalings characterized by a parameter $\ensuremath{\zeta}$ introduced such that ${m}_{h,0}^{2}\ensuremath{\sim}{t}^{\ensuremath{\zeta}},$ where ${m}_{h,0}$ is the bare mass of the magnetic induction field. We discuss the difficulties in identifying the renormalized magnetic induction mass with the photon mass. We show that the only way to have a critical regime with ${\ensuremath{\nu}}^{\ensuremath{'}}=\ensuremath{\nu}\ensuremath{\approx}2/3$ is having $\ensuremath{\zeta}\ensuremath{\approx}4/3,$ that is, with ${m}_{h,0}$ having the scaling behavior of the renormalized photon mass.

Nonadiabatic distortion in the current distribution around a moving vortex

We study the phase distribution around a vortex in uniform motion. We consider both the cases of neutral and charged superfluids. The motion of the vortex causes the density of the system to fluctuate. This in turn produces a compensating current, thus ensuring current conservation locally. We explicitly calculate this current.

Erratum: Vortex motion in charged and neutral superfluids: A hydrodynamic approach [Phys. Rev. B57, 575 (1998)

Erratum: Vortex motion in charged and neutral superfluids: A hydrodynamic approach [Phys. Rev. B<b>57</b>, 575 (1998)

Vortex motion in charged and neutral superfluids: A hydrodynamic approach

We derive a Galilean invariant expression for the electric field induced by a vortex moving through a charged superfluid at $T=0$, which holds for any superconductor, from the dirty to the superclean limit. The contribution of different areas around the vortex to the average electric field and to the charge distribution is analyzed. The results are extended to a neutral system, where the chemical potential takes over the role of the electrostatic potential in the charged situation. Different contributions to the vortex mass in charged and neutral superfluids are brought together for comparison and discussion.

ADIABATIC EFFECTIVE ACTION FOR VORTICES IN NEUTRAL AND CHARGED SUPERFLUIDS

Adiabatic effective action for vortices in neutral and charged superfluids at zero temperature are calculated using the topological Landau-Ginzburg theory recently proposed by Hatsuda, Yahikozawa, Ao and Thouless, and vortex dynamics are examined. The Berry phase term arising in the effective action naturally yields the Magnus force in both neutral and charged superfluids. It is shown that in neutral superfluid there is only one degree of freedom, namely the center of vorticities, and the vortex energy is proportional to the sum of all vorticities so that it is finite only for the vanishing total vorticity of the system. On the other hand the effective mass and the vortex energy for a vortex in charged superfluids are defined individually as expected. The effects of the vortex core on these quantities are also estimated. The possible depinning scenario which is governed by the Magnus force and the inertial mass is also discussed.

Theory of Cooper-pair mass spectroscopy by the current-induced contact-potential difference.

The creation of contactless Cooper-pair mass spectroscopy based on the Bernoulli-Venturi effect in thin superconducting films is suggested. The preparation of layered metal-insulator-superconductor-type heterostructures and standard electronics are necessary for the realization of the method. Two electrodes are patterned from the metallic layer: a circle and concentric-ring electrode. The currents in the superconducting film are induced by a drive coil concentric to the electrodes. The Bernoulli potential of the charged Cooper-pair superfluid creates a measurable electric polarization of gate electrodes of this plane-capacitor device. The current-induced contact-potential difference is limited by the Ginzburg-Landau potential -${\mathit{a}}_{\mathrm{GL}}$(T)= 1/2\ensuremath{\Elzxh}${\mathit{e}}^{\mathrm{*}}$${\mathit{H}}_{\mathit{c}2}$(T)/${\mathit{m}}^{\mathrm{*}}$c=${\mathrm{\ensuremath{\Elzxh}}}^{2}$/2${\mathit{m}}^{\mathrm{*}}$${\ensuremath{\xi}}^{2}$(T). The additional charge of the polarized circular electrode has the same sign as the free charge carriers of the superconductor.