Unconventional Superfluids Research Articles

Chirald-Wave Superfluid in Periodically Driven Lattices

A chiral d-wave superfluid is a preliminary example of interacting topological matter. However, unlike s-wave superfluids prevalent in nature, its existence requires a strong d-wave interaction, a criterion that is difficult to access in ordinary systems. There is no experimental observation of such unconventional superfluid at the moment. Here, we present a new principle for creating a two-dimensional (2D) chiral d-wave superfluid using periodically driven lattices. Because of an imprinted 2D pseudospin-orbit coupling, where the sublattice index serves as the pseudospin, the s-wave interaction between two hyperfine spin states naturally creates a chiral d-wave superfluid. This scheme can be directly implemented in current experiments.

Аномальная сверхпроводимость и сверхтекучесть в фермионных системах с отталкиванием

We discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We construct phase diagrams of these systems and find the areas of the superconducting state in free space, as well as on the lattice in the framework of the Fermi-gas model with hard-core repulsion, the Hubbard model, the Shubin-Vonsovsky model, and the $t-J$ model. We demonstrate that the critical superconducting temperature can be greatly increased in the spin-polarized case or in a two-band situation already at low densities. The proposed theory is based on the Kohn-Luttinger mechanism or its generalizations and explains or predicts anomalous $p$-, $d$-, and $f$-wave pairing in various materials, such as high-temperature superconductors, the idealized monolayer and bilayer of doped graphene, heavy-fermion systems, layered organic superconductors, superfluid $^3$He, spin-polarized $^3$He mixtures in $^4$He, ultracold quantum gases in magnetic traps, and optical lattices.

Absence of quasiclassical coherence in mean-field dynamics of bosons in a kinetically frustrated regime

We study numerically the dynamics of bosons on a triangular lattice after quenching both the on-site interactions and the external trapping potential to negative values. In a similar situation on the square lattice, the dynamics can be understood in terms of an effectively reversed Hamiltonian. On the triangular lattice, however, the kinetic part of the reversed Hamiltonian is frustrated and whether coherence can develop is an open question. The strength of the frustration can be changed by tuning the ratio of the hopping rates along different directions. We calculate time-of-flight images at different times after the quench for different values of the hopping anisotropy. We observe peaks at the maxima of the original non-interacting dispersion relation both in the isotropic case and also in the rhombic limit of high hopping anisotropy. For an intermediate value, however, no coherence develops up to the longest simulation times. These results imply that experiments along similar lines could study unconventional superfluidity of bosons and aspects of the conjectured spin-liquid behavior in the hard-core limit.

Unconventional superfluidity in quasi-one-dimensional systems

We show that an unconventional superfluid triggered by spin-orbit coupling is realized for repulsively interacting quasi-one-dimensional fermions. A competition between spin-singlet and -triplet pairings occurs due to the breaking of inversion symmetry. We show that both superfluid correlations decay algebraically with the same exponent except for special coupling constants for which a dominant superfluid is controlled by the spin-orbit coupling. We also discuss a possible experiment to observe such phases with cold atoms.

Unconventional superfluid in a two-dimensional Fermi gas with anisotropic spin-orbit coupling and Zeeman fields.

We study the phase diagram of a two-dimensional ultracold Fermi gas with the synthetic spin-orbit coupling (SOC) that has recently been realized at the National Institute of Standards and Technology (NIST). Because of the coexistence of anisotropic SOC and effective Zeeman fields in the NIST scheme, the system shows a rich structure of phase separation involving exotic gapless superfluid states and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states with different center-of-mass momenta. In particular, we characterize the stability region of FFLO states and demonstrate their unique features under SOC. We then show that the effective transverse Zeeman field in the NIST scheme can qualitatively change the landscape of the thermodynamic potential which leads to intriguing effects such as the disappearance of pairing instability, the competition between different FFLO states, and the stabilization of a fully gapped FFLO state. These interesting features may be probed, for example, by measuring the insitu density profiles or by the momentum-resolved radio-frequency spectroscopy.

State engineering for a Bose-Einstein condensate in an optical lattice by means of a periodic sublattice of dissipative sites

We introduce the notion of dissipative periodic lattice as an optical lattice with periodically distributed dissipative sites and argue that it allows to engineer unconventional Bose-Einstein superfluids with the complex-valued order parameter. We consider two examples, the one-dimensional dissipative optical lattice, where each third site is dissipative, and the dissipative honeycomb optical lattice, where each dissipative lattice site neighbors three non-dissipated sites. The tight-binding approximation is employed, which allows one to obtain analytical results. In the one-dimensional case the condensate is driven to a coherent Bloch-like state with non-zero quasimomentum, which breaks the translational periodicity of the dissipative lattice. In the two-dimensional case the condensate is driven to a zero quasimomentum Bloch-like state, which is a coherent superposition of four-site discrete vortices of alternating vorticity with the vortex centers located at the dissipative sites.

Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices

Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-T$_c$ superconductivity and unconventional magnetism. In contrast, phenomena in superfluids -- especially in ultracold quantum gases -- are commonly well described by the lowest orbital and a real order parameter. Here, we report on the observation of a novel multi-orbital superfluid phase with a {\it complex} order parameter in binary spin mixtures. In this unconventional superfluid, the local phase angle of the complex order parameter is continuously twisted between neighboring lattice sites. The nature of this twisted superfluid quantum phase is an interaction-induced admixture of the p-orbital favored by the graphene-like band structure of the hexagonal optical lattice used in the experiment. We observe a second-order quantum phase transition between the normal superfluid (NSF) and the twisted superfluid phase (TSF) which is accompanied by a symmetry breaking in momentum space. The experimental results are consistent with calculated phase diagrams and reveal fundamentally new aspects of orbital superfluidity in quantum gas mixtures. Our studies might bridge the gap between conventional superfluidity and complex phenomena of orbital physics.

Acoustic properties of superfluid 3He in 97% aerogel

Superfluid 3He in silica aerogel provides a unique system for studying the effect of quenched disorder in the unconventional superfluid. We have performed longitudinal ultrasound (5.7 MHz) attenuation and sound velocity measurements of the superfluid 3He in 97% porosity aerogel. The attenuation and sound velocity were determined by direct propagation of sound pulses through the medium in a wide range of temperatures, down to 400 μK. The superfluid transition, marked by the increase in sound velocity, is substantially suppressed from that in 98% aerogel used in most of studies. The superfluid fraction determined from the sound velocity is less than 0.02 even at the lowest temperature.

Effect of correlated disorder on the temperature of unconventional cooper pairing: 3He in aerogel

Using liquid 3He in aerogel as an example, it is shown that correlations in positions of impurities affect the temperature $T_c$ of transition of Fermi liquid in an unconventional superfluid or superconductive state. The effect is significant if the correlation length for impurities is greater than the coherence length in the superfluid or superconductive state $\xi_0$. For 3He in aerogel the suppression of $T_c$ is expressed in terms of the structure factor of aerogel. With the account of the fractal structure of aerogel a simple expression is obtained for the decrease of $T_c$ from its clean value. This expression is in a satisfactory agreement with experimental data.

Critical behavior in unconventional ferromagnetic superconductors

New critical behavior in unconventional superconductors and superfluids is established and described by the Wilson-Fisher renormalization-group method. For certain ordering symmetries a new type of fluctuation-driven first order phase transitions at finite and zero temperature are predicted. The results can be applied to a wide class of ferromagnetic superconducting and superfluid systems, in particular, to itinerant ferromagnets as UGe2 and URhGe.

Transport in unconventional superconductors: Application to liquidHe3in aerogel

We consider quite generally the transport of energy and momentum in unconventional superconductors and Fermi superfluids to which both impurity scattering (treated within the $t$-matrix approximation) and inelastic scattering contributes. A new interpolation scheme for the temperature dependence of the transport parameters is presented which preserves all analytical results available for $T\ensuremath{\rightarrow}0$ and $T\ensuremath{\rightarrow}{T}_{c}$ and allows for a particularly transparent physical representation of the results. The two scattering processes are combined using Matthiessen's rule coupling. This procedure is applied for the first time to $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$ in aerogel. Here, at the lowest temperatures, a universal ratio of the thermal conductivity and the shear viscosity is found in the unitary limit, which is akin to the Wiedemann-Franz law.

BCS-BEC Crossover in a Gas of Fermi Atoms with ap-Wave Feshbach Resonance

We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasimolecules with finite orbital angular momenta Lz=+/-1,0, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper pairs and molecules which are not Bose condensed.

Vortices Observed and to be Observed

Linear defects are generic in continuous media. In quantum systems they appear as lopological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density atomic Bose-Einstein condensates as quantized vortex lines. We discuss unconventional vortices in unconventional superfluids and superconductors, which have been observed or have to be observed, such as continuous singly and doubly quantized vortices in 3 He-A and chiral Bose condensates; half-quantum vortices (Alice strings) in 3 He-A and in nonchiral Bose condensates; Abrikosov vortices with fractional magnetic flux in chiral and d-wave superconductors; vortex sheets in 3 He-A and chiral superconductors; the nexus combined object formed by vortices and monopoles. Some properties of vortices related to the fermionic quasiparticles living in the vortex core are also discussed.

Superfluid [formula omitted] and unconventional superconductors

The properties of superfluid 3 He as a well-studied model system of unconventional superfluidity are reviewed. This will include a discussion of BCS theory extended to spin triplet p-wave states, the nodal structure of the energy spectrum and its implications for the thermodynamic and transport properties. Similarities with the model states proposed for the heavy fermion and high T c cuprate superconductors will be pointed out. Then, the existence of textures, vortices and other topological defects in the order parameter field of s- 3 He is discussed and contrasted with unconventional superconductivity in metals. Order parameter collective modes in s- 3 He and their possible counterparts in superconductors are considered. The role of the electric charge in superconductors and its coupling to the electromagnetic field will be analyzed. The last part will cover some recent results on nonlocal and nonlinear corrections to the magnetic penetration depth.

3He in Aerogel – an Inhomogeneously Disordered Unconventional Superfluid

We have examined the superfluidity of3He in 98.2% porous silica aerogel with up to 34% 4He at 21.6 bar. The mixture is phase-separated for4He fractions between ∼ 11% and 34%. The4He-rich, phase preferentially occupies the regions of highest silica density in the aerogel, thus modifying the distribution of the correlated disorder seen by superftuid3He. The3He Tcincreases slightly with4He content while the superfluid fraction decreases rapidly. This behavior is inconsistent with that of3He in a homogeneously scattering medium and is analogous to that of a granular superconductor.

Chiral fermions in gapless fermi superfluids and on vortices in superconductors

Gapless fermions exist in unconventional superfluids and superconductors and within the cores of vortices in conventional superconductors. They are responsible for the anomalous behavior of the Fermi systems at low T.

Spin-Polarized Quantum Fluids and Solids

The spin-polarized phases of the quantum fluids and solids, liquid 3He, solid 3He, and spin-aligned hydrogen have generated considerable excitement over the past fifteen years. The introduction of high magnetic fields (B ∼ 10–30 T) in conjunction with low temperatures (T ≲ 100 mK) has given rise to opportunities for exploring some of the new phases predicted for these materials. There is a broad range of physical phenomena that can be accessed in this regime of parameter space—unconventional superfluidity, unusual magnetic ordering, Bose-Einstein condensation and Kosterlitz-Thouless transitions, to name a few. This is most surprising since this plethora of complicated states of matter are present in some of the most uncomplicated materials. The rich variety of phases found in these materials are all examples of collective phenomena of quantum many-body systems, and they serve as prototypes for developing an understanding of magnetism and order/disorder processes in other systems, and for the design and characterization of new materials.

Anyonization of lattice Chern-Simons theory

We formulate Hamiltonian lattice Chern-Simons theory which has the property that the Chern-Simons gauge fields of the theory can be eliminated by making matter fields multivalued operators with anyonic statistics. We prove that, when the statistics parameter is an odd integer so that the anyons are bosons, the ground state, which consists of a condensate of bound pairs of flux tubes and fermions, breaks phase invariance. The ensuing long-range order implies that the system is an unconventional superfluid. We formulate a condition which may be useful as a numerical signal for symmetry breaking in the ground state for any statistics parameter. We also discuss an exotic lattice Chern-Simons theory, which makes explicit the relation of anyons to framed knot invariants. We discuss various lattice representations of the Chern-Simons term and find the unique local lattice Chern-Simons term with the appropriate naive continuum limit, which permits anyonization.

ANYONIZATION AND SUPERFLUIDITY OF LATTICE CHERN-SIMONS THEORY

We prove, working in the Hamiltonian formalism, that a U(1) Chern-Simons theory coupled to fermions on a lattice can be mapped exactly onto a theory of interacting lattice anyons. This map does not involve any singular gauge transformations, and is everywhere well defined. We also prove that, when the statistics parameter is an odd integer so that the anyons are bosons, the ground state, which consists of a condensate of bound pairs of flux tubes and fermions, breaks phase invariance. The ensuing long range order implies that the system is an unconventional superfluid.