Vortices in superfluid fermi gases through the BEC to BCS crossover

We have analyzed a single vortex at T=0 in a 3D superfluid atomic Fermi gas across a Feshbach resonance. On the BCS side, the order parameter varies on two scales: k(F)(-1)and the coherence length xi, while only variation on the scale of xi is seen away from the BCS limit. The circulating current has a peak value jmax which is a nonmonotonic function of 1/k(F)a(s) implying a maximum critical velocity approximately v(F) at unitarity. The number of fermionic bound states in the core decreases as we move from the BCS to the BEC regime. Remarkably, a bound state branch persists even on the BEC side reflecting the composite nature of bosonic molecules.     

Superfluid Fermi gases with large scattering length

We report quantum Monte Carlo calculations of superfluid Fermi gases with short-range two-body attractive interactions with infinite scattering length. The energy of such gases is estimated to be (0.44+/-0.01) times that of the noninteracting gas, and their pairing gap is approximately twice the energy per particle.     

BCS-BEC crossover and topological phase transition in 3D spin-orbit coupled degenerate Fermi gases

We investigate the BCS-BEC crossover in three-dimensional degenerate Fermi gases in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that the superfluid order parameter destroyed by a large Zeeman field can be restored by the SOC. With increasing strengths of the Zeeman field, there is a series of topological quantum phase transitions from a nontopological superfluid state with fully gapped fermionic spectrum to a topological superfluid state with four topologically protected Fermi points (i.e., nodes in the quasiparticle excitation gap) and then to a second topological superfluid state with only two Fermi points. The quasiparticle excitations near the Fermi points realize the long-sought low-temperature analog of Weyl fermions of particle physics. We show that the topological phase transitions can be probed using the experimentally realized momentum-resolved photoemission spectroscopy.     

Evidence for a magnetic collapse in the epsilon phase of solid oxygen

Solid oxygen is the only elementary molecular magnet. Under the very high pressure of 96 GPa oxygen transforms into a metal and a superconductor. Theory predicts a nonmagnetic state occurring before the transition into the superconducting xi phase. Nevertheless, until now there was no direct evidence of a magnetic collapse in high-pressure oxygen. For the first time direct information is provided on magnetic properties of the epsilon phase, which is sandwiched between the antiferromagnetic delta phase and the superconducting xi phase. We used magnetic neutron diffraction. The data show that the long-range magnetic order disappears at the delta-epsilon transition. The magnetic collapse occurs at P approximately equal to 8 GPa, far below the pressure of the insulator-metal (superconductor) transition. The collapse is preceded by a decrease in temperature of transition towards the long-range magnetically ordered state (T(LRO)) in the delta phase, at P = 7.6 GPa.     

Determination of the superfluid gap in atomic Fermi gases by quasiparticle spectroscopy

We present majority and minority radio frequency spectra of strongly interacting imbalanced Fermi gases of 6Li. We observed a smooth evolution in the nature of pairing correlations from pairing in the superfluid region to polaron binding in the highly polarized normal region. The imbalance induces quasiparticles in the superfluid region even at very low temperature. This leads to a local bimodal spectral response, which allowed us to determine the superfluid gap Delta and the Hartree energy U.     

Spin-orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas

Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin-orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin-orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin-orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin-orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.     

Signatures of superfluidity for Feshbach-resonant Fermi gases

We consider atomic Fermi gases where Feshbach resonances can be used to study the whole BCS-Bose-Einstein condensate crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-T(c) and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap also includes a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. The incoherent nature of the noncondensed pairs leads to broadening of the peak. The broadening decays below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.     

Surface Andreev bound states of superfluid (3)He and Majorana fermions

Superfluid (3)He is an intensively investigated and well characterized p-wave superfluid. In the bulk Balian-Werthamer state, which is commonly called the (3)He B phase, the superfluid gap is opened isotropically but near a flat boundary such as a wall of a container it can harbor interesting quasi-particle states inside the gap. These states are called surface Andreev bound states, and have not been experimentally explored in detail. Transverse acoustic impedance measurement has revealed their existence and provided spectroscopic details of the dispersion of the bound states. Recent theoretical arguments claim that the surface Andreev bound states of the superfluid (3)He B phase can be recognized as the edge states of the topological superfluid and be regarded as a Majorana fermion, a fancy particle which has not been confirmed in elementary particle physics. In this review, we present up-to-date knowledge on the surface Andreev bound states of the (3)He B phase revealed by acoustic spectroscopy and the possible realization of a Majorana fermion, along with related studies on this topic.     

Integrative models for asymmetric fermi superfluids: emergence of a new exotic pairing phase

We introduce an exactly solvable model to study the competition between the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) and breached-pair superfluid in strongly interacting ultracold asymmetric Fermi gases. One can thus investigate homogeneous and inhomogeneous states on equal footing and establish the quantum phase diagram. For certain values of the filling and the interaction strength, the model exhibits a new stable exotic pairing phase which combines an inhomogeneous state with an interior gap to pair excitations. It is proven that this phase is the exact ground state in the strong-coupling limit, while numerical examples in finite lattices show that also at finite interaction strength it can have lower energy than the breached-pair or LOFF states.     

Indication of charge-density-wave formation in Bi(111)

Photoemission spectroscopy of Bi(111) reveals a small hexagonal two-dimensional Fermi surface (FS) associated with an electron band centered in the surface Brillouin zone. Along the hexagon the Fermi momentum k(F) ranges from 0.053 to 0.061 A(-1). Temperature dependent valence band spectra show an anisotropic energy gap Delta near the Fermi level. We find a transition temperature of about 75 K. At 11 K, the gap is Delta=4 meV at the corner and Delta=7.5 meV at the side of the hexagon. Arguments based on susceptibility chi(--> q) calculations of a hexagonal FS are used to discuss an incommensurate charge-density-wave (CDW) formation associated with a q(CDW)=0.106 A(-1).     

Coulomb-blockade-induced bound quasiparticle states in a double-island structure

We determine the low temperature shape of the Coulomb-blockade staircase in a superconducting double-island device. For an odd number of electrons, in the ground state the intrinsic quasiparticle is bound to the tunneling contact. For a single channel contact the gap between the ground state and the continuum of excited states is of the order of the Josephson energy E(J). The temperature dependence of the Coulomb-blockade step width is nonmonotonic, with the minimal width occurring at T(i) approximately E(J)/ln(square root DeltaE(J)/delta), where Delta and delta are, respectively, the superconducting gap and mean level spacing in the island. For an even number of electrons, the Coulomb enhancement of the Josephson energy is shown to be significantly stronger than that for a single grain coupled to a lead. If the electrostatic energy favors a single broken Cooper pair, the resulting quasiparticles are bound to the contact at T=0.     

Superfluid pairing gap in strong coupling

The zero-temperature pairing gap is a fundamental property of interacting Fermions, providing a crucial test of many-body theories in strong coupling. We analyze recent cold-atom experiments on imbalanced Fermi systems using Quantum Monte Carlo results for the superfluid and normal phases. Through this analysis we extract, for the first time, the experimental zero-temperature pairing gap in the fully paired superfluid state at unitarity where the two-body scattering length is infinite. We find that the zero-temperature pairing gap is greater than 0.4 times the Fermi energy E(F), with a preferred value of (0.45+/-0.05) E(F). The ratio of the pairing gap to the Fermi Energy is larger here than in any other Fermi system measured to date.     

Probing the superconducting gap symmetry of PrOs4Sb12: a penetration depth study

We report measurements of the magnetic penetration depth lambda in single crystals of PrOs4Sb12 down to 0.1 K, with the ac field applied along the a, b, and c directions. In all three field orientations, lambda approximately T2 and superfluid density rho(s) approximately T2 for T<0.3T(c). Data are best fit by the 3He A-phase-like gap with multidomains, each having two point nodes along a cube axis, and parameter Delta(0)(0)/k(B)T(c)=2.6, suggesting that PrOs4Sb12 is a strong-coupling superconductor with two point nodes on the Fermi surface. We also confirm the double transitions at 1.75 and 1.85 K seen in other measurements.     

BCS and BEC p-wave pairing in Bose-Fermi gases

The pairing of fermionic atoms in a mixture of atomic fermion and boson gases at zero temperature is investigated. The attractive interaction between fermions, that can be induced by density fluctuations of the bosonic background, can give rise to a superfluid phase in the Fermi component of the mixture. The atoms of both species are assumed to be in only one internal state, so that the pairing of fermions is effective only in odd-l channels. No assumption about the value of the ratio between the Fermi velocity and the sound velocity in the Bose gas is made in the derivation of the energy gap equation. The gap equation is solved without any particular ansatz for the pairing field or the effective interaction. The p-wave superfluidity is studied in detail. By increasing the strength and/or decreasing the range of the effective interaction a transition of the fermion pairing regime, from the Bardeen-Cooper-Schrieffer state to a system of tightly bound couples can be realized. These composite bosons behave as a weakly-interacting Bose-Einstein condensate.     

E expansion for a Fermi gas at infinite scattering length

We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over E = 4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be mu/epsilon(F) =1/2 (E 3/2) + 1/16 (E 5/2) lnE -0.0246E (5/2) + ... and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Delta/mu =2E(-1) - 0.691 + ... . The minimum of the fermion dispersion curve is located at |p|=(2mepsilon(0))(1/2), where epsilon_(0)/mu=2+O(E). Extrapolation to d=3 gives results consistent with Monte Carlo simulations.     

Condensate fraction of asymmetric three-component Fermi gas

In this paper, we investigate the condensate fraction （CF） of fermionic pairs in the BCS-BEC crossover for three- component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.     

Crystalline order in superfluid (3)He films

We predict an inhomogeneous phase of superfluid (3)He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, D(c2)(T) < D < D(c1)(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, D(c2) approximately 9 xi (T), is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at D(c1) approximately 13 xi (T).     

Direct measurement of the energy gap of superfluid 3He-B in the low-temperature limit

The zero-temperature limit of the energy gap, Delta(P,T-->0), of superfluid 3He-B has been measured at T/T(c) less, similar0.25, near 0.1 and 4.8 bars, and in zero magnetic field. The energy gap was determined from the 2Delta pair-breaking edge of an acoustic signal obtained by novel, pulsed Fourier-Transform ultrasonic spectroscopy. Our results are independent of the temperature scale and the theoretical model of the gap. The values for Delta(P,T-->0) are lower than predicted by the weak-coupling-plus theory, and the Delta(P approximately 0.1 bars,T-->0) values are lower than predicted by BCS theory. The data indicate that Delta(P,T-->0) of superfluid 3He-B is not well modeled at the lowest pressures.     

Phase-transition phenomena of 0.8 microm superfluid 3He slab

We have investigated the transition phenomena of superfluid 3He in thin 0.8 microm slabs with a cw-NMR method. We found that, just below the phase-transition temperature, only the A phase appeared at any pressure. At lower temperatures, the phase transition to the B phase occurred between 0.3 and 2.74 MPa. We obtained a universal critical thickness delta as a function of pressure. When the reduced slab thickness, d/xi(T), is smaller than delta, only the A phase becomes stable.