Unitary Fermi gas at finite temperature in the epsilon expansion

Thermodynamics of the unitary Fermi gas at finite temperature is investigated from the perspective of the expansion over epsilon=4-d with d being the dimensionality of space. We show that the thermodynamics is dominated by bosonic excitations in the low temperature region T<<Tc. Analytic formulas for the thermodynamic functions as functions of the temperature are derived to the lowest order in epsilon in this region. In the high temperature region where T Tc, bosonic and fermionic quasiparticles are excited. We determine the critical temperature Tc of the superfluid phase transition and the thermodynamic functions around Tc to the leading and next-to-leading orders in epsilon.Comment: 13 pages, 7 figures, revtex4; version to appear in Phys. Rev.

Liberating Efimov physics from three dimensions

When two particles attract via a resonant short-range interaction, three particles always form an infinite tower of bound states characterized by a discrete scaling symmetry. It has been considered that this Efimov effect exists only in three dimensions. Here we review how the Efimov physics can be liberated from three dimensions by considering two-body and three-body interactions in mixed dimensions and four-body interaction in one dimension. In such new systems, intriguing phenomena appear, such as confinement-induced Efimov effect, Bose-Fermi crossover in Efimov spectrum, and formation of interlayer Efimov trimers. Some of them are observable in ultracold atom experiments and we believe that this study significantly broadens our horizons of universal Efimov physics.Comment: 17 pages, 5 figures, contribution to a special issue of Few-Body Systems devoted to Efimov Physic

Casimir interaction among heavy fermions in the BCS-BEC crossover

We investigate a two-species Fermi gas with a large mass ratio interacting by an interspecies short-range interaction. Using the Born-Oppenheimer approximation, we determine the interaction energy of two heavy fermions immersed in the Fermi sea of light fermions as a function of the s-wave scattering length. In the BCS limit, we recover the perturbative calculation of the effective interaction between heavy fermions. The p-wave projection of the effective interaction is attractive in the BCS limit while it turns out to be repulsive near the unitarity limit. We find that the p-wave attraction reaches its maximum between the BCS and unitarity limits, where the maximal p-wave pairing of heavy minority fermions is expected. We also investigate the case where the heavy fermions are confined in two dimensions and the p-wave attraction between them is found to be stronger than that in three dimensions.Comment: 11 pages, 6 figure

Marginally unstable Holmboe modes

Marginally unstable Holmboe modes for smooth density and velocity profiles are studied. For a large family of flows and stratification that exhibit Holmboe instability, we show that the modes with phase velocity equal to the maximum or the minimum velocity of the shear are marginally unstable. This allows us to determine the critical value of the control parameter R (expressing the ratio of the velocity variation length scale to the density variation length scale) that Holmboe instability appears R=2. We then examine systems for which the parameter R is very close to this critical value. For this case we derive an analytical expression for the dispersion relation of the complex phase speed c(k) in the unstable region. The growth rate and the width of the region of unstable wave numbers has a very strong (exponential) dependence on the deviation of R from the critical value. Two specific examples are examined and the implications of the results are discussed.Comment: Submitted to Physics of Fluid

Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories

We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the epsilon expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle spectrum, and the critical temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.Comment: 44 pages, 15 figures, contribution to Lecture Notes in Physics "BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerge

Universal four-component Fermi gas in one dimension

A four-component Fermi gas in one dimension with a short-range four-body interaction is shown to exhibit a one-dimensional analog of the BCS-BEC crossover. Its low-energy physics is governed by a Tomonaga-Luttinger liquid with three spin gaps. The spin gaps are exponentially small in the weak coupling (BCS) limit where they arise from the charge-density-wave instability, and become large in the strong coupling (BEC) limit because of the formation of tightly-bound tetramers. We investigate the ground-state energy, the sound velocity, and the gap spectrum in the BCS-BEC crossover and discuss exact relationships valid in our system. We also show that a one-dimensional analog of the Efimov effect occurs for five bosons while it is absent for fermions. Our work opens up a very rich new field of universal few-body and many-body physics in one dimension.Comment: 9 pages, 3 figures; (v2) Efimov effect for 5 bosons in 1D is discussed; (v3) expanded versio

Single crystal MgB2 with anisotropic superconducting properties

The discovery of superconductor in magnesium diboride MgB2 with high Tc (39 K) has raised some challenging issues; whether this new superconductor resembles a high temperature cuprate superconductor(HTS) or a low temperature metallic superconductor; which superconducting mechanism, a phonon- mediated BCS or a hole superconducting mechanism or other new exotic mechanism may account for this superconductivity; and how about its future for applications. In order to clarify the above questions, experiments using the single crystal sample are urgently required. Here we have first succeeded in obtaining the single crystal of this new MgB2 superconductivity, and performed its electrical resistance and magnetization measurements. Their experiments show that the electronic and magnetic properties depend on the crystallographic direction. Our results indicate that the single crystal MgB2 superconductor shows anisotropic superconducting properties and thus can provide scientific basis for the research of its superconducting mechanism and its applications.Comment: 7 pages pdf fil

Quantizing Majorana Fermions in a Superconductor

A Dirac-type matrix equation governs surface excitations in a topological insulator in contact with an s-wave superconductor. The order parameter can be homogenous or vortex valued. In the homogenous case a winding number can be defined whose non-vanishing value signals topological effects. A vortex leads to a static, isolated, zero energy solution. Its mode function is real, and has been called "Majorana." Here we demonstrate that the reality/Majorana feature is not confined to the zero energy mode, but characterizes the full quantum field. In a four-component description a change of basis for the relevant matrices renders the Hamiltonian imaginary and the full, space-time dependent field is real, as is the case for the relativistic Majorana equation in the Majorana matrix representation. More broadly, we show that the Majorana quantization procedure is generic to superconductors, with or without the Dirac structure, and follows from the constraints of fermionic statistics on the symmetries of Bogoliubov-de Gennes Hamiltonians. The Hamiltonian can always be brought to an imaginary form, leading to equations of motion that are real with quantized real field solutions. Also we examine the Fock space realization of the zero mode algebra for the Dirac-type systems. We show that a two-dimensional representation is natural, in which fermion parity is preserved.Comment: 26 pages, no figure

Counting Majorana zero modes in superconductors

A counting formula for computing the number of (Majorana) zero modes bound to topological point defects is evaluated in a gradient expansion for systems with charge-conjugation symmetry. This semi-classical counting of zero modes is applied to some examples that include graphene and a chiral p-wave superconductor in two-dimensional space. In all cases, we explicitly relate the counting of zero modes to Chern numbers.Comment: 21 pages, 3 figure