Spinon phonon interaction and ultrasonic attenuation in quantum spin liquids

Several experimental candidates for quantum spin liquids have been discovered in the past few years which appear to support gapless fermionic S=1/2 excitations called spinons. The spinons may form a Fermi sea coupled to a U(1) gauge field, and may undergo a pairing instability. We show that despite being charge neutral, the spinons couple to phonons in exactly the same way that electrons do in the long wavelength limit. Therefore, we can use sound attenuation to measure the spinon mass and lifetime. Furthermore, transverse ultrasonic attenuation is a direct probe of the onset of pairing because the Meissner effect of the gauge field causes a "rapid fall" of the attenuation at T(c) in addition to the reduction due to the opening of the energy gap. This phenomenon, well known in clean superconductors, may reveal the existence of the U(1) gauge field.     

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.     

Weak ferromagnetic exchange and anomalous specific heat in ZnCu3(OH)6Cl2

Experimental evidence for a plethora of low energy spin excitations in the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2 may be understandable in terms of an extended Fermi surface of spinons coupled to a U(1) gauge field. We carry out variational calculations to examine the possibility that such a state may be energetically viable. A Gutzwiller-projected wave function reproduces the dimerization of a kagome strip found previously by the density matrix renormalization group. Application to the full kagome lattice shows that the inclusion of a small ferromagnetic next-nearest-neighbor interaction favors a ground state with a spinon Fermi surface.     

Fractionalization and Fermi-surface volume in heavy-fermion compounds: the case of YbRh2Si2

We establish an effective theory for heavy-fermion compounds close to a zero temperature antiferromagnetic (AFM) transition. Coming from the heavy Fermi liquid phase across to the AFM phase, the heavy electron fractionalizes into a light electron, a bosonic spinon, and a new excitation: a spinless fermionic field. Assuming this field acquires dynamics and dispersion when one integrates out the high energy degrees of freedom, we give a scenario for the volume of its Fermi surface through the phase diagram. We apply our theory to the special case of YbRh2(Si1-xGex)2 where we recover, within experimental resolution, several low temperature exponents for transport and thermodynamics.     

Transport in the heavy-fermion superconductor UPt3

We report new theoretical results and analysis for the transport properties of superconducting UPt₃ based on the leading models for the pairing symmetry. We use Fermi surface data and the measured inelastic scattering rate to show that the low-temperature thermal conductivity and transverse sound attenuation in the A- and B-phase of UPt₃ are in excellent agreement with pairing states belonging to the two-dimensional orbital E_2u representation.     

New mean-field theory of the tt't'J model applied to high-T(c) superconductors

We introduce a new mean-field approach to the tt't'J model that incorporates both electron-like quasiparticle and spinon excitations as suggested by some experiments and numerical studies. It leads to a mean-field phase diagram which is consistent with that of hole and electron doped cuprates. Moreover, it provides a framework to describe the observed evolution of the electron spectral function from the undoped insulator to the overdoped Fermi metal for both hole and electron doping. The theory also provides a new non-BCS mechanism leading to superconductivity.     

Fulde–Ferrell–Larkin–Ovchinnikov states in equally populated Fermi gases in a two-dimensional moving optical lattice

We study the possibility of stabilizing a Fulde–Ferrell–Larkin–Ovchinnikov(FFLO) state in an equally populated two-component Fermi gas trapped in a moving two-dimensional optical lattice. For a system with nearly half filling, we find that a finite pairing momentum perpendicular to the moving direction can be spontaneously induced for a proper choice of lattice velocity. As a result, the total pairing momentum is tilted towards the nesting vector to take advantage of the significant enhancement of the density of states.     

Magnetism and pairing of two-dimensional trapped fermions

The emergence of local phases in a trapped two-component Fermi gas in an optical lattice is studied using quantum Monte Carlo simulations. We treat temperatures that are comparable to or lower than those presently achievable in experiments and large enough systems that both magnetic and paired phases can be detected by inspection of the behavior of suitable short-range correlations. We use the latter to suggest the interaction strength and temperature range at which experimental observation of incipient magnetism and d-wave pairing are more likely and evaluate the relation between entropy and temperature in two-dimensional confined fermionic systems.     

How are spin gap and pairing correlations of doped Mott insulators controlled by the geometry of the lattice structure?

Proposals to enhance the spin excitation gap and the pairing correlations in doped Mott insulators are reviewed. Design and tuning of flat dispersions near the Fermi level extend the critical region of the metal-to-Mott insulator transition thereby inducing stronger pairing instabilities. Several one- and two-dimensional decorated lattices are studied. We also discuss the tuning for stronger d-wave pairing instabilities in a microscopic model of high-T_c cuprates.     

d-wave superconductivity and pomeranchuk instability in the two-dimensional hubbard model

We present a systematic stability analysis for the two-dimensional Hubbard model, which is based on a new renormalization group method for interacting Fermi systems. The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations. More unexpectedly, we find that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface.     

Rotonlike Fulde-Ferrell collective excitations of an imbalanced Fermi gas in a two-dimensional optical lattice

We address the question of whether superfluidity can survive in the case of fermion pairing between different species with mismatched Fermi surfaces using as an example a population-imbalanced mixture of 6Li atomic Fermi gas loaded in a two-dimensional optical lattice at nonzero temperatures. The collective mode is calculated from the Bethe-Salpeter equations in the general random phase approximation assuming a Fulde-Ferrell order parameter. The numerical solution shows that, in addition to low-energy (Goldstone) mode, two rotonlike minima exist, and therefore, the superfluidity can survive in this imbalanced system.     

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.     

Competing types of order in two-dimensional bose-fermi mixtures

Using a functional renormalization group approach we study the zero temperature phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms in optical lattices, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. For spin-1/2 fermions we obtain a phase diagram, which shows a competition of pairing phases of various orbital symmetry (s, p, and d) and antiferromagnetic order. We determine the value of the gaps of various phases close to half filling, and identify subdominant orders as well as short-range fluctuations from the renormalization group flow. For spinless fermions we find that p-wave pairing dominates the phase diagram.     

Local electronic structure of a single nonmagnetic impurity as a test of the pairing symmetry of electrons in (K,Tl)FexSe2 superconductors

We study the effect of a single nonmagnetic impurity on the recently discovered (K,Tl)Fe(x)Se(2) superconductors, within both a toy two-band model and a more realistic five-band model. We find that, out of five types of pairing symmetry under consideration, only the d(x(2)-y(2))-wave pairing gives rise to impurity resonance states. The intragap states have energies far away from the Fermi energy. The existence of these intragap states is robust against the presence or absence of interband scattering. However, the interband scattering does tune the relative distribution of local density of states at the resonance states. All these features can readily be accessed by STM experiments, and are proposed as a means to test the pairing symmetry of the new superconductors.     

Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice

We show that the spin-liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin-liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin-liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface.     

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.     

Breached superfluidity via p-wave coupling

Anisotropic pairing between fermion species with different Fermi momenta opens two-dimensional areas of gapless excitations, thus producing a spatially homogeneous state with coexisting superfluid and normal fluids. This breached pairing state is stable and robust for arbitrarily small mismatch and weak p-wave coupling.     

Amperean pairing instability in the U1 spin liquid state with fermi surface and application to kappa-(BEDT-TTF)2Cu2(CN)3

Recent experiments on the organic compound kappa-(BEDT-TTF)2Cu2(CN)3 raise the possibility that the system may be described as a quantum spin liquid. Here we propose a pairing state caused by the "Amperean" attractive interaction between spinons on a Fermi surface mediated by the U(1) gauge field. We show that this state can explain many of the observed low temperature phenomena and discuss testable consequences.