Fermion superfluid with hybridized <Emphasis Type="Italic">s</Emphasis>- and <Emphasis Type="Italic">p</Emphasis>-wave pairings

Ever since the pioneering work of Bardeen, Cooper and Schrieffer in the 1950s, exploring novel pairing mechanisms for fermion superfluids has become one of the central tasks in modern physics. Here, we investigate a new type of fermion superfluid with hybridized s- and p-wave pairings in an ultracold spin-1/2 Fermi gas. Its occurrence is facilitated by the co-existence of comparable s- and p-wave interactions, which is realizable in a two-component ⁴⁰K Fermi gas with close-by s- and p-wave Feshbach resonances. The hybridized superfluid state is stable over a considerable parameter region on the phase diagram, and can lead to intriguing patterns of spin densities and pairing fields in momentum space. In particular, it can induce a phase-locked p-wave pairing in the fermion species that has no p-wave interactions. The hybridized nature of this novel superfluid can also be confirmed by measuring the s- and p-wave contacts, which can be extracted from the high-momentum tail of the momentum distribution of each spin component. These results enrich our knowledge of pairing superfluidity in Fermi systems, and open the avenue for achieving novel fermion superfluids with multiple partial-wave scatterings in cold atomic gases.     

Extended s-wave pairing symmetry on the triangular lattice heavy fermion system

We investigate the pairing symmetry of the Kondo-Heisenberg model on triangular lattice, which is believed to capture the core competition of Kondo screening and local magnetic exchange interaction in heavy electron compounds. On the dominant background of the heavy fermion state, the introduction of the Heisenberg antiferromagnetic interaction (J _H ) leads to superconducting pairing instability. Depending on the strength of the interactions, it is found that the pairing symmetry favours an extended s-wave for small J _H and high conduction electron density but a chiral \(d_{x^2 - y^2 } + id_{xy}\)-wave for large J _H and low conduction electron density, which provides a phase diagram of pairing symmetry from the calculations of the ground-state energy. The transition between these two pairing symmetries is found to be first-order. Furthermore, we also analyze the phase diagram from the pairing strengths and find that the phase diagram obtained is qualitatively consistent with that based on the ground-state energy. In addition, we propose an effective single-band BCS Hamiltonian, which is able to describe the low-energy thermodynamic behaviors of the heavy fermion superconducting states. These results further deepen the understanding of the antiferromagnetic interaction which results in a geometric frustration for the model studied. Our work may provide a possible scenario to understand the pairing symmetry of the heavy fermion superconductivity, which is one of active issues in very recent years.     

Positions of the magnetoroton minima in the fractional quantum Hall effect

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like Λ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called “magnetoroton” minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B 48, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar et al. [Phys. Rev. Lett. 117, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence s/ (2s + 1) and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar et al.’s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar et al.’s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence s/ (2s ± 1) in the lowest Landau level and the n = 1 Landau level of graphene.     

Nonlinear generation of vorticity in thin smectic films

The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems that contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli–de Gennes–Matricon branches with different approach zero energy level at p_z → 0. The density of states of the bound fermions diverges at zero energy giving rise to the \(\sqrt \Omega \) dependence of the density of states in the polar phase of superfluid ³He rotating with the angular velocity Ω and to the \(\sqrt B \) dependence of the density of states for superconductors in the (d_xz + id_yz)-wave pairing state.     

Role of a fermion condensate in the structure of high-temperature pairing in cuprates

The anomalous properties of a pairing gap in cuprate superconductors have been explained under the assumption that their electron systems in the normal phase exhibit a fermion condensate, i.e., a set of dispersionless states close to the nominal Fermi surface. It has been shown that exactly the fermion condensate is responsible for D-state pairing in cuprates. More specifically, the effective Coulomb repulsion in the Cooper channel, which prevents the existence of superconductivity in normal metals in the S channel, makes it high-temperature in the D channel.     

Spin-resolved correlations in the warm-dense homogeneous electron gas

We have studied spin-resolved correlations in the warm-dense homogeneous electron gas by determining the linear density and spin-density response functions, within the dynamical self-consistent mean-field theory of Singwi et al. The calculated spin-resolved pair-correlation function g _{σ σ′}(r) is compared with the recent restricted path-integral Monte Carlo (RPIMC) simulations due to Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)], while interaction energy E _int and exchange-correlation free energy F _xc with the RPIMC and very recent ab initio quantum Monte Carlo (QMC) simulations by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. g _↑↓(r) is found to be in good agreement with the RPIMC data, while a mismatch is seen in g _↑↑(r) at small r where it becomes somewhat negative. As an interesting result, it is deduced that a non-monotonic T-dependence of g(0) is driven primarily by g _↑↓(0). Our results of E _int and F _xc exhibit an excellent agreement with the QMC study due to Dornheim et al., which deals with the finite-size correction quite accurately. We observe, however, a visible deviation of E _int from the RPIMC data for high densities (~8% at r _s = 1). Further, we have extended our study to the fully spin-polarized phase. Again, with the exception of high density region, we find a good agreement of E _int with the RPIMC data. This points to the need of settling the problem of finite-size correction in the spin-polarized phase also. Interestingly, we also find that the thermal effects tend to oppose spatial localization as well as spin polarization of electrons.     

Robustness of <Emphasis Type="Italic">s</Emphasis>-wave pairing symmetry in iron-based superconductors and its implications for fundamentals of magnetically driven high-temperature superconductivity

Based on the assumption that the superconducting state belongs to a single irreducible representation of lattice symmetry, we propose that the pairing symmetry in all measured iron-based superconductors is generally consistent with the A _1g s-wave. Robust s-wave pairing throughout the different families of iron-based superconductors at different doping regions signals two fundamental principles behind high-T _c superconducting mechanisms: (i) the correspondence principle: the short-range magnetic-exchange interactions and the Fermi surfaces act collaboratively to achieve high-T _c superconductivity and determine pairing symmetries; (ii) the magnetic-selection pairing rule: superconductivity is only induced by the magnetic-exchange couplings from the super-exchange mechanism through cation-anion-cation chemical bonding. These principles explain why unconventional high-T _c superconductivity appears to be such a rare but robust phenomena, with its strict requirements regarding the electronic environment. The results will help us to identify new electronic structures that can support high-T _c superconductivity.     

Full t-matrix approach to quasiparticle interference in non-centrosymmetric superconductors

We develop the full t-matrix theory of quasiparticle interference (QPI)for non-centrosymmetric (NCS) superconductors with Rashba spin-orbit coupling. We give aclosed solution for the QPI spectrum for arbitrary combination and strength of nonmagnetic(V _c ) and magnetic(V _m ) impurity scattering potentials interms of integrated normal and anomalous Green’s functions. The theory is applied to arealistic 2D model of the Ce-based 131-type heavy fermion superconductors. We discuss theQPI dependence on frequency, composition and strength of scattering and compare with Bornapproximation results. We show that the QPI pattern is remarkably stable against changesin the scattering model and can therefore give reliable information on the properties ofRashba-split Fermi surface sheets and in particular on the accidental nodal position ofthe mixed singlet-triplet gap function in NCS superconductors.     

Specific Heat Anomalies in Solids Described by a Multilevel Model

In the field of condensed matter physics, specific heat measurements can be considered as a pivotal experimental technique for characterizing the fundamental excitations involved in a certain phase transition. Indeed, phase transitions involving spin (de Souza et al. Phys. B Condens. Matter 404, 494 (2009) and Manna et al. Phys. Rev. Lett. 104, 016403 (2010)), charge (Pregelj et al. Phys. Rev. B 82, 144438 (2010)), lattice (Jesche et al. Phys. Rev. B 81, 134525 (2010)) (phonons) and orbital degrees of freedom, the interplay between ferromagnetism and superconductivity (Jesche et al. Phys. Rev. B 86, 020501 (2012)), Schottky-like anomalies in doped compounds (Lagos et al. Phys. C Supercond. 309, 170 (1998)), electronic levels in finite correlated systems (Macedo and Lagos J. Magn. Magn. Mater. 226, 105 (2001)), among other features, can be captured by means of high-resolution calorimetry. Furthermore, the entropy change associated with a first-order phase transition, no matter its nature, can be directly obtained upon integrating the specific heat over T, i.e., C(T)/T, in the temperature range of interest. Here, we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels Δ_i = (E_i?E₀) and the degeneracy of each energy level g_i, we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of \({\Delta }_{2}/{\Delta }_{1}\thickapprox \) 10 between the energy levels and a high degeneracy of one of the energy levels define the two-peaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach, we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak associated with the FM transition remains unaffected.     

Vortex-antivortex oscillation and tunneling in Bose-Einstein condensates

We study interacting condensates in anisotropic traps. Employing a two-level mean-field theory, which is valid provided the interaction energy is much smaller than ?ω_x and ?ω_y and the number of particles N is much larger than unity, we see that even a small interaction can drastically modify the dynamics of the system as predicted by García-Ripoll et al. [Phys. Rev. Lett. 87, 140403 (2001)]. In the present work, we supplement the discussion of the previous work and point out the important role of coupling between population difference and phase difference between two p states in the x and y directions. We also explore the stability of the vortex state for small systems with N ～ O(1), for which the mean-field theory is inapplicable. We performed the full quantum mechanical calculations using up to six single-particle states and showed that, when N is comparable to unity, quantum tunneling between the vortex and antivortex states can occur even though the interaction coefficient is so large that the vortex-antivortex oscillation is prohibited within the mean-field theory.     

Superconducting pairing symmetry in frustrating t-J model: Electronic Raman absorption

Motivated by the controversy on the pairing symmetry of layered organic superconductors,we study electronic Raman scattering spectra on a frustrating lattice. A two-dimensionalt-t′-J-J′model and the Gutzwiller projectional variational method is used. The pairing symmetry isobtained self-consistently. Basing on this, we perform a systematic investigation of thedensity of states and electronic Raman spectra as a function oft′/t: ranging fromt′ = 0, the square lattice model, tot′ = t, the isotropic triangular latticemodel. We discuss the polarization dependence of the Raman spectra, which could be used toidentify the relevant superconducting pairing symmetry of frustrating systems such aslayered organic superconductors.     

Topological Hall Effect of Spin-2 Condensate in a Time and Space-Dependent Magnetic Field

We simulate the dynamics of spin-2 ⁸⁷Rb condensate in a time and space-dependent magnetic field with a time-dependent variational approach. The topological Hall effect is observed, which has been realized in the experiment of spin-1 ²³Na condensate [Phys. Rev. Lett. 111, 245301 (2013)]. A driving-induced resonance behavior is observed.     

Meissner effect in superconductors with a finite pair momentum

The features of the Meissner effect in superconductors with a finite pairing momentum are analyzed. Response to a weak magnetic field is calculated for various cases covering a pair momentum range from q ? Δ/v ₀ to q ～ p ₀, including q = Δ₀/v ₀ (v ₀ is the velocity on the Fermi surface and Δ₀ is the order parameter at zero temperature; the system of units where ? = 1 is used). The response of a superconductor carrying the transport current at a temperature close to the critical temperature T _c is determined. It is shown that, at a certain critical momentum (current), the response parallel to the momentum vanishes and the London length is infinite. The response perpendicular to the momentum remains unchanged. The response of the superconductor in the current state at zero temperature is calculated. A new contribution to the paramagnetic current is found, and its mechanism is determined. This contribution can be large for high momenta q ～ p ₀. The Meissner effect is analyzed in detail for the state proposed by Larkin and Ovchinnikov, Zh. Éksp. Teor. Fiz. 47, 1136 (1964) [Sov. Phys. JETP 20, 762 (1964)], as well as by Fulde and Ferrel, Phys. Rev. A 135, 550 (1964). It is shown that the response parallel to the vector q is nonzero and diamagnetic. On the contrary, the response perpendicular to the momentum vanishes at the optimal momentum q ₀. The sensitivity of the Meissner effect to the fine features of the superconducting state such as the quasiparticle spectrum, coherent factors, etc. is demonstrated.     

A brief review on <Emphasis Type="Italic">μ</Emphasis>SR studies of unconventional Fe- and Cr-based superconductors

Muon spin relaxation/rotation (μSR) is a vital technique for probing the superconducting gap structure, pairing symmetry and time reversal symmetry breaking, enabling an understanding of the mechanisms behind the unconventional superconductivity of cuprates and Fe-based high-temperature superconductors, which remain a puzzle. Very recently double layered Fe-based super- conductors having quasi-2D crystal structures and Cr-based superconductors with a quasi-1D structure have drawn considerable attention. Here we present a brief review of the characteristics of a few selected Fe- and Cr-based superconducting materials and highlight some of the major outstanding problems, with an emphasis on the superconducting pairing symmetries of these materials. We focus on μSR studies of the newly discovered superconductors ACa₂Fe₄As₄F₂ (A = K, Rb, and Cs), ThFeAsN, and A₂Cr₃As₃ (A = K, Cs), which were used to determine the superconducting gap structures, the presence of spin fluctuations, and to search for time reversal symmetry breaking in the superconducting states. We also briefly discuss the results of μSR investigations of the superconductivity in hole and electron doped BaFe₂As₂.     

Resistivity of two-dimensional systems in a magnetic field at the filling factor ν = 1/2

Experimental data on the diagonal resistivity ρ _xx of GaAs/AlGaAs heterostructures in a magnetic field at the filling factor ν = 1/2 have been compared with the existing theoretical predictions [B. I. Halperin et al., Phys. Rev. B 47, 7312 (1993) and F. Evers et al., Phys. Rev. B 60, 8951 (1999)]. The experimental results have been found to follow the relation ρ _xx (1/2) ∝ n ^?2 d ^?1.64, which disagrees with the predictions.     

A Ping-Pong Quantum Dialogue Scheme Using Genuine Four-Particle Entangled States

Based on the genuine four-particle entangled state (Yeo and Chua in Phys. Rev. Lett. 96:060502, 2006) and the ping-pong protocol (Boström and Felbinger in Phys. Rev. Lett. 89:187902, 2002), an efficient quantum dialogue scheme is proposed. Since some subtle methods are employed, the information leakage doesn’t exist in this scheme. There are two security-check processes in this scheme, one is accomplished by using the four-particle entanglement pairs and the other by using the d particles.     

A More Efficient Contextuality Distillation Protocol

Based on the fact that both nonlocality and contextuality are resource theories, it is natural to ask how to amplify them more efficiently. In this paper, we present a contextuality distillation protocol which produces an n-cycle box B ? B ^′ from two given n-cycle boxes B and B ^′. It works efficiently for a class of contextual n-cycle (n ≥?4) boxes which we termed as “the generalized correlated contextual n-cycle boxes”. For any two generalized correlated contextual n-cycle boxes B and B ^′, B ? B ^′ is more contextual than both B and B ^′. Moreover, they can be distilled toward to the maximally contextual box C H _n as the times of iteration goes to infinity. Among the known protocols, our protocol has the strongest approximate ability and is optimal in terms of its distillation rate. What is worth noting is that our protocol can witness a larger set of nonlocal boxes that make communication complexity trivial than the protocol in Brunner and Skrzypczyk (Phys. Rev. Lett. 102, 160403 2009), this might be helpful for exploring the problem that why quantum nonlocality is limited.     

Coulomb repul sion of hole s and competition between $${d_{{x^2} - {y^2}}}$$ -wave and s-wave paring s in cuprate superconductor s

The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin–polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO₂ plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin–fermion coupling. The investigation of the possibility of implementation of superconducting phases with d-wave and s-wave of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-consistency equations, while there is no solution for the s-wave pairing. This result completely corresponds to the experimental data on cuprate HTSC. It has been demonstrated analytically that the intersite Coulomb interaction does not affect the superconducting d-wave pairing, because its Fourier transform V _q does not appear in the kernel of the corresponding integral equation.     

Superfluid density in the slave-boson theory

Despite of the success of the slave-boson theory in capturing qualitative physics of high-temperature superconductors like cuprates, it fails to reproduce the correct temperature-dependent behavior of superfluid density, let alone the independence of the linear temperature term on doping in the underdoped regimes of hole-doped cuprate, a common experimental observation in different cuprates. It remains puzzling up to now in spite of intensive theoretical efforts. For electron-doped case, even qualitative treatment is not reported at present time. Here we revisit these problems and provide an alternative superfluid density formulation by using the London relation instead of employing the paramagnetic current-current correlation function. The obtained formula, on the one hand, provides the correct temperature-dependent behavior of the superfluid density in the whole temperature regime, on the other hand, makes the doping dependence of the linear temperature term substantially weaken and a possible interpretation for its independence on doping is proposed. As an application, electron-doped cuprate is studied, whose result qualitatively agrees with existing experiments and successfully explains the origin of d- to anisotropic s-wave transition across the optimal doping. Our result remedies some failures of the slave-boson theory as employed to calculate superfluid density in cuprates and may be useful in the understanding of the related physics in other strongly correlated systems, e.g. Na_xCoO₂·yH₂O and certain iron-based superconductors with dominating local magnetic exchange interaction.     

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a _F . Applying this approach to the calculation of the dimmer-dimer scattering length a _B , we recover exactly the already known result a _B = 0.6 a _F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.