P-wave Pairing Research Articles

Two-dimensional Fermi gases near a p -wave resonance: Effect of quantum fluctuations

We study the stability of p-wave superfluidity against quantum fluctuations in two-dimensional Fermi gases near a p-wave Feshbach resonance . An analysis is carried out in the limit when the interchannel coupling is strong. By investigating the effective potential for the pairing field via the standard loop expansion, we show that a homogeneous p-wave pairing state becomes unstable when two-loop quantum fluctuations are taken into account. This is in contrast to the previously predicted $p + ip$ supefluid in the weak-coupling limit [V. Gurarie et al., Phys. Rev. Lett. 94, 230403 (2005)]. It implies a possible onset of instability at certain intermediate interchannel coupling strength. Alternatively, the instability can also be driven by lowering the particle density. We also discuss the validity of our analysis.

On the theory of superfluidity of dense neutron matter with anisotropic spin-triplet p-wave pairing in strong magnetic fields

The previously derived nonlinear integral equations for the components of the order parameter (OP) of dense superfluid neutron matter (SNM) with anisotropic spin-triplet p-wave pairing (similar to 3He-A), taking into account the effects of magnetic field and finite temperatures, are reduced here to the equations for the two components of OP at the limit of zero temperature. In this article, these equations (which are valid for arbitrary parametrization of the effective Skyrme interaction in neutron matter) are specified and solved numerically for the generalized BSk21 parametrization of the effective Skyrme forces (with additional terms dependent on density n) in neutron matter. The primary result is the splitting of the energy gap, calculated in the energy spectrum of neutrons in SNM (nonlinearly increasing under a moderately strong magnetic field H), which has a nonlinear dependency on density n in the limiting case of zero temperature. A small asymmetry (nonlinearly increasing with magnetic field) of the energy gap splitting has also been obtained in the range of moderately strong magnetic fields 1016 G ≤ H ≤ 1017 G. Neutron matter phase transitions to superfluid states of such a type and magnetic field strength might occur (and exist) at subnuclear and supranuclear densities, as in the liquid outer core of magnetars (strongly magnetized neutron stars).

Distinction between critical current effects and intrinsic anomalies in the point-contact Andreev reflection spectra of unconventional superconductors**Project supported by the National Key Basic Research Program of China (Grant Nos. 2015CB921000, 2016YFA0300301, and 2017YFA0302902), the National Natural Science Foundation of China (Grant Nos. 11674374 and 1474338), the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDB-SSW-SLH008), the

In this work, we discuss the origin of several anomalies present in the point-contact Andreev reflection spectra of (Li1−xFex)OHFeSe, LiTi2O4, and La2−xCexCuO4. While these features are similar to those stemming from intrinsic superconducting properties, such as Andreev reflection, electron-boson coupling, multigap superconductivity, d-wave and p-wave pairing symmetry, they cannot be accounted for by the modified Blonder–Tinkham–Klapwijk (BTK) model, but require to consider critical current effects arising from the junction geometry. Our results point to the importance of tracking the evolution of the dips and peaks in the differential conductance as a function of the bias voltage, in order to correctly deduce the properties of the superconducting state.

Topology from triviality

We show that bringing into proximity two topologically trivial systems can give rise to a topological phase. More specifically, we study a 1D metallic nanowire proximitized by a 2D superconducting substrate with a mixed s-wave and p-wave pairing, and we demonstrate both analytically and numerically that the phase diagram of such a setup can be richer than reported before. Thus, apart from the two "expected" well-known phases (i.e., where the substrate and the wire are both simultaneously trivial or topological), we show that there exist two peculiar phases in which the nanowire can be in a topological regime while the substrate is trivial, and vice versa.

Chiral p-wave pairing of ultracold fermionic atoms due to a quadratic band touching**Project supported by the National Natural Science Foundation of China (Grant No. 11675116) and the Soochow University, China.

We study the superfuild ground state of ultracold fermions in optical lattices with a quadratic band touching. Examples are a checkerboard lattice around half filling and a kagome lattice above one third filling. Instead of pairing between spin states, here we focus on pairing interactions between different orbital states. We find that our systems have only odd-parity (orbital) pairing instability while the singlet (orbital) pairing instability vanishes thanks to the quadratic band touching. In the mean field level, the ground state is found to be a chiral p-wave pairing superfluid (mixed with finite f-wave pairing order-parameters) which supports Majorana fermions.

Phase diagram of a generalized off-diagonal Aubry–André model with p-wave pairing

Off-diagonal Aubry–André (AA) model has recently attracted a great deal of attention as they provide condensed matter realization of topological phases. We numerically study a generalized off-diagonal AA model with p-wave superfluid pairing in the presence of both commensurate and incommensurate hopping modulations. The phase diagram as functions of the modulation strength of incommensurate hopping and the strength of the p-wave pairing is obtained by using the multifractal analysis. We show that with the appearance of the p-wave pairing, the system exhibits mobility-edge phases and critical phases with various number of topologically-protected zero-energy modes. Predicted topological nature of these exotic phases can be realized in a cold atomic system of incommensurate bichromatic optical lattice with induced p-wave superfluid pairing by using a Raman laser in proximity to a molecular Bose–Einstein condensation.

Fulde-Ferrell-Larkin-Ovchinnikov state in bilayer dipolar systems

We study the phase diagram of fermionic polar molecules in a bilayer system, with an imbalance of molecular densities of the layers. For the imbalance exceeding a critical value the system undergoes a transition from the uniform interlayer superfluid to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with a stripe structure, and at sufficiently large imbalance a transition from the FFLO to normal phase. Compared to the case of contact interactions, the FFLO regime is enhanced by the long-range character of the interlayer dipolar interaction, which can combine the s-wave and p-wave pairing in the order parameter.

Fermion superfluid with hybridized s- and p-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 $^{40}$K 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 $s$-wave 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.

Superconducting proximity in three-dimensional Dirac materials: Odd-frequency, pseudoscalar, pseudovector, and tensor-valued superconducting orders

We find that a conventional s-wave superconductor in proximity to three dimensional Dirac material (3DDM), to all orders of perturbation in tunneling, induces a combination of s and p-wave pairing only. We show that the Lorentz invariance of the superconducting pairing prevents the formation of Cooper pairs with higher orbital angular momenta in the 3DDM. This no-go theorem acquires stronger form when the probability of tunneling from the conventional superconductor to positive and negative energy states of 3DDM are equal. In this case all the p-wave contribution except for the lowest order, identically vanish and hence we obtain an exact result for the induced p-wave superconductivity in 3DDM. Fierz decomposing the superconducting matrix we find that temporal component of the vector superconducting order and spatial components of the pseudo-vector order are odd-frequency pairing. We find that the latter is odd with respect to exchange of position and chirality of the electrons in the Cooper pair and is spin-triplet which is necessary for NMR detection of such an exotic pseudo- vector pairing. Moreover, we show that the tensorial order breaks into a polar vector and an axial vector and both of them are conventional pairing except for being spin-triplet. According to our study, for gapless 3DDM the tensorial superconducting order will be the only order which is odd with respect to the chemical potential {\mu}. Therefore we predict that a transverse p-n junction binds Majorana fermions. This effect can be used to control the neutral Majorana fermions with electric fields.

Time-reversal-invariant topological superfluids in Bose-Fermi mixtures

A mixed dimensional system of fermions in two layers immersed in a Bose-Einstein condensate (BEC) is shown to be a promising setup to realise topological superfluids with time-reversal symmetry (TRS). The induced interaction between the fermions mediated by the BEC gives rise to a competition between p-wave pairing within each layer and s-wave pairing between the layers. When the layers are far apart, intra-layer pairing dominates and the system forms a topological superfluid either with or without TRS. With decreasing layer separation or increasing BEC coherence length, inter-layer pairing sets in. We show that this leads either to a second order transition breaking TRS where the edge modes gradually become gapped, or to a first order transition to a topologically trivial s-wave superfluid. Our results provide a realistic roadmap for experimentally realising a topological superfluid with TRS in a cold atomic system.

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

We investigate the Anderson localization in non-Hermitian Aubry-Andr\'e-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

Josephson effect in a multiorbital model for Sr2RuO4

We study Josephson current between s-wave/spin-triplet superconductor junctions by taking into account details of band structures in Sr$_{2}$RuO$_{4}$ such as three conduction bands, spin-orbit interaction in the bulk and that at the interface. We assume five superconducting order parameters in Sr$_{2}$RuO$_{4}$: a chiral p-wave symmetry and four helical p-wave symmetries. We calculate current-phase relationship $I(\varphi)$ in these junctions, where $\varphi$ is the macroscopic phase difference between two superconductors. The results for a chiral p-wave pairing symmetry show that $\cos(\varphi)$ term appears in the current-phase relation due to time-reversal symmetry (TRS) breaking. On the other hand, $\cos(\varphi)$ term is absent in the helical pairing states which preserve the TRS. We also study the dependence of maximum Josephson current $I_c$ on an external magnetic flux $\Phi$ in a corner junction. The calculated results of $I_c(\Phi)$ show a relation $I_{c}(\Phi) \neq I_{c}(-\Phi)$ in a chiral state and $I_{c}(\Phi)=I_{c}(-\Phi)$ in a helical state. We calculate $I_c(\Phi)$ in a corner and a symmetric SQUIDs geometry. In a symmetric SQUID geometry, the relation $I_{c}(\Phi)=I_{c}(-\Phi)$ is satisfied for all the pairing states and it is impossible to distinguish chiral state from helical one. On the other hand, results for a corner SQUID always show $I_{c}(\Phi) \neq I_{c}(-\Phi)$ and $I_{c}(\Phi)=I_{c}(-\Phi)$ for a chiral and a helical states, respectively. Experimental tests of these relations in a corner junctions and SQUIDs may serve as a tool for unambiguous determination of the pairing symmetry in Sr$_{2}$RuO$_{4}$.

Bound state, phase separation and superconductivity in presence of Rashba spin-orbit coupling

We have investigated the phase diagram for the t−J model at low electronic densities in presence of Rashba spin-orbit coupling (RSOC). We have rigorously derived a bound state criterion which arises out of a competition between the kinetic energy of the electrons and the exchange coupling between them. Further, we have obtained that the phase diagram consists of three phases, namely, a gas of electrons, a gas of bound pairs, and a fully phase separated state. Subsequently an extension of the pairing scenario is done at finite densities by solving a BCS gap equation. Finite superconducting correlations are observed for J values much lower than that required for the formation of a single bound pair, thereby indicating that pairing in a many particle environment requires weaker interaction strengths than that in the dilute case. We have further obtained that the RSOC increases the transition temperature for a p-wave pairing state, while it diminishes the same for an s-wave pairing correlations.

Disorder-enhanced topological protection and universal quantum criticality in a spin-32topological superconductor

We study the Majorana surface states of higher-spin topological superconductors (TSCs) that could be realized in ultracold atomic systems or doped semimetals with spin-orbit coupling. As a paradigmatic example, we consider a model with p-wave pairing of spin-3/2 fermions that generalizes ${}^3\text{He-}B$. This model has coexisting linear and cubic dispersing Majorana surface bands. We show that these are unstable to interactions, which can generate a spontaneous surface thermal quantum Hall effect (TQHE). By contrast, nonmagnetic quenched disorder induces a surface conformal field theory (CFT) that is stable against weak interactions: topological protection is enhanced by disorder. Gapless surface states of higher-spin TSCs could therefore be robustly realized in solid state systems, where disorder is inevitable. The surface CFT is characterized by universal signatures that depend only on the bulk topological winding number, and include power-law scaling of the density of states, a universal multifractal spectrum of local density of states fluctuations, and a quantized ratio of the longitudinal thermal conductivity $\kappa_{xx}$ divided by temperature $T$. By contrast, $\kappa_{xx}/T$ for the clean surface without TQHE order would diverge as $T \rightarrow 0$. Since disorder stabilizes the conducting Majorana surface fluid and quantizes thermal transport, our results suggest a close analogy between bulk TSCs and the integer quantum Hall effect.

Bound-state dynamics in one-dimensional multispecies fermionic systems

In this work we provide for a description of the low-energy physics of interacting multi-species fermions in terms of the bound-states that are stabilized in these systems when a spin gap opens. We argue that, at energies much smaller than the spin gap, these systems are described by a Luttinger liquid of bound-states that depends, on top of the charge stiffness $\nu$ and the charge velocity $u$, on a "Fermi" momentum $P_F$ satisfying $qP_F = Nk_F$ where $q$ is the charge of the bound-state, $N$ the number of species and $k_F$ is the Fermi momentum in the non-interacting limit. We further argue that for generic interactions, generic bound-states are likely to be stabilized. They are associated with emergent, in general non-local, symmetries and are in the number of five. The first two consist of either a charge $q=N$ local $SU(N)$ singlet or a charge $q=N$ bound-state made of two local $SU(p)$ and $SU(N-p)$ singlets. In this case the Fermi momentum $P_F=k_F$ is preserved. The three others have an enhanced Fermi vector $P_F$. The latter are either charge $q=2$ bosonic p-wave and s-wave pairs with $SO(N)$ and $SP(N)$ symmetry and $P_F=Nk_F/2$ or a composite fermion of charge $q=1$ with $P_F=Nk_F$. The instabilities of these Luttinger liquid states towards incompressible phases and their possible topological nature are also discussed.

Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

We reveal an edge spin triplet p–wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

We reveal an edge spin triplet p-wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

Quantum phase transition and entanglement of one-dimensional spinless fermion model

Motivated by recent developments in the field of 1D topological superconductors (TSCs), we investigate the phase transition properties of p-wave superconductor with 50 sites. In this paper, we first map the p-wave fermion model into the transverse [Formula: see text] model with an incommensurate modulated transverse field. We study the phase transition from TSC phase to Anderson localization phase by using imaginary time-evolving block decimation (TEBD) algorithm. By calculating the correlation function [Formula: see text], we numerically calculate the average correlation function in different p-wave pairing amplitude [Formula: see text]. By plotting the average correlation function versus the strength of incommensurate [Formula: see text] for [Formula: see text] and [Formula: see text], we identify the phase transition from TSC phase to Anderson localization phase [X. M. Cai et al., Phys. Rev. Lett. 110, 176403 (2013)]. Last but not least, we give an average measure of the entanglement of a single site with the rest of the system and von Neumann entropy of two boundary sites for the same parameters showing that the system possesses very strong entanglement at the critical point. The finite size effect and Majorana fermions are discussed in this paper.

Spectral statistics, finite-size scaling and multifractal analysis of quasiperiodic chain with p-wave pairing

We study the spectral and wavefunction properties of a one-dimensional incommensurate system with p-wave pairing and unveil that the system demonstrates a series of particular properties in its ciritical region. By studying the spectral statistics, we show that the bandwidth distribution and level spacing distribution in the critical region follow inverse power laws, which however break down in the extended and localized regions. By performing a finite-size scaling analysis, we can obtain some critical exponents of the system and find these exponents fulfilling a hyperscaling law in the whole critical region. We also carry out a multifractal analysis on system's wavefuntions by using a box-counting method and unveil the wavefuntions displaying different behaviors in the critical, extended and localized regions.

Amperean Pairing at the Surface of Topological Insulators.

The surface of a 3D topological insulator is described by a helical electron state with the electron's spin and momentum locked together. We show that in the presence of ferromagnetic fluctuations the surface of a topological insulator is unstable towards a superconducting state with unusual pairing, dubbed Amperean pairing. The key idea is that the dynamical fluctuations of a ferromagnetic layer deposited on the surface of a topological insulator couple to the electrons as gauge fields. The transverse components of the magnetic gauge fields are unscreened and can mediate an effective interaction between electrons. There is an attractive interaction between electrons with momenta in the same direction which makes the pairing to be of Amperean type. We show that this attractive interaction leads to a p-wave pairing instability of the Fermi surface in the Cooper channel.