P-wave Pairing States Research Articles

Spin triplet pairing and superconducting states in square lattices

In this work we study the pairing symmetry in a square lattice within a generalized Hubbard model, in which a second-neighbor correlated hopping is included in addition to the on-site and nearest-neighbor repulsions. When an infinitesimal distortion of the right angles in the square lattice is considered, we observe a spin triplet p-wave ground state for the case of electrons, but for holes a finite distortion is required, contrary to the d-wave case. In general, this spatial distortion induces a splitting of the doubly degenerate p-wave pairing states and one of them could become the ground state. On the other hand, this study has been extended to a finite density of electrons within the BCS formalism and the results show a maximum critical temperature of p-wave superconductivity around a 2/3 band-filling, close to the Fermi energy in the γ-band of Sr 2RuO 4 estimated by band-structure calculations.

Third Order Perturbation Analysis of Pairing Symmetry in Two-Dimensional Hubbard Model

We study the superconducting instabilities of singlet and triplet pairing in a two-dimensional Hubbard model on the basis of the third-order perturbation theory (TOPT). We investigate the effect of the vertex correction that is given by TOPT, comparing with the study with only the second-order effective interaction. In our results, a stable p-wave pairing state spreads from low to intermediate electron density. A dx2-y2-wave pairing is dominant for the high density near a half-filling. It is shown that the vertex correction plays an essential role in making the p-wave pairing state dominant.

Feedback effect in p-wave pairing state

We argue feedback effects that come from the chirality of the unconventional Cooper pair. These effects play roles to lift the degeneracy of several p-wave pairing states in quasi-two-dimension and work to favor the chiral state.

Theory of the spin-triplet superconductivity in Sr 2RuO 4 based on perturbation approach to three-band Hubbard model

We investigate a mechanism of the spin-triplet superconductivity in Sr 2RuO 4 by solving Eliashberg equation for three-band Hubbard model, where the effective pairing interaction is expanded perturbatively up to the third order with respect to the Coulomb integrals and the transition temperature is estimated numerically. The most significant momentum dependence of the effective interaction for the spin-triplet p-wave superconductivity does not originate from that of the spin susceptibility, but is brought by the third order vertex corrections. The results show that the p-wave pairing state is stabilized for not so strong inter-orbit couplings.

Josephson effect test for triplet pairing symmetry

The critical current modulation and the spontaneous flux of the vortex states in corner Josephson junctions between ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ and a conventional s-wave superconductor are calculated as a function of the crystal orientation and the magnetic field. For ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ we assume two nodeless p-wave pairing states. Also we use the nodal f-wave states ${B}_{1g}\ifmmode\times\else\texttimes\fi{}{E}_{u}$ and ${B}_{2g}\ifmmode\times\else\texttimes\fi{}{E}_{u},$ and one special p-wave state having line nodes. It is seen that the critical current depends solely on the topology of the gap.

Fluctuation Conductivity in Unconventional Superconductors near Critical Disorder

The fluctuation conductivity $\sigma_{\rm s}$ in bulk superconductors with non s-wave pairing and with nonmagnetic disorder of strength $D$ is studied at low $T$ and within the Gaussian approximation. It is shown by assuming a quasi two-dimensional (2D) electronic state that, only if the gap function $d_\mu({\p})$ is, as in a 2D p-wave pairing state, linear in the in-plane (relative) momentum ${\p}_\perp$, the in-plane fluctuation conductivity on the line $D=D_c$ is weakly divergent in low $T$ limit. The present result may be useful in clarifying the true gap function of spin-triplet ${\rm Sr_2RuO_4}$ through resistivity measurements.

Mechanism of superconductivity in a two-dimensional double-exchange system with spin-orbit coupling

We propose a mechanism of unconventional superconductivity in a two-dimensional double-exchange system with spin-orbit coupling. We show that a Chern-Simons term is induced by integrating out the conduction-electron fields. In the presence of the Chern-Simons term, the conduction electrons behave like skyrmion or antiskyrmion excitations for the core spin system, which leads to a disordered state of the core spins. After magnetic long-range order is destroyed, the Chern-Simons term becomes dominant for the low-energy physics and leads to a p-wave pairing state of conduction electrons.

Charge transport in singlet superconductor/triplet superconductor junctions

The first Fourier component of AC Josephson current in singlet s-wave superconductor/insulator/triplet p-wave superconductor (S/I/TS) junctions is calculated with taking account of the spin–orbit coupling at the interface of the junction. As a triplet p-wave pairing state we select one of the unitary pairing states which is a promising candidate for the superconducting state in Sr 2RuO 4. It is shown that the first Fourier component, which vanishes due to the difference of the parity between the two superconductors, recovers to be finite due to the spin–orbit coupling.

On a feedback mechanism for chiral p-wave pairing states

In a quasi-two-dimensional p-wave superconductor there are six degenerated Cooper pairing states within the weak-coupling approach. We show that a feedback effect lifts the degeneracy and supports the so-called chiral p-wave state. The anomalous coupling between charge and current in a system with broken time reversal symmetry and parity causes this effect.

Broken time reversal symmetry in unconventional superconductors

Broken time reversal symmetry occurs in several unconventional superconductors at subdominant instabilities within the superconducting phase. The time reversal symmetry breaking state is, in general, stabilized through the additional opening of a gap. This is the case for both bulk and local instabilities at surfaces or interfaces. The time reversal symmetry breaking state in Sr 2RuO 4 is the residual degeneracy of the p-wave pairing state resulting from special properties of spin-orbit coupling.

Nonlinear electrodynamics ofp-wave superconductors

We consider the Maxwell-London electrodynamics of three dimensional superconductors in p-wave pairing states with nodal points or lines in the energy gap. The current-velocity relation is then nonlinear in the applied field, cubic for point nodes and quadratic for lines. We obtain explicit angular and depth dependent expressions for measurable quantities such as the transverse magnetic moment, and associated torque. These dependences are different for point and line nodes and can be used to distinguish between different order parameters. We discuss the experimental feasibility of this method, and bring forth its advantages, as well as limitations that might be present.

Collective order-parameter modes for hypotheticalp-wave superconducting states inSr2RuO4

We have calculated all order-parameter collective modes and their contributions to the spin and charge susceptibilities for possible p-wave pairing states in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$ The susceptibilities are calculated for pairing states having gaps without and with nodes, and for wave vectors $\mathbf{q}=0$ and nesting vector $\mathbf{q}=\mathbf{Q}$ associated with the \ensuremath{\alpha} and \ensuremath{\beta} bands of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$ Important for the observability of the spin-fluctuation modes, for example, by spin resonance or neutron scattering, and of the charge-fluctuation modes by ultrasound, is the effect of quasiparticle damping. This effect is taken into account and discussed in connection with recent neutron-scattering data on ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$

Prospects forp-wave paired Bardeen-Cooper-Schrieffer states of fermionic atoms

We present theoretical prospects for creating p-wave paired BCS states of magnetic trapped fermionic atoms. Based on our earlier proposal of using dc electric fields to control both the strength and anisotropic characteristic of an atom-atom interaction and our recently completed multichannel atomic collision calculations we discover that p-wave pairing with ${}^{40}\mathrm{K}$ and ${}^{82,84,86}\mathrm{Rb}$ in the low field seeking maximum spin-polarized state represents excellent choices for achieving superfluid BCS states and may be realizable with current technology in laser cooling, magnetic trapping, and evaporative/sympathetic cooling, provided the required strong electric field can be applied. We also comment on the prospects of similar p-wave paired BCS states in ${}^{6}\mathrm{Li}$, and more generally on creating other types of exotic BCS states. Our study will open a new area in the vigorous pursuit to create a quantum degenerate fermionic atom vapor.

Composite-fermion pairing in bilayer quantum Hall systems

We derive the effective Hamiltonian for the composite fermion in double-layer quantum Hall systems with inter-layer tunneling at total Landau-level filling factor $\nu=1/m$, where $m$ is an integer. We find that the ground state is the triplet p-wave BCS pairing state of the composite fermions. At $\nu=1/2$, the ground state of the system evolves from the Halperin $(3,3,1)$-state toward the Pfaffian-state with increasing the tunneling amplitude. On the other hand, at $\nu=1$, the pairing state is uniquely determined independent of tunneling amplitude.

Broken symmetry of two-component nu =1/2 quantum Hall states.

We show that the recently discovered $\nu=1/2$ quantum Hall states in bilayer systems are triplet p-wave pairing states of composite Fermions, of exactly the same form as $^{3}$He superfluids. The observed persistence (though weakening) of the $\nu=1/2$ state in the two- to one-component crossover region corresponds to a continuous deformation of the so-called (331) state towards the ``Pfaffian" state, identical to the well known A to A$_{1}$ transition in $^{3}$He. This deformation also demonstrates the remarkable fact that electrons can release and capture ``vortices" in a continuous and incompressible manner through spin rotations. The broken symmetry of the triplet pairing state is a ``pairing" vector ${\bf d}$. It also implies a (pseudo-spin) magnetization $\propto i{\bf d}\times {\bf d}^{\ast}$. In the presence of layer tunneling, the (331) state ({\bf d} real) is unstable against other states with a magnetization ({\bf d} complex). The recently observed persistence of the $\nu=5/2$ state in single layer systems in the two- to one-component crossover region is also consistent with triplet pairing interpretation.

Paired Hall state at half filling.

The existence of a novel incompressible quantum liquid for spinless fermions at \ensuremath{\nu}=1/2 in the Hall effect is suggested. This state is plausibly related by smooth extrapolation in quantum statistics to a strong p-wave pairing state of fermions in zero magnetic field, and reduces to a state previously proposed by Halperin in the (unrealistic) limit of tightly bound pairs. It supports unusual excitations, including neutral fermions and charge-e/4 anyons with statistical parameter \ensuremath{\theta}=\ensuremath{\pi}/8. Numerical experiments are presented, which provide evidence for several aspects of our theory.

THE THEORY OF SUPERCONDUCTIVITY IN KONDO LATTICE

S-wave and P-wave superconductivity in Kondo lattice is theoretically studied in connection with heavy-fermion superconductivity (HFS). The hybridization between f-electron and conduction electron is investigated consistently and the corresponding quantities have been calculated in detail in the generalized Nambu formalism. It is shown that if one thinks f-electrons are responsible for superconductivity, for S-wave paired state, the superconducting transition temperature is in agreement with that of Tachiki et al., but the specific heat jump is not, our result is more appropriate than theirs. For P-wave paired state, the HFSs described by a Kondo lattice model are essentially almost localized Fermi superfluids, with a small modification. The effects of impurities on S- and P-wave paired states have been studied in detail respectively, and the conditions of the appearence of gapless superconductivity have been obtained for each case .

P-wave superconductivity in heavy fermion systems

After reviewing classification of p-wave states in metals with spin-orbit coupling, the depairing effect due to normal impurities is discussed. It depends on the form of the p-wave pairing states. States with lines of zeros are always in gapless regime even for weak impurity scattering.