P-wave Solution Research Articles

H − T phase diagrams of a holographic p-wave superfluid

We study the competition between the p-wave and the p+ip superfluid solutions in a holographic model with applied magnetic field intensity H. We find that when H is turned on, both the grand potential and the critical temperature of the p+ip solution are shifted, while the p-wave solution is only slightly affected. Combining the effect of H and back reaction parameter b, we build H − T phase diagrams with a slit region of p+ip phase. The zero (or finite) value of H at the starting point of the slit region is related to second (or first) order of the p-wave phase transition at zero magnetic intensity, which should be universal in systems with degenerate critical points (spinodal points) at zero magnetic field.

The holographic p + ip solution failed to win the competition in dRGT massive gravity

In this paper, the holographic p-wave superfluid model with charged complex vector field is studied in dRGT massive gravity beyond the probe limit. The stability of p-wave and p + ip solutions are compared in the grand canonical ensemble. The p-wave solution always get lower value of grand potential than the p + ip solution, showing that the holographic system still favors an anisotropic (p-wave) solution even with considering a massive gravity theory in bulk. In the holographic superconductor models with dRGT massive gravity in bulk, a key scaling symmetry is found to be violated by fixing the reference metric parameter c_0. Therefore, in order to get the dependence of condensate and grand potential on temperature, different values of horizon radius should be considered in numerical work. With a special choice of model parameters, we further study the dependence of critical back-reaction strength on the graviton mass parameter, beyond which the superfluid phase transition become first order. We also give the dependence of critical temperature on the back reaction strength b and graviton mass parameter m^2.

Mixed states of exciton condensation in two dimensional semiconductors

We study the exciton condensation phenomena in low-buckled two-dimensional semiconductors. Starting from the tight-binding effective Hamiltonian and considering the spin–orbit coupling as well as Rashba interaction induced by external electric field, we solve the gap equation analogous to BCS theory. Our calculation, with a careful analysis of Coulomb interaction, shows that the ground state is a mixture of s-wave and p-wave solutions. It is also a mixed state of singlet and triplet states and hence, can be probed with optical means. Furthermore, we studied the midgap state in a three-layer structure and proposed experiments to verify the existence of mixed states.

Vortex structure in p-wave superconductors

We study vortices in p-wave superconductors in a Ginzburg-Landau setting. The state of the superconductor is described by a pair of complex wave functions, and the p-wave symmetric energy functional couples these in both the kinetic (gradient) and potential energy terms, giving rise to systems of partial differential equations which are nonlinear and coupled in their second derivative terms. We prove the existence of energy minimizing solutions in bounded domains Ω ⊂ ℝ2 and consider the existence and qualitative properties (such as the asymptotic behavior) of equivariant solutions defined in all of ℝ2. The coupling of the equations at highest order changes the nature of the solutions, and many of the usual properties of classical Ginzburg-Landau vortices either do not hold for the p-wave solutions or are not immediately evident.

Backreacting p-wave superconductors

We study the gravitational backreaction of the non-abelian gauge field on the gravity dual to a 2+1 p-wave superconductor. We observe that as in the $p+ip$ system a second order phase transition exists between a superconducting and a normal state. Moreover, we conclude that, below the phase transition temperature $T_c$ the lowest free energy is achieved by the p-wave solution. In order to probe the solution, we compute the holographic entanglement entropy. For both $p$ and $p+ip$ systems the entanglement entropy satisfies an area law. For any given entangling surface, the p-wave superconductor has lower entanglement entropy.

Superconductivity in a two-dimensional Fermi gas: Evolution from Cooper pairing to Bose condensation.

We study a two-dimensional continuum model of a dilute gas of fermions at T=0 interacting via a given two-body potential, with an aim to investigate superconductors with coherence length of the order of the interparticle spacing [${k}_{F}$${\ensuremath{\xi}}_{0}$\ensuremath{\sim}O(1)], a striking feature of the high-${T}_{c}$ materials. We find that a two-body bound state in vacuum is a necessary and sufficient condition for an s-wave pairing instability. We also find that the existence of such a bound state in a higher-angular-momentum (lg0) channel is not a necessary condition for an l-wave pairing instability. We further investigate using a variational ansatz the evolution from a state with large overlapping Cooper pairs (${k}_{F}$${\ensuremath{\xi}}_{0}$\ensuremath{\gg}1) to one with Bose condensation of composite bosons (${k}_{F}$${\ensuremath{\xi}}_{0}$\ensuremath{\ll}1). For the s-wave case an exact solution of the variational equations shows a smooth crossover from one regime to the other at T=0. The p-wave solution has a weak singularity when the chemical potential goes through zero, which is the bottom of the band. We show, quite generally, independent of the dimensionality and of model details, that the gap--to--single-particle excitations is nodeless, even if the anisotropic pair wave function has nodes, when the coupling is strong enough that the chemical potential is negative.

Singlet pairs, covalent bonds, superexchange, and superconductivity

The possibility of superconductivity arising from interactions involving nearest neighbor singlet pairs is discussed. It is shown that the strong coupling effective Hamiltonian for the Hubbard model only admits extended s-wave solutions, and it is argued that those are suppressed by the Hubbard U. Neglecting hopping terms in the effective Hamiltonian involving three sites while keeping nearest neighbor superexchange and/or density interactions introduces spurious d- and p-wave solutions. A related but more fundamental interaction describing covalent bonds between polarizable ions can give rise to extended s-wave superconductivity, and the relationship with the resonating valence bond picture is discussed.

P‐wave fault‐plane solutions and the generation of surface waves by earthquakes in the western United States

Surface waves recorded at regional distances are used to study the source mechanisms of seven earthquakes in the western United States with magnitudes between 4.3 and 5.5. The source mechanisms of events in or on the margins of the Basin and Range show T‐axis with an azimuth of N85°W +/− 16° and a plunge of 12° +/− 16°. Of the seven events, four have P‐wave solutions that are inconsistent with surface‐wave observations. Azimuths of the T‐axis obtained from the surface‐wave mechanisms and from the P‐wave solutions differ by up to 45°. These events have dip‐slip or oblique‐slip mechanisms, and the source depths for three of the events are 5 km or less. Their source mechanisms and small magnitudes make identification of the P‐wave first motion difficult due to poor signal‐to‐noise ratio of the initial P‐wave and close arrivals of pP or sP with significant amplitude. We suggest that mis‐identification of the P‐wave first motion and distortion of the body‐wave ray paths due to non‐planar structure were sources of error in determining the nodal planes for these events.

The effect of a velocity gradient at the base of the mantle on diffractedPwaves in the shadow

Asymptotic expressions for the P-wave solution near a turning point may be combined with the boundary conditions prevailing at the mantle-core boundary to obtain an asymptotic expression for the reflection coefficient at this boundary that preserves the diffraction effects of curvature and velocity gradient. Increasing the velocity gradient is shown to increase the decay coefficient for the diffracted wave in the shadow. Consideration of recent published data and some new short-period data suggests that regional differences in the decay of this signal may be due to difference in the gradient at the base of the mantle.

Analysis of Pion-Pion Scattering through Chew-Mandelstam Equation

Low energy pion-pion scattering is investigated by using the Chew-Mandelstam representa­ tion. By treating the cutoff momentum as an adjustable parameter, an excellent agreement with experiment has been obtained for the S waves without using the CDD ambiguity. The P-wave solution is also consistent with experiment. The agreement is better than that cal· culated by using the momentum dependent Breit-Wigner formula.

A comparison of some S-wave studies of earthquake mechanisms

Abstract Graphical and analytical techniques for using S-waves in focal mechanism studies are compared. In previous applications the analytical technique has shown little or no agreement with the results of fault-plane solutions from P-waves, whereas for other groups of earthquakes the graphical methods have shown good agreement between the S-waves and the P-wave solutions. It is shown that the graphical and analytical techniques are identical in principle and that when the graphical methods are applied to the same three earthquakes to which the analytical technique had been applied the identical results are obtained. Closer examination of the graphical presentation of the data, however, shows that the disagreement between the S-waves and the fault plane solutions from P is largely apparent. The discrepancy follows upon the peculiar scatter in the S-wave data and the chance occurrence of observations of S at stations located along closely parallel planes of polarization of S. Once this is understood, it is seen that the direction of polarization of S-waves is in substantial agreement with the methods of analysis of focal mechanisms from P-waves, and that the data are consistent with a simple dipole as the point model of the earthquake focus.