Maxwell Complex Vector Research Articles

Holographic p-Wave Superconductor with Excited States in 4D Einstein–Gauss–Bonnet Gravity

We construct a holographic p-wave superconductor with excited states in the 4D Einstein–Gauss–Bonnet gravity using the Maxwell complex vector field model. In the probe limit, we observe that, the higher curvature correction or the higher excited state can hinder the vector condensate to be formed in the full parameter space, which is different from the holographic s-wave superconductor. Regardless of the choice of the vector mass by selecting the value of m2L2 or m2Leff2, we note that the critical chemical potential becomes evenly spaced for the number of nodes and that the difference of the critical chemical potential between the consecutive states depends on the curvature correction. Moreover, we find that the higher curvature correction or the higher excited state will alter the universal relation of the gap frequency, and the pole and delta function of the conductivity for the excited states can be broadened into the peaks with the finite width as the curvature correction increases.

Holographic p-wave superfluid in the AdS soliton background with RF2 corrections

We investigate the holographic p-wave superfluid in the background metric of the AdS soliton with RF2 corrections. Two models, namely, the Maxwell complex vector field model and Yang-Mills theory, are studied in the above context by employing the Sturm-Liouville approach as well as the shooting method. When turning on the spatial components of the gauge field, one observes that, in the probe limit, the inclusion of RF2 corrections hinders the superfluid phase transition. On the other hand, however, in the absence of the superfluid velocity, it is found that the RF2 corrections lead to distinct effects for the two models. Regardless of either the RF2 correction or the spatial component of the gauge field, the phase transition of the system is observed to be always of the second order. Moreover, a linear relationship between the charge density and chemical potential is largely established near the critical point in both holographic superfluid models.

Holographic p-wave superconductor with high-order derivative correction

In the probe limit, we numerically study the holographic p-wave superconductor phase transition in the high-order derivative theory. Concretely, we study the influences of the high-order derivative correction term αRF2 on the Maxwell complex vector model (MCV) in the five-dimensional AdS black hole and soliton backgrounds, respectively. In the black hole background, the improving correction parameter α increases the critical temperature and thus enhances the conductor/superconductor phase transition. Meanwhile, as the RF2 correction becomes stronger, the ratio of the energy gap to the critical temperature decreases from 9.858 to 5.995, which obviously deviates from the universal value. In the soliton background, we find that the correction does not affect the critical chemical potential. However, as the correction parameter α increases, the vector condensate grows faster, which might suggest that the improving α enhances the insulator/superconductor in some sense. The location of the second pole of imaginary part of conductivity increases with α, which implies that the energy of the quasiparticle excitation increases with the improving correction. In addition, the effects of α on the superfluid density agree with the one on the critical value as well as the condensate in both models. Furthermore, the critical exponent of condensate and superfluid density near the critical point is always 1/2 and 1, respectively.

Holographic p-wave superfluid in Gauss–Bonnet gravity

We construct the holographic p-wave superfluid in Gauss-Bonnet gravity via a Maxwell complex vector field model and investigate the effect of the curvature correction on the superfluid phase transition in the probe limit. We obtain the rich phase structure and find that the higher curvature correction hinders the condensate of the vector field but makes it easier for the appearance of translating point from the second-order transition to the first-order one or for the emergence of the Cave of Winds. Moreover, for the supercurrents versus the superfluid velocity, we observe that our results near the critical temperature are independent of the Gauss-Bonnet parameter and agree well with the Ginzburg-Landau prediction.

Holographic vector superconductor in Gauss–Bonnet gravity

In the probe limit, we numerically study the holographic p-wave superconductor phase transitions in the higher curvature theory. Concretely, we study the influences of Gauss–Bonnet parameter α on the Maxwell complex vector model (MCV) in the five-dimensional Gauss–Bonnet–AdS black hole and soliton backgrounds, respectively. In the two backgrounds, the improving Gauss–Bonnet parameter α and dimension of the vector operator Δ inhibit the vector condensate. In the black hole, the condensate quickly saturates a stable value at lower temperature. Moreover, both the stable value of condensate and the ratio ωg/Tc increase with α. In the soliton, the location of the second pole of the imaginary part increases with α, which implies that the energy of the quasiparticle excitation increases with the improving higher curvature correction. In addition, the influences of the Gauss–Bonnet correction on the MCV model are similar to the ones on the SU(2) p-wave model, which confirms that the MCV model is a generalization of the SU(2) Yang–Mills model even without the applied magnetic field to some extent.

Holographic p-wave superconductor models with Weyl corrections

We study the effect of the Weyl corrections on the holographic p-wave dual models in the backgrounds of AdS soliton and AdS black hole via a Maxwell complex vector field model by using the numerical and analytical methods. We find that, in the soliton background, the Weyl corrections do not influence the properties of the holographic p-wave insulator/superconductor phase transition, which is different from that of the Yang–Mills theory. However, in the black hole background, we observe that similarly to the Weyl correction effects in the Yang–Mills theory, the higher Weyl corrections make it easier for the p-wave metal/superconductor phase transition to be triggered, which shows that these two p-wave models with Weyl corrections share some similar features for the condensation of the vector operator.

Magnetic-field effects on p-wave phase transition in Gauss–Bonnet gravity

In the probe limit, we study the holographic p-wave phase transition in the Gauss–Bonnet gravity via numerical and analytical methods. Concretely, we study the influences of the external magnetic field on the Maxwell complex vector model in the five-dimensional Gauss–Bonnet–AdS black hole and soliton backgrounds, respectively. For the two backgrounds, the results show that the magnetic field enhances the superconductor phase transition in the case of the lowest Landau level, while the increasing Gauss–Bonnet parameter always hinders the vector condensate. Moreover, the Maxwell complex vector model is a generalization of the SU(2) Yang–Mills model all the time. In addition, the analytical results backup the numerical results. Furthermore, this model might provide a holographic realization for the QCD vacuum instability.

Lifshitz effects on vector condensate induced by a magnetic field

By numerical and analytical methods, we study in detail the effects of the Lifshitz dynamical exponent $z$ on the vector condensate induced by an applied magnetic field in the probe limit. Concretely, in the presence of the magnetic field, we obtain the Landau level independent of $z$, and we also find the critical value by coupling a Maxwell complex vector field and an SU(2) field into a ($3+1$)-dimensional Lifshitz black hole, respectively. The research results show that for the two models with the lowest Landau level, the increasing $z$ improves the response of the critical temperature to the applied magnetic field even without the charge density, and the analytical results uphold the numerical results. In addition, we find that, even in the Lifshitz black hole, the Maxwell complex vector model is still a generalization of the SU(2) Yang-Mills model. Furthermore, we construct the square vortex lattice and discuss the implications of these results.