Lifshitz effects on vector condensate induced by a magnetic field

Abstract

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.

Holographicp-wave superfluid

“…1(a), 1(b), and 1(c) denote the superconducting phases without superfluid velocity (i.e., S y = 0), from which we find that, when the temperature gradually decreases, there is always a critical value below which the second-order phase transition occurs. This is just the conductor-superconductor phase transition [14,17,19]. The critical temperature T 0 with S y = 0 for different values of mass is listed in Table I; it follows that the increasing mass squared m 2 makes the phase transition more difficult, which is clear from the effective mass of the vector field ρ x (r), i.e., Eq.…”

“…Interestingly, the results showed that due to the nonminimal coupling between the vector field and the Maxwell field, the increasing magnetic field can induce superconductor phase transition even without charge density, which is similar to the QCD vacuum instability triggered by the strong magnetic field to develop the ρ-meson condensate [15]. Moreover, the investigation about the response of the external magnetic field on the p-wave phase transition also showed that the SU(2) YM model is a special case of the MCV model in five-dimensional (5D) soliton and 4D Lifshitz black holes [16][17][18]. Furthermore, considering the backreaction, the MCV model exhibits the rich phase structures, especially "retrograde condensation" [19][20][21].…”

“…where an important role in the presence of the external magnetic field [14,[16][17][18]. However, we will consider the case without the magnetic field in this paper; hence, it will not contribute to our work.…”

“…Comparing with the superconductor model, such as in Refs. [14,17,18], what is different is that we have turned on the spatial component of the gauge field A y (r) to model the superfluid. Substituting the above Ansätze (5) into Eqs.…”

Revisiting holographic superconductors with hyperscaling violation

“…Other generalized investigations based on this new p-wave model can be found, for example, in Refs. [55][56][57][58][59][60][61]. Considering the increasing interest in study of the holographic p-wave model, we will also extend the study to the holographic pwave superconductor with hyperscaling violation, which has not been constructed as far as we know.…”