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

Abstract

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. Int. J. Mod. Phys. A 2014.29. Downloaded from www.worldscientific.com by MICHIGAN STATE UNIVERSITY on 02/03/15. For personal use only. Y.-B. Wu et al.symmetry of the system, which therefore models the s-wave superconductor phase transition, whereafter, holographic p-wave and d-wave superconductors were built, respectively, for details, see Refs. 4 and 5. Meanwhile, the critical behavior of the holographic model was studied analytically via the Sturm-Liouville (SL) eigenvalue method in Ref. 6. However, all the above works were investigated in the probe limit, where the backreaction of the matter field on the background is neglected, beyond which the holographic model was further investigated in Ref. 7. In addition to above conductor/superconductor models, the insulator/superconductor phase transition was modeled in the AdS soliton background. 8 Moreover, the holographic superconductor models were studied in the system including the magnetic field, [9][10][11][12] and were also extended in various backgrounds, especially in the Gauss-Bonnet space-times and the Lifshitz space-times, for example, in Refs. 13-24, where the results showed that the increasing magnetic field and the Gauss-Bonnet parameter as well as the Lifshitz exponent hinder the phase transition.On the other hand, the authors of Ref. 25 proposed a holographic p-wave superconductor model in the four-dimensional Schwarzschild-AdS black hole coupled to a Maxwell complex vector (MCV) field in the probe limit. The results showed that, for the lowest Landau level, even without the charge density, the vector condensate can be triggered when the applied magnetic field increases to a critical value, which is reminiscent of the quantum chromodynamics (QCD) vacuum phase transition, 26-28 while for the excited Landau level (i.e. the excited Landau level), the strong magnetic field protects the stability, which is similar to the case of the ordinary superconductors. 9,10,22 In Ref. 29, the holographic insulator/superconductor phase transition induced by the magnetic field was studied in the five-dimensional AdS soliton coupled to such a MCV field and the SU(2) Yang-Mills (YM) field, respectively. It was shown that the results are similar to the cas...

Holographicp-wave superfluid

“…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].…”

“…[2,3,10,14,17,18], in the absence of the spatial component of the gauge field A y (r), i.e., the superconductor model, the system always suffers the second-order phase transition in the probe limit. However, with the presence of A y (r) in the superfluid model, we find that the phase transition will switch from the second order to the first order in the case of a sufficiently high superfluid velocity.…”

“…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.…”