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

Abstract

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 $$c_0$$ 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 $$m^2$$ m 2 .

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

“…[16], the p+ip solution with finite condensate is realized in the new holographic p-wave model [9], and is discovered to be the same stable with the p-wave solution in the probe limit. However, the p+ip solution is less stable than the p-wave solution with considering the back-reaction on metric, and further study in DRGT massive gravity also failed to stabilize the p+ip solution beyond the probe limit [21]. Although the p+ip order is isotropic in x-y plane, it breaks the chiral symmetry.…”

“…In the new holographic p-wave model [9], the authors using charged complex vectors, which are also known as Proca fields, to extend the holographic p-wave superfluid model to more general values of the charge and the mass parameters. Therefore a lot of study emerge to consider the more general p-wave superfluid in various setups [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Further investigations also involve in both the s-wave and p-wave orders together to study the competition and coexistence between the two different orders in holography [24][25][26][27][28][29][30][31][32][33]36].…”

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

“…[16], the p+ip solution with finite condensate is realized in the new holographic p-wave model [9], and is discovered to be the same stable with the p-wave solution in the probe limit. However, the p+ip solution is less stable than the p-wave solution with considering the back-reaction on metric, and further study in DRGT massive gravity also failed to stabilize the p+ip solution beyond the probe limit [21].…”

“…In the new holographic pwave model [9], the authors using charged complex vectors, which are also known as Proca fields, to extend the holographic p-wave superfluid model to more general values of the charge and the mass parameters. Therefore a lot of study emerge to consider the more general p-wave superfluid in various setups [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Further investigations also involve in both the s-wave and p-wave orders together to study the competition and coexistence between the two different orders in holography [24][25][26][27][28][29][30][31][32][33][34].…”

Entanglement entropy and Page curve of black holes with island in massive gravity

“…For another massive object, the the structure of neutron star was investigated in the context of massive gravity [80]. Furthermore, the effects of massive gravity on s-/p-wave holographic superconductors have been explored in [81][82][83].…”