Holographic p-wave superconductors with momentum relaxation

Abstract In the probe limit, we construct the p-wave conductor/superconductor phase transition with momentum relaxation originated from the axion fields by both numerical and analytical methods, and then study the effects of relaxation parameter ( k / μ ) on the superconductor model. Concretely, the increasing k / μ decreases monotonously the critical temperature and thus hinders the phase transition. The stable value of condensate ( C 00 ≡ 〈 J x 〉 1 / ( Δ + 1 ) / μ | T ≈ 0.15 T c ) and the coefficient ( C 1 ) of condensate ( 〈 J x 〉 / μ 1 / ( Δ + 1 ) = C 1 1 − T / T c | T ≈ T c ) always decrease with the larger k / μ . Near the critical point, the system suffers from a second order phase transition. Meanwhile, for fixed value of k / μ , the larger mass of vector field also suppresses the vector condensate to emerge. As for the above conclusions, the analytical results from the improved trial function agree with the numerical ones. The calculation of the ratio of energy gap to the critical temperature shows that the present superconductor indeed involves strong interaction, which increases with the increasing k / μ .