Holographic s+p superconductors with axion induced translation symmetry breaking

Abstract We construct a holographic model for an s+p superconductor with axion induced translation symmetry breaking within the framework of gauge/gravity duality, working in the probe limit. The equations of motion are solved numerically to investigate the influence of the parameter k / T on the competition and coexistence between the s-wave and p-wave orders. We find that increasing k / T suppresses the thermodynamic stability of both the single condensate s-wave and p-wave solutions. With the $$k-\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>-</mml:mo> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> phase diagram and the condensate curves, we see that the region dominated by the single condensate p-wave phase gradually decreases with the increasing of k / T , finally leaving only the single condensate s-wave phase in the large k / T region, which is explained by the grand potential curves showing a slower decreasing of the thermodynamic stability for the s-wave solution than that for the p-wave solution. Furthermore, a larger minimum ratio of the charges $$q_p/q_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> </mml:math> is required to stabilize the s+p coexistent phase as k / T increases, and we determine the precise dependence of this critical ratio on k / T . Finally, our study of the optical conductivity reveals that the gap frequency increases with k / T . A characteristic kink, associated with the s+p coexistent phase, is identified in the dependence of gap frequency on k / T , which could serve as a potential experimental signature for detecting multi-condensate superconductivity.