Lifshitz scaling effects on holographic superconductors. (English) Zbl 1325.82019
Summary: Via numerical and analytical methods, the effects of the Lifshitz dynamical exponent \(z\) on the holographic superconductor models are studied in some detail, including \(s\)-wave and \(p\)-wave models. Working in the probe limit, we calculate the condensation and conductivity in both Lifshitz black hole and soliton backgrounds with a general \(z\). For both the \(s\)-wave and \(p\)-wave models in the black hole backgrounds, as \(z\) increases, the phase transition becomes difficult and the conductivity is suppressed. For the Lifshitz soliton background, when \(z\) increases, the critical chemical potential increases in both the \(s\)-wave model (with a fixed mass of the scalar field) and \(p\)-wave model. For the \(p\)-wave model in both the Lifshitz black hole and soliton backgrounds, the anisotropy between the AC conductivity in different spatial directions is suppressed when \(z\) increases. In all cases, we find that the critical exponent of the condensation is always 1/2, independent of \(z\) and spacetime dimension. The analytical results from the Sturm-Liouville variational method uphold the numerical calculations. The implications of these results are discussed.
MSC:
| 82D55 | Statistical mechanics of superconductors |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81V17 | Gravitational interaction in quantum theory |
| 83C57 | Black holes |
| 35C08 | Soliton solutions |
| 34B24 | Sturm-Liouville theory |
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