arXiv 2212.062312022-12hep-th

探索高温全息超导体

Towards high temperature holographic superconductors

Mahya Mohammadi, Ahmad Sheykhi

AI总结：

本文研究了实标量场与规范场非最小耦合的全息超导体模型，分析了多种耦合函数形式下非最小耦合参数对凝聚、临界温度和电导率的影响，并发现超标度破坏效应会显著提高临界温度并改变电导率的频率能隙关系。

摘要：

我们探索了一个实标量场与规范场非最小耦合的全息超导体模型。我们考虑了多种非最小耦合函数 h($ψ$) 的形式，包括指数型、双曲型（cosh）、幂律型和分式型。我们研究了非最小耦合参数 $α$ 对凝聚、临界温度和电导率的影响。我们将结果分为两组。在第一组中，对于较大的 $α$ 值，导体/超导体相变更容易发生；而在第二组中，非最小耦合的更强效应使得标量毛的形成更加困难。尽管电导率的实部和虚部受到不同 h($ψ$) 形式的影响，但它们遵循一些普适行为，例如在低频区域通过 Kramers-Kronig 关系相互关联，或在低温下出现频率能隙。我们找到了能提供更优信息的非最小耦合函数形式，适用于广泛的非最小耦合常数和温度范围。通过选择最佳的 h($ψ$) 形式，我们构建了一族全息导体/超导体相变解，以探究在规范场和标量场非最小耦合时超标度破坏的影响。我们发现，对于更高的超标度破坏效应 $θ$ 和非最小耦合常数 $α$，临界温度随之升高。增加这两个参数会得到较低的凝聚值，这意味着导体/超导体相变将更容易发生。此外，我们发现超标度破坏会影响全息超导体的电导率 $σ$，并改变频率能隙中的预期关系。我们观察到了一些普适行为，如无限大的直流电导率。

英文摘要：

We explore a holographic superconductor model in which a real scalar field is non-minimally coupled to a gauge field. We consider several types of the non-minimal coupling function h($ψ$) including exponential, hyperbolic (cosh), power-law and fractional forms. We investigate the influences of the non-minimal coupling parameter $α$ on condensation, critical temperature and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of $α$, while in the second group stronger effects of the non-minimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h($ψ$), they follow some universal behaviors such as connecting with each other through Kramers-Kronig relation in low frequency regime or the appearance of gap frequency at low temperatures. We find the best form of forms of non-minimal coupling function that gives us better information in wide range of non-minimal coupling constant and temperature. Choosing the best form of h($ψ$), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are non-minimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation $θ$ and non-minimal coupling constant $α$. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity $σ$ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed.

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