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Thermodynamics of Eliashberg theory in the weak-coupling limit

机译：ELIASHBERG理论在弱耦合极限中的热力学

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摘要

The weak-coupling limits of the gap and critical temperature computed within Eliashberg theory surprisingly deviate from the BCS theory predictions by a factor of 1 / e~(1/2). Interestingly, however, the ratio of these two quantities agrees for both theories. Motivated by this result, here we investigate the weak-coupling thermodynamics of Eliashberg theory, with a central focus on the free energy, specific heat, and the critical magnetic field. In particular, we numerically calculate the difference between the superconducting and normal-state specific heats, and we find that this quantity differs from its BCS counterpart by a factor of 1 /e~(1/2), for all temperatures below T_c. We find that the dimensionless ratio of the specific-heat discontinuity to the normal-state specific heat reduces to the BCS prediction given by △C_V(T_c)/C_(V,n)(T_c) ≈ 1.43. This gives further evidence to the expectation that all dimensionless ratios tend to their "universal values" in the weak-coupling limit.
机译：ELIASHBERG理论内的间隙和临界温度的弱耦合限制令人惊讶地偏离了BCS理论预测，〜（1/2）的因子。然而，有趣的是，这两种数量的比例同意这两个理论。通过这种结果，我们在这里研究了ELIASHBERG理论的弱耦合热力学，其中中心对焦于自由能，比热和临界磁场。特别地，我们在数值上计算超导和正常状态特定热量之间的差异，并且发现该数量与其BCS对应物的不同1 / E〜（1/2），用于低于T_C的所有温度。我们发现比率不连续性到正常状态热的无量纲比率降低到△C_v（t_c）/ c_（v，n）（t_c）≈1.43给出的BCS预测。这提供了进一步证明期望所有无量纲比率倾向于在弱耦合极限中倾向于其“普遍值”。

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  • 来源
    《Physical review.B.Condensed matter and materials physics》 |2020年第21期|214505.1-214505.6|共6页
  • 作者

    Sepideh Mirabi; Rufus Boyack; F. Marsiglio;

  • 作者单位

    Department of Physics and Theoretical Physics Institute University of Alberta Edmonton Alberta Canada T6G 2E1;

    Department of Physics and Theoretical Physics Institute University of Alberta Edmonton Alberta Canada T6G 2E1;

    Department of Physics and Theoretical Physics Institute University of Alberta Edmonton Alberta Canada T6G 2E1;

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