Mean field analysis on Homers’s law

Sung Po Chao^1*

¹Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan

* Presenter:Sung Po Chao, email:t4088@nknu.edu.tw

An empirical relation named Homes’s law shows an interesting scaling relation, that the superfluid density at zero temperature is proportional to the superconducting transition temperature T_c times the DC conductivity σ in many different type of “dirty”[1] superconductors (conventional, cuprate, iron-based, organic, etc. [2]). It is shown by V. G. Kogan [3], by using BCS theory, that in isotropic superconductor the validity of the scaling can be extended to ξ≈l_F . We use mean field theory to analyze the case of anisotropic superconductor, and discuss if this scaling could be extended to two dimensions or even lower than two.

Ref:
[1] ”Dirty” here means zero temperature superconducting coherence length "ξ" much greater than electron mean free path "l_F" at its normal state.
[2] S. V. Dordevic, D. N. Basov, and C. C. Homes. Sci. Rep. 3, 1713 (2013)
[3] V. G. Kogan. Phys. Rev. B. 87, 220507(R) (2013)

Keywords: superconductivity, scaling