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Eliashberg theory in the weak-coupling limit: results on the real frequency axis | | Sepideh Mirabi
; Rufus Boyack
; F. Marsiglio
; | | Date: |
19 Dec 2019 | | Abstract: | We formulate and solve the Eliashberg equations on the imaginary frequency
axis at temperatures below $T_c$ in the weak-coupling limit. We find an
excellent scaling at all temperatures, for a given coupling strength, and the
normalized order parameter exhibits a BCS-like temperature dependence. The
hybrid real-imaginary axis equations are also solved to obtain numerically
exact analytic continuations from the imaginary frequency axis to the real
frequency axis. This provides a determination of the gap edge, which, in the
weak-coupling limit, is identical to the order parameter from the imaginary
axis. The analytical result for the zero-temperature gap edge deviates from the
BCS result by a factor of $1/sqrt{e}$, which was also obtained for the
transition temperature $T_c$. We show that the normalized gap function on both
the real and imaginary frequency axes, for an electron-phonon Einstein spectrum
($delta$-function) of a given strength, is a universal function of frequency,
independent of temperature. The $1/sqrt{e}$ correction is a result of this
non-trivial frequency dependence in the gap function. This modification, in the
gap edge and in $T_{c}$, serves to preserve various dimensionless ratios to
their BCS values. | | Source: | arXiv, 1912.9460 | | Services: | Forum | Review | PDF | Favorites | |
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