Plasmon Effect on the Coulomb Pseudopotential μ^* in the McMillan Equation

Abstract

We examine the Coulomb pseudopotential µ * in the McMillan equation applying to the superconductivity of heavily doped semiconductors. Systematic calculation using the first-principles calculation suggests that µ * should be considered as a variable quantity depending on carrier density n in semiconductors, although it is usually considered as a constant about 0.1. To clarify n−dependence of µ * , we solve the McMillan equation inversely for µ * by combining the result of the first-principles calculation and that of experiments. It indicates that µ * decreases with n and becomes negative under n ∼ 5 × 10 −21 [cm −3 ]. This reduction is explained by the effect of plasmon which may play an important role in the superconductivity of low carrier systems such as heavily doped semiconductors.

First-Principles Study and Orbital-Fluctuation Effect on the Superconductivity in Tungsten Bronze AxWO3

“…[1]. We find that the calculated value of T c is in good agreement with the experimental one, where we assume that the Coulomb pseudopotential µ * in the McMillan equation depends on the carrier density x due to the plasmon effect [11], although it is usually considered as a constant of about 0.1 which yields T c inconsistent with the experimental one for the case with Na x WO 3 . In the actual calculation in Fig.…”

Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals

“…This suggests that the electronphonon coupling only affects the critical temperature perturbatively in YPtBi and we thus expect no isotopic ef-fect for this material. However, this observation cannot be generalized to all Luttinger semimetals and further work is needed to understand the situation where the electron-phonon coupling and the Coulomb repulsion compete [63,64].…”

Transition Temperature of Superconductivity in Sodium Tungsten Bronze -Theoretical Study Based on First-principles Calculations-

“…17) However, µ * is dependent on the electron density of the system, n for n < ∼ 10 22 cm −3 owing to the effect of plasmons. 18,22) When n decreases, µ * also decreases and it even becomes negative at n ∼ 3 × 10 21 cm −3 . 22,26) In the system of Na x WO 3 , n is given by ≃ 1.7 × 10 22 cm −3 for x = 1, and µ * is expected to be considerably smaller than 0.1 in the region of x < ∼ 0.5.…”

“…14) Assuming the phonon-mediated superconductivity, we estimate T c as a function of x on the basis of the McMillan formulation [15][16][17] including the effect of plasmons. [18][19][20][21][22] Since T c can be obtained with high accuracy by first-principles calculations, we may obtain a clue distinguishing whether the observed HTS can be explained by the conventional mechanism or not.…”

“…Although it is a simple approximation, it allows us to systematically analyze the electronic state of Na x WO 3 for x ≤ 1. 22,25) Hereafter, we denote the result obtained by adopting RBA for the WO 3 system as WO RBA− 3 at an arbitrary x, whereas that for NaWO 3 as NaWO RBA+ 3 . Here, the notation of RBA− means the case of electron doping in WO 3 , and RBA+ means that of hole doping in NaWO 3 .…”