A facile approach to calculating superconducting transition temperatures in the bismuth solid phases

Abstract

All solid phases of bismuth under pressure, but one, have been experimentally found to superconduct. From Bi-I to Bi-V, avoiding Bi-IV, they become superconductors and perhaps Bi-IV may also become superconductive. To investigate the influence of the electronic properties N(E ) and the vibrational properties F(ω) on their superconductivity we have ab initio calculated them for the corresponding experimental crystalline structures, and using a BCS approach have been able to determine their critical temperatures T c obtaining results close to experiment: For Bi-I (The Wyckoff Phase) we predicted a transition temperature of less than 1.3 mK and a year later a T c of 0.5 mK was measured; for Bi-II T c is 3.9 K measured and 3.6 K calculated; Bi-III has a measured T c of 7 K and 6.5 K calculated for the structure reported by Chen et al ., and for Bi-V T c ~ 8 K measured and 6.8 K calculated. Bi-IV has not been found to be a superconductor, but we have recently predicted a T c of 4.25 K.

Emergence of magnetism in bulk amorphous palladium

“…This, together with the overflow of electrons from the d shell to the sp shells may be an indicator of an unexpected behaviour. However, since identifying unambiguously the cutoff value to calculate the nn in amorphous metals is a controversial subject [10] we opted for a complementary, direct approach in a manner similar to our previous calculations on bismuth [16,17], and obtained the densities of electronic states with α spins and with β spins to see if they indicate a net magnetic moment, and they do, Fig. 4(a).…”

Structural and electronic properties of the incommensurate host-guest Bi-III phase

“…This approximant yielded reasonably good agreements to experimental values of density, but a very broad pressure stability range for Bi-III, almost twice its experimental value. Nevertheless, this approximant became the standard numerical scheme for calculating Bi-III, used also in more recent studies calculating phonon spectra and superconductivity transitions 4,16,17 . Although very useful and computationally reasonable, the quality of this commensurate approximation has not been established, and the sensitivity of the various physical properties of the material to it have not been systematically studied.…”

The effect of negative pressures on the superconductivity of amorphous and crystalline bismuth

“…Bismuth was first found to be a superconductor when in the amorphous phase at ambient pressure 6 , 7 , with a superconducting transition temperature of ∼ 6 K. Then, when the Wyckoff crystalline phase (a rhombohedral structure with the R-3 m space group, at room temperature and atmospheric pressure) was subjected to positive pressures it changed crystalline structures but maintained the superconducting properties for most of the new topologies (see Refs. 8 , 9 , and references contained therein). However, the possible superconductivity of c-Bi in the Wyckoff structure had not been found so we decided to study it based on the experimental results for the amorphous phase.…”

“…To search for variations of superconductivity, we have to apply the approach stated in Ref. 8 , to study the effect of the expansion on the electronic and vibrational properties of the material, and from there calculate T c .…”