Superconductivity in Bismuth. A New Look at an Old Problem

Abstract

To investigate the relationship between atomic topology, vibrational and electronic properties and superconductivity of bismuth, a 216-atom amorphous structure (a-Bi216) was computer-generated using our undermelt-quench approach. Its pair distribution function compares well with experiment. The calculated electronic and vibrational densities of states (eDOS and vDOS, respectively) show that the amorphous eDOS is about 4 times the crystalline at the Fermi energy, whereas for the vDOS the energy range of the amorphous is roughly the same as the crystalline but the shapes are quite different. A simple BCS estimate of the possible crystalline superconducting transition temperature gives an upper limit of 1.3 mK. The e-ph coupling is more preponderant in a-Bi than in crystalline bismuth (x-Bi) as indicated by the λ obtained via McMillan’s formula, λc = 0.24 and experiment λa = 2.46. Therefore with respect to x-Bi, superconductivity in a-Bi is enhanced by the higher values of λ and of eDOS at the Fermi energy.

Possible superconductivity in the Bismuth IV solid phase under pressure

“…For this we use an expression due to Grimvall 15 , that we utilized in ref. 1 with good results. F(ω) is the vDoS of the supercell under consideration, Fig.…”

“…Previously we performed some estimations of the critical temperature of the Wyckoff phase by calculating from first principles the eDoS and the vDoS and correlating them to the corresponding values of the amorphous phase 1 . We use the same successful approach for the Wyckoff and the Bismuth IV phases, using the results depicted in Figs 4 and 5 , to investigate the possible existence of superconductivity in Bi-IV.…”

“…In a very recent work 1 we computationally generated an amorphous structure of bismuth ( a -Bi), characterized its topology, showed that it agreed remarkably well with experiment and then proceeded to calculate its electronic, N ( E ), and vibrational, F ( ω ), densities of states to study their effect on the superconducting properties of this amorphous Bi phase. By comparing these results with the corresponding ones for the crystalline (Wyckoff) structure at atmospheric pressure we predicted that the crystalline material should become a superconductor at a temperature T c ≤ 1.3 mK 1 . A year later an experimental group reported that, in fact, the Wyckoff phase is superconductive with a transition temperature of 0.53 mK 2 , in agreement with our prediction.…”

“…The known superconducting transition temperatures are shown. For Bi-I we include the value we predicted 1 and the one measured 2 . Figure (1) adapted with permission from ref.…”

“…By now, all of them except Bi-IV have been found to superconduct. Bi-I has a superconducting transition temperature of ~1 mK 1 , 2 ; Bi-II has a T c of 3.9 K; for Bi-III the transition temperature is 7 K and for Bi-V it is 8 K 7 . Under these circumstances Bi-IV seems to be out of place since no superconducting transition temperature has been reported for this structure; however, it may be possible that superconductivity in Bi-IV has not been found since this phase does not exist at low temperatures.…”