Theory of Ultra Low Tc Superconductivity in Bismuth: Tip of an Iceberg ?

Abstract: Superconductivity with an ultra low Tc $\sim$ 0.5 mK was discovered recently in bismuth, a semimetal. To develop a model and scenario for Bi we begin with a cubic reference lattice, close to A7 (dimerized cubic) structure of Bi. Three valence electrons hop among 6p$_x$, 6p$_y$ and 6p$_z$ orbitals and form \textit{quasi one dimensional chains at half filling}. An interesting interplay follows: i) Mott localization tendency in the chains, ii) metallization by interchain hopping and iii) lattice dimerization by electron-phonon coupling. In our proposal, a potential high Tc superconductivity from RVB mechanism is lost in the game. However some superconducting fluctuations survive. Tiny fermi pockets seen in Bi are viewed as remnant \textit{evanescent Bogoliubov quasi particles} in an anomalous normal state. Multi band character admits possibility of PT violating \textit{chiral singlet superconductivity}. Bi has a strong spin orbit coupling; Kramers theorem protects our proposal for the bulk by replacing real spin by Kramer pair. Control of chain dimerization might resurrect high Tc superconductivity in Bi, Sb and As.