Evidence for Bose liquid state from anomalous shot noise in beta-tantalum junction

Spin Hall effect (SHE) is usually interpreted as a single-particle mechanism. However, β-Ta, one of the most efficient known SHE materials, exhibits “bad” metallicity - a non-divergent increase of resistivity with decreasing temperature T inconsistent with Fermi liquid picture. To elucidate its electronic state, we study shot noise produced by β-Ta tunnel junctions (TJs) and nanocontacts. The slope of the dependence of shot noise on bias, characterized by the Fano factor F, provides information about the elementary carrier charge, q=eF in TJs. In all the studied junctions, at cryogenic temperatures F is substantially larger than 1 expected for Fermi liquids, with values close to 2, 4, and 8. The integer values of Fano factors rule out blockage effect as causes of enhanced shot noise. Similarly, for pinhole junctions the values of F are substantially larger than 1/3 expected for q=e. Our results suggest that β-Ta may host the long-sought Bose liquid state characterized by correlated electron groups that are not limited to Cooper pairs. The correlated nature of beta-Ta is supported by the ab-initio calculations based on the r²scan approximation, which shows a suppressed single-particle density of states near the Fermi level reminiscent of the pseudo-gap in cuprates.