Unconventional band structure and pseudogap of liquid metals on a crystalline insulator

Abstract

A key to understand how electrons behave in crystalline solids is the band structure that connects the energy of electron waves to their wavenumber (k). Even in the phase of matter with only short-range order (liquid), the coherent part of electron waves still possesses a band structure. Theoretical models for the band structure of liquid metals were formulated more than 5 decades ago1-15, but so far, it has remained unobserved experimentally. Here, we reveal the band structure of liquid metals using the interface between liquid dopants (alkali metals) and a crystalline insulator (black phosphorus). We find that the conventional parabolic band structure of free electrons bends back towards zero k with the isotropic pseudogap of 30-240 meV from the Fermi level. This is the k renormalization caused by resonance scattering that leads to the formation of quasi-bound states in the scattering potential of liquid alkali-metal ions. The depth of this potential tuned by different kinds of alkali metal (Na, K, Rb, and Cs) allows us to classify the pseudogap of p-wave and d-wave resonance. Our results provide a key clue to the pseudogap phase of various materials16-20, a common aspect of which is the crystalline insulator doped by disordered (liquid) dopants.