Pseudogap in a crystalline insulator doped by disordered metals

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 ago 1-15 , 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 nd 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 alkalimetal 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 materials [16][17][18][19][20] , a common aspect of which is the crystalline insulator doped by disordered (liquid) dopants.

A Tunable Fano Resonator with High Sensitivity Based on Black Phosphorus in the Terahertz Band

“…In addition, both sides of the BP layer are covered with SiO 2 layers, which provide protection as well as support. As the electron doping level of the BP changes from 1.0 × 10 12 cm −2 to 7.0 × 10 13 cm −2 , [ 24,38 ] the operating frequency of the Fano resonator shifts 48 GHz to the right, the resonance peak increases, and its resonance curve becomes sharper, as shown in Figure 4b. As the change in electronic doping of BP affects the refractive index of BP, the tunable performance of the Fano resonator can be achieved.…”

Evolution of the Electronic Structure of Ultrathin MnBi2Te4 Films

“…Except for the drastic difference of the TSSs, the bulk band structure, including the dispersion and the bulk band gap, is quite similar in the film and bulk sample, suggesting that the surface situation and doping level are crucial for the dispersion of the TSSs. Interestingly, surface doping of alkali metals, by applying an effective electric field on the sample surface (Figure f), can effectively tune both the surface situation and doping level, which has been widely applied to modulate the electronic structure of different materials. − We will use this method to investigate the difference between the electronic structures of the film and bulk MnBi 2 Te 4 .…”