Pseudogap in a crystalline insulator doped by disordered metals.

Key to our understanding of how electrons behave in crystalline solids is the band structure that connects the energy of electron waves to their wavenumber. Even in phases of matter with only short-range order (liquid or amorphous solid), the coherent part of electron waves still has a band structure. Theoretical models for the band structure of liquid metals were formulated more than five decades ago1-15, but, so far, band-structure renormalization and the pseudogap induced by resonance scattering have remained unobserved. Here we report the observation of the unusual band structure at the interface of a crystalline insulator (black phosphorus) and disordered dopants (alkali metals). We find that a conventional parabolic band structure of free electrons bends back towards zero wavenumber with a pseudogap of 30-240 millielectronvolts from the Fermi level. This is wavenumber renormalization caused by resonance scattering, leading to the formation of quasi-bound states in the scattering potential of alkali-metal ions. The depth of this potential tuned by different kinds of disordered alkali metal (sodium, potassium, rubidium and caesium) allows the classification of the pseudogap of p-wave and d-wave resonance. Our results may provide a clue to the puzzling spectrum of various crystalline insulators doped by disordered dopants16-20, such as the waterfall dispersion observed in copper oxides.

Black phosphorus as a bipolar pseudospin semiconductor.

Semiconductor devices rely on the charge and spin of electrons, but there is another electronic degree of freedom called pseudospin in a two-level quantum system1 such as a crystal consisting of two sublattices2. A potential way to exploit the pseudospin of electrons in pseudospintronics3-5 is to find quantum matter with tunable and sizeable pseudospin polarization. Here, we propose a bipolar pseudospin semiconductor, where the electron and hole states have opposite net pseudospin polarization. We experimentally identify such states in anisotropic honeycomb crystal-black phosphorus. By sublattice interference of photoelectrons, we find bipolar pseudospin polarization greater than 95% that is stable at room temperature. This pseudospin polarization is identified as a consequence of Dirac cones merged in the highly anisotropic honeycomb system6,7. The bipolar pseudospin semiconductor, which is a pseudospin analogue of magnetic semiconductors, is not only interesting in itself, but also might be useful for pseudospintronics.