Composite structure of single-particle spectral function in lightly-doped Mott insulators

The internal structure of doped holes in the Mott insulator may provide important insight into the physics of doped cuprates. Its observability via a single-particle probe by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES) is explored in this paper. Specifically, we study the single-particle spectral function based on a two-hole variational ground-state wave function [J.-Y. Zhao et al., Phys. Rev. X 12, 011062 (2022)] in the $t\text{\ensuremath{-}}J$ model. The latter as a strongly correlated state possesses a dichotomy of $d$-wave Cooper pairing and $s$-wave ``twisted'' hole pairing. This pairing structure will give rise to two branches of local spectral function at finite energies. The low-lying one corresponds to a nodal-like quasiparticle excitation and the higher branch is associated with the pair breaking of ``twisted'' quasiparticles, with the threshold energy resembling a pseudogap, which is consistent with the recent STS observation. It can be further extended into energy spectra in momentum space measurable by ARPES, where the low-energy dispersion is also shown to agree well with the quantum Monte Carlo numerical result for a single hole. It implies that the dominant pairing force arises from the twisted holes showing up in the high-energy branch. The effect of the next-nearest-neighbor hopping integral ${t}^{\ensuremath{'}}$ is also examined, which shows an interesting distinction between ${t}^{\ensuremath{'}}/t>0$ and ${t}^{\ensuremath{'}}/t\ensuremath{\le}0$ with a dramatic shift of the low-lying excitation from the nodal region to the antinodal region, but with the high-energy branch remaining insensitive to ${t}^{\ensuremath{'}}$. Finally, a possible ``orthogonality catastrophe'' effect, namely, a ``dark matter'' component in the strongly correlated wave function that cannot be directly detected by the single-electron spectroscopy, is briefly discussed.