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 photo-emission spectroscopy (ARPES) is explored in this paper. Specifically we study the single-particle spectral function based on a two-hole variational ground state wavefunction [Phys. Rev. X 12, 011062 (2022)] in the $t$-$J$ 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 $t'$ is also examined, which shows interesting distinction between $t'/t > 0$ and $t'/t \leq 0$ 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 $t'$. Finally, a possible ``orthogonality catastrophe'' effect, namely, a ``dark matter'' component in the strongly correlated wavefunction that cannot be directly detected by the single-electron spectroscopy, is briefly discussed.