Characterizing Featureless Mott Insulating State by Quasiparticle Interferences - A Dynamical Mean Field Theory Prospect
The quasiparticle interferences (QPIs) of a Mott insulator are investigated using the $T$-matrix formalism implemented with the dynamical mean-field theory ($T$-DMFT). In Mott insulating state, because DMFT predicts a singularity in the real part of the electron self energy $\Re Σ(ω) \sim η/ω$ at low frequency, where $η$ can be considered as the 'order parameter' for Mott insulating state, QPIs are completely washed out at the small bias voltage. However, a further analysis shows that $\Re Σ(ω)$ in fact serves as an energy-dependent chemical potential shift. As a result, the effective bias voltage seen by the system is $eV' = eV - \Re Σ(eV)$. Due to the singular behavior of $\Re Σ(ω)$, a critical bias voltage $eV_c = \sqrtη$ satisfying $eV'=0$ exists if and only if in Mott insulating state. Consequently, the same QPI patterns produced by the non-interacting Fermi surfaces appears at this critical bias voltage $eV_c$ in Mott insulating state. We propose that this reentry of non-interacting QPI patterns at $eV_c$ could serve as an experimental signature of Mott insulating state, and the 'order parameter' can be experimentally measured as $η\sim (eV_c)^2$.