Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism

TL;DR

This work addresses how localized impurities reveal topology in strongly correlated Mott insulators by contrasting non-interacting T-matrix results with a composite-operator method (COM) for interacting systems. It shows that impurity-induced subgap ring states primarily emerge from band mixing between emergent holon and doublon excitations, and that Green's function zeros can form ring states (Mott zeros ring states) under similar mixing conditions. Ring states occur in both topological and topologically trivial bands, with the Mixture of orbital content and holon-doublon hybridization being the decisive factor, rather than topology alone. The study analyzes Chern-Hubbard and BHZ-Hubbard models, including slight symmetry-breaking cases, and provides a unified framework linking bulk Green's function topology to real-space impurity spectroscopy in correlated electron systems, with implications for identifying topological vs trivial Mott phases via impurities.

Abstract

We study the formation of subgap impurity states in strongly correlated Mott insulators. We use a composite operator method that gives us access to both the bulk Green's function, as well as to the real-space Green's function in the presence of an impurity. Similar to the non-interacting systems, we show that the formation of impurity subgap states at large impurity potential ("Mott ring states") depends rather on the band-mixing, than on the topological character of the system. Thus even a trivial Mott insulator can under certain conditions exhibit ring states. For the system studied here the band mixing is that between the holon and doublon elementary excitations rather than an orbital mixing. Moreover we study the formation of bands of zeros in the correlated Green's function, believed to exhibit a free quasiparticle-like behavior. We show that in the presence of an impurity the same conclusion can be applied, i.e. ``Mott zeros ring states" form in the presence of topological bands of zeros, but also for trivial quasi-flat bands of zeros with band mixing.

Figures (5)

• Figure 1: Formation of impurity-induced subgap states in a two-band model with finite bandwidth. Panels (A), and (C) illustrate orbitally resolved bulk bands for a two-band Chern insulator: (A) trivial bands with uniform orbital character ($M=3.0t$), and (C) topological bands ($M=1.0 t$). In panels (B), and (D), the corresponding correction of the average density of states $\delta\rho(\omega)$ is shown as a function of impurity strength. For this example only the topological phase exhibits stable subgap states.
• Figure 2: Schematic representation of the self-consistent phase diagram from Ref. pangburn2024topological, showing the dependence on the crystal field $M$ and the intra-orbital Coulomb repulsion $U_s$, while keeping the Coulomb repulsion on the other orbital $U_p$ fixed. The white region of the phase diagram represents a trivial Mott insulator (MI). The blue region corresponds to the TMZ phase, characterized by topological Green's function zeros, while the red region denotes the TMBI phase, where the topology is associated with Green's function poles.
• Figure 3: Formation of impurity-induced subgap states in the Chern-Hubbard insulator. The first column depicts the orbitally resolved bulk bands (also denoted bands of poles). The third column depicts the orbitally resolved bands of Green's function zeros (also denoted bands of zeros). The first line corresponds to a trivial Mott insulator, characterized by trivial bands of both poles and zeros. The second line illustrates the TMBI phase, where the poles exhibit topological behavior and a mixed orbital character, while the zeros remain trivial. The third line corresponds to the TMZ phase, for which the poles are topologically trivial, while the zeros are topological and exhibit a mixed orbital character. The panels in the second column depict the correction to the average density of states, $\delta\rho(\omega)$, as a function of energy and impurity strength. Each panel corresponds to a band-of-poles configuration from the first column. Similarly the panels in the fourth column depict $\min[\rm{eig}(\mathcal{G}_V)]$ as a function of energy and impurity strength, each panel corresponding to a configuration for a band of zeroes from the third column. The main observation is the formation of Mott ring states and correspondingly of Mott zeros ring states in the presence of topological sets of bands with band mixing. The COM parameters used to generate this figure are given in App. \ref{['App:Params']}.
• Figure 4: Formation of ring states in topologically trivial models. In the first column, we present the band structure of a ribbon with a width of 64 and a length of 128 (in the periodic direction) for three distinct models: The first line corresponds to a trivial non-interacting model with weak edge state hybridization with $\Delta_\tau=0.1t$, $M=1.0 t$ and $\alpha^{SOC}=0.05t$. In (B) we depict the corresponding spin-resolved impurity contribution to the density of states $\delta \rho_\sigma(\omega)$. The second line illustrates a trivial Mott insulator derived from the TSMBI phase by introducing a small gap in the edge states, with the resulting average density of states in the presence of an impurity $\delta \rho(\omega)$ shown in panel (D). The third line depicts a trivial Mott insulator obtained by slightly breaking time-reversal symmetry in a TSMZ phase, with $\min[|\lambda(\mathcal{G}_V)|]$ shown in panel (F). The COM parameters used to generate this figure are given in App. \ref{['App:Params']}.
• Figure 5: Comparison of numerical and analytical predictions for the positions of impurity-induced subgap states in flat-band systems. In panels (A) and (C), orbitally-resolved bands are displayed for (A) topological bands and (C) trivial bands with mixed orbital character. This corresponds to a flattened two-band Chern insulator with $M=1.0t$ (A) and $M=2.05t$ (C). In panels (B) and (D), the correction to the density of states is shown as a function of impurity strength for the corresponding bands. The analytical prediction for the asymptotic position of the subgap state at large impurity strength, indicated by the dashed line, aligns precisely with the numerical computation.