Bound States at Semiconductor -- Mott Insulator Interfaces

TL;DR

The paper addresses bound-state formation at interfaces between Mott insulators and semiconductors within a unified Fermi-Hubbard framework. It introduces a hierarchy of correlations with a $1/Z$ expansion to derive Schrödinger-like equations for coupled doublon and holon amplitudes atop unpolarized and Mott–Néel mean-field backgrounds, enabling analytical boundary-value analyses. The main contributions include explicit conditions for interface-bound states, minimum interface perturbations $\Delta V_{\min}$ in various band-alignments, and the description of standing-wave bound states in a Mott region between two semiconductors, along with decay constants $\kappa_{\mathrm{Mott}}$ and $\kappa_{\mathrm{semi}}$. The results illuminate how spin background, band offsets, and interface perturbations control bound-state existence and localization, suggesting mechanisms for interfacial metallicity and guiding experimental material choices and tuning via gate voltages. This framework provides a tractable, semi-analytic route to predict and engineer bound states in correlated heterostructures with potential implications for oxide electronics and quantum well devices.

Abstract

Utilizing the hierarchy of correlations in the context of a Fermi-Hubbard model, we deduce the presence of quasi-particle bound states at the interface between a Mott insulator and a semiconductor, as well as within a semiconductor-Mott-semiconductor heterostructure forming a quantum well. In the case of the solitary interface, the existence of bound states necessitates the presence of an additional perturbation with a minimal strength depending on the spin background of the Mott insulator. Conversely, within the quantum well, this additional perturbation is still required to have bound states while standing-wave solutions even exist in its absence.

Figures (11)

• Figure 1: Density of states $D(E)$ of the Mott insulator (blue dashed) and the semiconductor (red solid) together with the delta-peaks of the bound states shown as the black dashed vertical lines.
• Figure 2: Bound state for the holon wave function $p_\mu^0$ and quasi particle probability distribution $|p_\mu^0|^2$ at the interface for the unpolarized background with $E=1.16U$. The parameters are $V=1.1U$, $T=0.4U$ and $\Delta V=0.2U$.
• Figure 3: Minimally needed interface perturbation $\Delta V_\mathrm{min}$ in the positive (solid) and negative (dashed) case as a function of the on-site potential offset $V$. The hopping strength $T=0.4U$ is fixed. The annotations give the approximate formula in the $\Delta V>0$ case. The vertical lines give the band offsets for $\mathrm{SrTiO}_3$ interface with $\mathrm{SmTiO}_3$ and $\mathrm{LaVO}_3$, respectively.
• Figure 4: The decay constant $\kappa_{\text{semi}}$ in the unpolarized semiconducting half-space is shown as a function of the interface perturbation for different band offsets $V$. The hopping strength is fixed at $T=0.2U$. Note that gap in the $0.2 U$ data.
• Figure 5: The decay constant $\kappa_{\text{Mott}}$ in the unpolarized Mott half-space is shown for different band offsets $V$ as a function of the interface perturbation $\Delta V$. The hopping strength is fixed at $T=0.2U$.