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arXiv:2506.08264 · Physical review. B./Physical review. B

Bound states at semiconductor–Mott insulator interfaces

Jan Verlage, Peter Kratzer

Published Dec 17, 2025• 1 citation
arXivHTMLPDF

Abstract

Utilizing the hierarchy of correlations in the context of a Fermi-Hubbard model, we deduce the presence of quasiparticle 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.

DOI
10.1103/ywd2-bh2w

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Utilizing the hierarchy of correlations in the context of a Fermi-Hubbard model, we deduce the presence of quasiparticle 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.
Abstract As a prototypical example for a heterostructure combining a weakly and a strongly interacting quantum many-body system, we study the interface between a semiconductor and a Mott insulator. Via the hierarchy of correlations, we derive and match the propagating or evanescent (quasi) particle solutions on both sides and assume that the interactions among the electrons in the semiconducting regions can be absorbed by an effective potential. While the propagation is described by a band-like dispersion in both the weakly and the strongly interacting case, the inverse decay length across the interface follows a different dependence on the band gap in the Mott insulator and the semiconductor. As one consequence, tunnelling through a Mott insulating layer behaves quite differently from a semiconducting (or band insulating) layer. For example, we find a strong suppression of tunnelling for energies in the middle between the upper and lower Hubbard band of the Mott insulator.
A heterostructure of a semi-infinite metal and a Mott insulator is considered. It is supposed that both materials have an identical lattice spacing and hopping integrals and differ in the Hubbard repulsion, which is negligible in the metal and exceeds the critical value for the Mott transition in the insulator. At half-filling and for low temperatures, the insulator has the long-range antiferromagnetic order. Its low-lying elementary excitations are standing spin waves and a spin-wave mode which is localized near the interface and has a two-dimensional dispersion. This mode ejects bulk modes from the boundary region. The antiferromagnetic ordering of the insulator induces an antiferromagnetic order in the metal where the magnetization decays exponentially with distance from the interface. This decay is characterized by the correlation length equal to 5–6 lattice spacings.
A heterostructure of a semi-infinite metal and a Mott insulator is considered. It is supposed that both materials have an identical lattice spacing and hopping integrals and differ in the Hubbard repulsion which is negligible in the metal and exceeds the critical value for the Mott transition in the insulator. At half-filling and for low temperatures the insulator has long-range antiferromagnetic order. Its low-lying elementary excitations are standing spin waves and a spin-wave mode which is localized near the interface and has a two-dimensional dispersion. This mode ejects bulk modes from the boundary region. The antiferromagnetic ordering of the insulator induces an antiferromagnetic order in the metal where the magnetization decays exponentially with distance from the interface. This decay is characterized by the correlation length of about 6 lattice spacings.
The possibility of novel behavior at interfaces between strongly and weakly correlated materials has come under increased study recently. In this paper, we use determinant quantum Monte Carlo to determine the interpenetration of metallic and Mott-insulator physics across an interface in the two-dimensional Hubbard Hamiltonian. We quantify the behavior of the density of states at the Fermi level and the short- and long-range antiferromagnetism as functions of the distance from the interface and with different interaction strength, temperature, and hopping across the interface. Induced metallic behavior into the insulator is evident over several lattice spacings, whereas antiferromagnetic correlations remain small on the metallic side. At large interface hopping, singlets form between the two boundary layers, shielding the two systems from each other.
For the Fermi-Hubbard model in the Mott insulator phase, we employ the hierarchy of correlations to study how doublon and holon quasi-particle excitations are affected by adding disorder to the system. We study two types of disorder: charge disorder, in the form of on-site potential randomness; and spin disorder, in the form of a fixed, randomly generated background spin arrangement. By analysing the quasi-particle eigen-spectra and quantifying the degree to which the corresponding eigen-states localise, we find both an energetic and spatial separation between localised and delocalised states in the charge disorder. In contrast, the spin disorder results in localised states throughout the quasi-particle bands. Finally, we repeat our calculations using strong-coupling perturbation theory, and compare the results obtained from both methods.
The problem of doping Mott insulators is of fundamental importance and long-standing interest in the study of strongly correlated electron systems. The advent of semiconductor based moiré materials opens a new ground for simulating the Hubbard model on the triangular lattice and exploring its rich phase diagram as a function of doping and external magnetic field. Based on our recent identification of spin polaron quasiparticle in Mott insulator, in this work we predict the emergence of a pseudogap metal phase at small doping below half filling and an intermediate range of fields, which exhibits a single-particle gap and a doping-dependent magnetization plateau.