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arXiv:2303.13507 · International Journal of Theoretical Physics

Quasi-particle Propagation Across Semiconductor–Mott Insulator Interfaces

Jan Verlage, Friedemann Queißer, Nikodem Szpak, Jürgen König, Peter Kratzer, Ralf Schützhold

Published Nov 6, 2024• 4 citations
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Abstract

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.

DOI
10.1007/s10773-024-05814-5

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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.
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.
We study the effect of spatial inhomogeneity on the physics of a strongly correlated electron system exhibiting a metallic phase and a Mott insulating phase, represented by the simple Hubbard model. In three dimensions, we consider various geometries, including vacuum-metal-vacuum, a junction between a weakly and a strongly correlated metal, and finally the double junctions metal-Mott insulator-metal and metal-strongly correlated metal-metal. We apply the self-consistent Gutzwiller technique recently developed in our group, whose approximate nature is compensated by an extreme flexibility, ability to treat very large systems, and physical transparency. The main general result is a clear characterization of the position-dependent metallic quasiparticle spectral weight. Its behavior at interfaces reveals the ubiquitous presence of exponential decays and crossovers with decay lengths of clear physical significance. The decay length of the metallic strength in a weakly-strongly correlated metal interface is due to poor screening in the strongly correlated side. That from a metal into a Mott insulator is due to tunneling. In both cases, the decay length is a bulk property and diverges with a critical exponent ($\ensuremath{\sim}1/2$ in the present approximation, mean field in character) as the (continuous, paramagnetic) Mott transition is approached.
Via the hierarchy of correlations, we study the Mott insulator phase of the Fermi-Hubbard model in the limit of strong interactions and derive a quantum Boltzmann equation describing its relaxation dynamics. In stark contrast to the weakly interacting case, we find that the scattering cross sections strongly depend on the momenta of the colliding quasiparticles and holes. Therefore, the relaxation towards equilibrium crucially depends on the spectrum of excitations. For example, for particle-hole excitations directly at the minimum of the (direct) Mott gap, the scattering cross sections vanish such that these excitations can have a very long lifetime.
In strongly correlated electron systems, the emergence of states in the Mott gap in the single-particle spectrum following the doping of the Mott insulator is a remarkable feature that cannot be explained in a conventional rigid-band picture. Here, based on an analysis of the quantum numbers and the overlaps of relevant states, as well as through a demonstration using the ladder and bilayer $t\text{\ensuremath{-}}J$ models, it is shown that in a continuous Mott transition due to hole doping, the magnetically excited states of the Mott insulator generally emerge in the electron-addition spectrum with the dispersion relation shifted by the Fermi momentum in the momentum region where the lower Hubbard band is not completely filled. This implies that the dispersion relation of a free-electron-like mode in the electron-addition spectrum eventually transforms into essentially the momentum-shifted magnetic dispersion relation of the Mott insulator, while its spectral weight gradually disappears toward the Mott transition. This feature reflects the spin-charge separation 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.
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.