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arXiv:1208.3234 · Physical Review B

Density of states and magnetic correlations at a metal-Mott insulator interface

Mi Jiang, G. G. Batrouni, Richard T. Scalettar

Published Nov 12, 2012• 11 citations
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Abstract

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.

DOI
10.1103/physrevb.86.195117

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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.
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.
We study the conductivity, density of states, and magnetic correlations of a two-dimensional, two-band fermion Hubbard model using determinant quantum Monte Carlo (DQMC) simulations. We show that an orbitally selective Mott transition (OSMT) occurs in which the more weakly interacting band can be metallic despite complete localization of the strongly interacting band. The DQMC method allows us to test the validity of the use of a momentum independent self-energy which has been a central approximation in previous OSMT studies. In addition, we show that long range antiferromagnetic order (LRAFMO) is established in the insulating phase, similar to the single band, square lattice Hubbard Hamiltonian. Because the critical interaction strengths for the onset of insulating behavior are much less than the bandwidth of the itinerant orbital, we suggest that LRAFMO plays a key role in the transitions.
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.
We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard model on a two-dimensional square lattice using determinant quantum Monte Carlo. Evaluation of the temperature dependence of the conductivity demonstrates that the metallic region extends for a finite range of interaction values. The Mott phase at strong coupling is accompanied by antiferromagnetic order. Inclusion of these intersite correlations changes the phase diagram qualitatively compared to dynamical mean field theory.
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.
The Hubbard model at temperatures above the Néel transition, despite being a paramagnet, can exhibit rich physics due to the interplay of Fermi surface, on-site interaction U and thermal fluctuations. Nevertheless, the understanding of the crossover physics remains only at a qualitative level, because of the intrinsically smooth behavior. Employing an improved variant of the numerically exact auxiliary-field quantum Monte Carlo algorithm equipped with numerical analytic continuation, we obtain a broad variety of thermodynamic and dynamical properties of the three-dimensional Hubbard model at half filling, quantitatively determine the crossover boundaries, and observe that the metal-insulator crossover regime, in which antiferromagnetic spin correlations appear strongest, exists over an extended regime in between the Fermi liquid for small U and the Mott insulator for large U. In particular, the location of the most rapid suppression of double occupancy as U increases, is found to fully reside in the metallic Fermi liquid regime, in contrast to the conventional intuition that it is a representative feature for entering the Mott insulator. Beside providing a reliable methodology for numerical study of crossover physics, our work can also serve as a timely and important guideline for the most recent optical lattice experiments.