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arXiv:0911.0718 · Physical Review B

Strongly correlated metal interfaces in the Gutzwiller approximation

Giovanni Borghi, Michele Fabrizio, Erio Tosatti

Published Mar 23, 2010• 25 citations
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Abstract

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.

DOI
10.1103/physrevb.81.115134

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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∼1/2\ensuremath{\sim}1/2\ensuremath∼1/2 in the present approximation, mean field in character) as the (continuous, paramagnetic) Mott transition is approached.
Introduction In this chapter we study metal–insulator transitions which occur due to correlations between the charge carriers. This quantum phase transitions results from the competition between kinetic energy and Coulomb repulsion where the latter has the tendency to localise the electrons. The simplest model which describes this competition is the one-band Hubbard model with its two energy scales, the bandwidth W and the Coulomb repulsion U between electrons of opposite spins on the same site. For a fixed density of electrons, n = 1; as the ratio U/W increases, we expect to find a zero-temperature phase transition from a metallic state to an insulator where the electrons are frozen at the lattice sites. The method employed here to investigate this transition is the Gutzwiller approach (Gutzwiller, 1965). This is a variational method which played an important role in providing a framework for the ideas of Mott on the problem of the metal–insulator transition (Mott, 1974). On the metallic side of the transition, this approach describes a metal with renormalised Fermi liquid parameters, essentially with enhanced effective mass and uniform susceptibility. This is the so-called highly correlated electron gas (Brinkman and Rice, 1970) for which the metal oxide V 2 O 3 is the prototype system. In the insulating side, Gutzwiller's approximation yields a noninteracting system of localised electrons. This insulating phase is incompressible , i.e. has zero compressibility and infinite zero temperature susceptibility. The latter is not a consequence of interactions but simply due to the divergence of the Curie susceptibility, χ ∝ 1 /T , of non-interacting moments at T = 0. Then, in Gutzwiller's approach the transition is from a paramagnetic metal to a paramagnetic insulator. We will continue using the designation Mott transition to describe this type of phase transition where the insulating phase has no long-range magnetic order. In real systems, most frequently, localisation due to interactions is accompanied by the appearance of antiferromagnetic order.
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.
We investigate by means of the time-dependent Gutzwiller approximation the transport properties of a strongly correlated slab subject to Hubbard repulsion and connected with to two metallic leads kept at a different electrochemical potential. We focus on the real-time evolution of the electronic properties after the slab is connected to the leads and consider both metallic and Mott insulating slabs. When the correlated slab is metallic, the system relaxes to a steady state that sustains a finite current. The zero-bias conductance is finite and independent of the degree of correlations within the slab as long as the system remains metallic. On the other hand, when the slab is in a Mott insulating state, the external bias leads to currents that are exponentially activated by charge tunneling across the Mott-Hubbard gap, consistent with the Landau-Zener dielectric breakdown scenario.
The dynamical mean-field theory (DMFT) is employed to study the correlation-driven metal-insulator transition in the semi-infinite Hubbard model at half-filling and zero temperature. We consider the low-index surfaces of the three-dimensional simple-cubic lattice, and systematically vary the model parameters at the very surface, the intralayer and interlayer surface hopping, and the surface Coulomb interaction. Within the DMFT the self-energy functional is assumed to be local. Therewith, the problem is self-consistently mapped onto a set of coupled effective impurity models corresponding to the inequivalent layers parallel to the surface. Assuming that the influence of the high-energy Hubbard bands on the low-energy quasiparticle resonance can be neglected at the critical point, a simplified ``linearized DMFT'' becomes possible. The linearized theory, however, is formally equivalent to the Weiss molecular-field theory for the semi-infinite Ising model. This implies that qualitatively the rich phenomenology of the Landau description of second-order phase transitions at surfaces has a direct analog for the surface Mott transition. Motivated by this formal analogy, we work out the predictions of the linearized DMFT in detail. It is found that under certain circumstances the surface of a Mott insulator can be metallic, while a Mott-insulating surface of a normal metal is not possible. We derive the corresponding phase diagrams, the (mean-field) critical exponents and the critical profiles of the quasiparticle weight. The results are confirmed by a fully numerical evaluation of the DMFT equations using the exact-diagonalization (ED) method. By means of the ED approach, we especially investigate the noncritical parts of the phase diagrams and discuss the U and layer dependence of the quasi-particle weight. For strong modifications of the surface model parameters, the surface low-energy electronic structure dynamically decouples from the bulk.
We consider a heterostructure of a metal and a paramagnetic Mott insulator using an adaptation of dynamical mean-field theory to describe inhomogeneous systems. The metal can penetrate into the insulator via the Kondo effect. We investigate the scaling properties of the metal-insulator interface close to the critical point of the Mott insulator. At criticality, the quasiparticle weight decays as 1/x;{2} with distance x from the metal within our mean-field theory. Our numerical results (using the numerical renormalization group as an impurity solver) show that the prefactor of this power law is extremely small.
Abstract: The metal–insulator transition (MIT) constitutes one of the most profound and persistent problems in condensed matter physics, sitting at the intersection of electronic structure theory, many-body physics, and emergent quantum phenomena. Conventional band theory, which successfully classifies materials as metals or insulators according to the filling of their electronic bands, fails dramatically when confronted with a class of compounds transition metal oxides chief among them that ought to be metallic by band-counting arguments yet are robustly insulating in the laboratory. The resolution of this paradox required abandoning the independent-electron picture entirely and recognizing that strong Coulomb repulsion between electrons can, by itself, drive localization. This insight, formalized by Mott and later distilled into the Hubbard model, established correlation-driven insulation as a phenomenon distinct from band insulation. The present paper offers a theoretical exploration of the MIT problem, tracing its conceptual development from the Mott criterion through the Hubbard Hamiltonian, the Brinkman–Rice scenario of quasiparticle mass divergence, and the watershed development of dynamical mean-field theory (DMFT), which rendered the Mott transition quantitatively tractable for the first time. We argue that the competition between the electronic bandwidth and the on-site interaction encoded in the ratio U/W provides the unifying organizing principle for the field. Building toward the modern frontier, we examine how the Mott transition connects to quantum phase transitions and quantum criticality, where zero-temperature instabilities governed by quantum rather than thermal fluctuations produce non-Fermi-liquid behavior and anomalous scaling. Case studies of vanadium oxides, rare-earth nickelates, and doped cuprates illustrate the diversity and subtlety of real correlated materials. We conclude that the MIT remains a central and unresolved problem whose continued study is increasingly entangled with the development of quantum materials and quantum technologies. Keywords: Metal–Insulator Transition; Mott Insulator; Strongly Correlated Electrons; Hubbard Model; DMFT; Quantum Criticality; Quantum Materials; Condensed Matter Physics