Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0805.0566 · Physical Review Letters

Kondo Proximity Effect: How Does a Metal Penetrate into a Mott Insulator?

R. W. Helmes, Theo A. Costi, Achim Rosch

Published Aug 6, 2008• 79 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.101.066802

Related papers

Dynamical Mean Field Theory of inhomogeneous correlated systems

R. W. Helmes

In the last one and a half decade, the Dynamical Mean Field Theory (DMFT) allowed to get insight into the Mott metal-insulator transition (MMIT) and many long-standing questions about the nature of the transition could be answered, at least in the limit of infinite dimensions. In this thesis, the adaption of the DMFT to inhomogeneous systems is studied, opening the possibility to study a rich variety of systems and challenging physical questions. Firstly, the basic problem is studied, how a metal penetrates into a Mott insulator, where analytically found power-laws at the critical point can be confirmed with numerics. Secondly, the phase separation between metal and insulator is investigated, which can occur since the MMIT is a first order transition. The spontaneous build up of domains is observed in numerical simulations and the domain walls are examined. Finally, the MMIT of fermionic atoms in an optical lattice is studied.

•Jan 1, 2008•2 citations

Mott quantum criticality in the one-band Hubbard model: Dynamical mean-field theory, power-law spectra, and scaling

Heike Eisenlohr, Seung‐Sup B. Lee, Matthias Vojta C

Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e., power-law) solutions, corresponding to the metastable insulator at the boundary of the metal-insulator coexistence region; these solutions can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization-group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures and hence is difficult to access numerically, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a different power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. We connect our findings to experiments on tunable Mott materials.

arXiv:1906.05293•Physical review. B./Physical review. B•Oct 31, 2019•27 citations

Strongly correlated metal interfaces in the Gutzwiller approximation

Giovanni Borghi, Michele Fabrizio, Erio Tosatti

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.

arXiv:0911.0718•Physical Review B•Mar 23, 2010•25 citations

Mott transition at large orbital degeneracy: Dynamical mean-field theory

Serge Florens, Antoine Georges, Gabriel Kotliar +1 more

We study analytically the Mott transition of the N-orbital Hubbard model using dynamical mean-field theory and a low-energy projection onto an effective Kondo model. It is demonstrated that the critical interaction at which the insulator appears ${(U}_{c1})$ and the one at which the metal becomes unstable ${(U}_{c2})$ have a different dependence on the number of orbitals as the latter becomes large: ${U}_{c1}\ensuremath{\propto}\sqrt{N}$ while ${U}_{c2}\ensuremath{\propto}N.$ An exact analytical determination of the critical coupling ${U}_{c2}/N$ is obtained in the large-N limit. The metallic solution close to this critical coupling has many similarities at low-energy with the results of slave boson approximations, to which a comparison is made. We also discuss how the critical temperature associated with the Mott critical endpoint depends on the number of orbitals.

arXiv:cond-mat/0205263•Physical review. B, Condensed matter•Nov 8, 2002•79 citations

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

E. Z. Kuchinskii, I. A. Nekrasov, M. V. Sadovskii

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.

arXiv:0706.2618•Journal of Experimental and Theoretical Physics•Mar 1, 2008•24 citations

Excitations near the boundary between a metal and a Mott insulator

A. Sherman, Michael Schreiber

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.

Journal of Physics Conference Series•Jan 1, 2010•2 citations
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.
In the last one and a half decade, the Dynamical Mean Field Theory (DMFT) allowed to get insight into the Mott metal-insulator transition (MMIT) and many long-standing questions about the nature of the transition could be answered, at least in the limit of infinite dimensions. In this thesis, the adaption of the DMFT to inhomogeneous systems is studied, opening the possibility to study a rich variety of systems and challenging physical questions. Firstly, the basic problem is studied, how a metal penetrates into a Mott insulator, where analytically found power-laws at the critical point can be confirmed with numerics. Secondly, the phase separation between metal and insulator is investigated, which can occur since the MMIT is a first order transition. The spontaneous build up of domains is observed in numerical simulations and the domain walls are examined. Finally, the MMIT of fermionic atoms in an optical lattice is studied.
Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e., power-law) solutions, corresponding to the metastable insulator at the boundary of the metal-insulator coexistence region; these solutions can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization-group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures and hence is difficult to access numerically, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a different power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. We connect our findings to experiments on tunable Mott materials.
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.
We study analytically the Mott transition of the N-orbital Hubbard model using dynamical mean-field theory and a low-energy projection onto an effective Kondo model. It is demonstrated that the critical interaction at which the insulator appears (Uc1){(U}_{c1})(Uc1​) and the one at which the metal becomes unstable (Uc2){(U}_{c2})(Uc2​) have a different dependence on the number of orbitals as the latter becomes large: ${U}_{c1}\ensuremath{\propto}\sqrt{N}$ while ${U}_{c2}\ensuremath{\propto}N.$ An exact analytical determination of the critical coupling Uc2/N{U}_{c2}/NUc2​/N is obtained in the large-N limit. The metallic solution close to this critical coupling has many similarities at low-energy with the results of slave boson approximations, to which a comparison is made. We also discuss how the critical temperature associated with the Mott critical endpoint depends on the number of orbitals.
The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.
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.