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:2212.14352 · Physical review. B./Physical review. B

Correlated Mott insulators in a strong electric field: The effects of phonon renormalization

Tommaso Maria Mazzocchi, Daniel Werner, Paolo Gazzaneo, Enrico Arrigoni

Published Apr 4, 2023• 7 citations
arXivHTMLPDF

Abstract

We characterize the response of a Mott insulating system to a static electric field in terms of its conducting and spectral properties. Dissipation is included by a coupling to fermionic baths and to either optical or acoustic phonons. This paper extends and completes the analysis made in a previous work by the authors [Mazzocchi et al., Phys. Rev. B 106, 125123 (2022)]. In the present work, phonons are included diagrammatically within the Migdal approximation by also including self-consistency from the electronic feedback. The nonequilibrium steady state is addressed by means of the dynamical mean-field theory based on the nonequilibrium Green's function approach, while the so-called auxiliary master equation approach is employed as impurity solver. With optical phonons the self-consistency suppresses the steady-state current for field strengths comparable to the band gap with respect to the non-self-consistent case. This is due to the interaction of phonons with the hot electrons of the lattice which increases their temperature, thus providing a less effective relaxation channel for the current-induced Joule heat. In addition, in the case of optical phonons, the results are essentially independent of the temperature of the fermionic baths, as the latter is sensibly smaller than their characteristic frequency. On the other hand, with acoustic phonons the steady-state current is slightly suppressed by the self-consistent treatment only at field strengths close to half of the gap and especially at very small phonon frequency. Also, in this case, the results seem to slightly depend on the temperature of the fermionic baths.

DOI
10.1103/physrevb.107.155103

Related papers

Correlated Mott insulators in strong electric fields: Role of phonons in heat dissipation

Tommaso Maria Mazzocchi, Paolo Gazzaneo, Jan Lotze +1 more

We study the spectral and transport properties of a Mott insulator driven by a static electric field into a nonequilibrium steady state. For the dissipation, we consider two mechanisms: wide band fermion reservoirs and phonons included within the Migdal approximation. The electron correlations are treated via nonequilibrium dynamical mean field theory with an impurity solver suitable for strong correlations. We find that dissipation via phonons is limited to restricted ranges of field values around Wannier-Stark resonances. To cover the full range of field strengths, we allow for a small coupling with fermionic baths, which stabilizes the solution. When considering both dissipation mechanisms, we find that phonons enhance the current for field strengths close to half of the gap while lowering it at the gap resonance as compared to the purely electronic dissipation used by Murakami and Werner [Murakami and Werner, Phys. Rev. B 98, 075102 (2018)]. Once phonons are the only dissipation mechanism, the current in the metallic phase is almost one order of magnitude smaller than the typical values obtained by coupling to a fermionic bath. In this case, the transport regime is characterized by an accumulation of charge in the upper Hubbard band described by two effective chemical potentials.

arXiv:2207.01921•Physical review. B./Physical review. B•Sep 15, 2022•12 citations

Impact of disorder and phonons on the Hubbard bands of Mott insulators in strong electric fields

Tommaso Maria Mazzocchi, Daniel Werner, Enrico Arrigoni

We characterize the current-carrying nonequilibrium steady state (NESS) in a single-band Hubbard model confronted with a static electric field in the presence of quenched disorder. Beyond the linear response regime, the electric field amplitude must compensate for at least half of the band gap to have a non-negligible stationary current. As the disorder is not expected to dissipate the extra energy injected by the field, optical phonons assisted by a fermionic heat bath serve as dissipation channels for the current-induced Joule heat generated by the accelerated electrons. The NESS of the system is addressed employing the dynamical mean-field theory using the so-called auxiliary master equation approach as impurity solver. Disorder effects are treated locally via the coherent potential approximation (CPA) and the self-consistent Born (SCB) approach. In the regime in which the two schemes yield similar results, we employ the SCB as it is computationally cheaper than the CPA. We show that, in a purely electronic setup, the disorder-induced dephasing cannot contribute states within the gap but only smear out the edges of the Hubbard bands. When phonons are taken into account, the different nature of disorder-induced dephasing and phonon-related dissipation becomes clear. We show that although both disorder and electron-phonon interaction enhance the current at off-resonant fields, disorder effects play a marginal role since they cannot provide in-gap states which are instead brought about by phonons and represent the privileged relaxation pathway for excited electrons.

arXiv:2310.11833•Physical review. B./Physical review. B•Jan 10, 2024•3 citations

Impact ionization processes in a photodriven Mott insulator: Influence of phononic dissipation

Paolo Gazzaneo, Tommaso Maria Mazzocchi, Jan Lotze +1 more

We study a model for photovoltaic energy collection consisting of a Mott-insulating layer in presence of acoustic phonons, coupled to two wide-band fermion leads at different chemical potentials and driven into a nonequilibrium steady state by a periodic electric field. We treat electron correlations with nonequilibrium dynamical mean-field theory using the so-called auxiliary master-equation approach as impurity solver and include dissipation by acoustic phonons via the Migdal approximation. For a small hybridization to the leads, we obtain a peak in the photocurrent as a function of the driving frequency which can be associated with impact ionization processes. For larger hybridizations the shallow peak suggests a suppression of impact ionization with respect to direct photovoltaic excitations. Acoustic phonons slightly enhance the photocurrent for small driving frequencies and suppress it at frequencies around the main peak at all considered hybridization strengths.

arXiv:2208.14752•Physical review. B./Physical review. B•Nov 21, 2022•10 citations

Transport through a correlated interface: Auxiliary master equation approach

Irakli Titvinidze, Antonius Dorda, Wolfgang von der Linden +1 more

We present improvements of a recently introduced numerical method [E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)] to compute steady-state properties of strongly correlated electronic systems out of equilibrium. The method can be considered as a nonequilibrium generalization of exact diagonalization based dynamical mean-field theory (DMFT). The key modification for the nonequilibrium situation consists in addressing the DMFT impurity problem within an auxiliary system consisting of the correlated impurity, ${N}_{b}$ uncorrelated bath sites, and two Markovian environments (sink and reservoir). Algorithmic improvements in the impurity solver allow to treat efficiently larger values of ${N}_{b}$ than previously in DMFT. This increases the accuracy of the results and is crucial for a correct description of the physical behavior of the system in the relevant parameter range including a semiquantitative description of the Kondo regime. To illustrate the approach, we consider a monoatomic layer of correlated orbitals, described by the single-band Hubbard model, attached to two metallic leads. The nonequilibrium situation is driven by a bias voltage applied to the leads. For this system, we investigate the spectral function and the steady-state current-voltage characteristics in the weakly as well as in the strongly interacting limit. In particular, we investigate the nonequilibrium behavior of quasiparticle excitations within the Mott gap of the correlated layer. We find for low-bias voltage Kondo-type behavior in the vicinity of the insulating phase. In particular, we observe a splitting of the Kondo resonance as a function of the bias voltage.

arXiv:1508.02953•Physical Review B•Dec 21, 2015•24 citations

Keldysh field theory of a driven dissipative Mott insulator: Nonequilibrium response and phase transitions

S. G. Sankar, Vikram Tripathi

Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics, dynamical constraints, and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady-state DC transport regime and the role of dissipation in it, and electric-field-driven phase transitions. Despite tremendous efforts over the past decade employing various numerical and analytical approaches, the manner in which a nonequilibrium steady state gets established has remained an unresolved problem. We develop here an effective large-$\mathcal{N}$ Keldysh field theory for studying nonequilibrium transport in a regular one-dimensional dissipative Mott insulator system subjected to a uniform electric field. Upon abruptly turning on the electric field (a quench), a transient oscillatory current response reminiscent of Bloch oscillations is found. In the regime of small tunneling conductance the amplitude of these oscillations, over a large time window, decreases as an inverse square power law in time, ultimately going over to an exponential decay beyond a large characteristic time ${\ensuremath{\tau}}_{d}$ that increases with $\mathcal{N}.$ Such a relaxation to a steady-state DC response is absent in the dissipation-free Hubbard chain at half filling. The steady-state current at small fields is governed by large-distance cotunneling, a process absent in the equilibrium counterpart. The low-field DC current has a Landau-Zener-Schwinger form but qualitatively differs from the expression for pair-production probability for the dissipation-free counterpart. The breakdown of perturbation theory in the Mott phase possibly signals a nonequilibrium phase transition to a metallic phase. Our study sheds light on the approach of a driven, dissipative strongly correlated system to a nonequilibrium steady state and also provides a general analytic microscopic framework for understanding other nonequilibrium phenomena in these systems.

arXiv:1808.07064•Physical review. B./Physical review. B•Jun 7, 2019•8 citations

Nonequilibrium effects in strongly correlated systems

Petra Schmidt

The dynamical mean field theory is extended using the Keldysh Green's function formalism to study strongly correlated systems away from equilibrium. This technique has been applied to two different systems, whose insulating behavior is due to electronic correlation effects: excitonic insulators and Mott insulators. The real-time development of the electronic properties of excitonic insulators, such as the distribution function and the gap, after an ultrashort intense is studied. The appropriate self-consistency equations turned out to be matrix equations in frequency and Keldysh space. The self-consistency equations derived for the two-plane Hubbard model with a periodic time-dependent coupling between the two planes are matrix equations in energy sidebands due to quasi-energy conservation modulo the external frequency. Numerical results are shown for the local density of states and the nonequilibrium optical conductivity, both exhibiting a sideband structure, with the number and weight of the sidebands depending on the strength of the perpendicular coupling.

•Jan 1, 2004•0 citations
We characterize the response of a Mott insulating system to a static electric field in terms of its conducting and spectral properties. Dissipation is included by a coupling to fermionic baths and to either optical or acoustic phonons. This paper extends and completes the analysis made in a previous work by the authors [Mazzocchi et al., Phys. Rev. B 106, 125123 (2022)]. In the present work, phonons are included diagrammatically within the Migdal approximation by also including self-consistency from the electronic feedback. The nonequilibrium steady state is addressed by means of the dynamical mean-field theory based on the nonequilibrium Green's function approach, while the so-called auxiliary master equation approach is employed as impurity solver. With optical phonons the self-consistency suppresses the steady-state current for field strengths comparable to the band gap with respect to the non-self-consistent case. This is due to the interaction of phonons with the hot electrons of the lattice which increases their temperature, thus providing a less effective relaxation channel for the current-induced Joule heat. In addition, in the case of optical phonons, the results are essentially independent of the temperature of the fermionic baths, as the latter is sensibly smaller than their characteristic frequency. On the other hand, with acoustic phonons the steady-state current is slightly suppressed by the self-consistent treatment only at field strengths close to half of the gap and especially at very small phonon frequency. Also, in this case, the results seem to slightly depend on the temperature of the fermionic baths.
We study the spectral and transport properties of a Mott insulator driven by a static electric field into a nonequilibrium steady state. For the dissipation, we consider two mechanisms: wide band fermion reservoirs and phonons included within the Migdal approximation. The electron correlations are treated via nonequilibrium dynamical mean field theory with an impurity solver suitable for strong correlations. We find that dissipation via phonons is limited to restricted ranges of field values around Wannier-Stark resonances. To cover the full range of field strengths, we allow for a small coupling with fermionic baths, which stabilizes the solution. When considering both dissipation mechanisms, we find that phonons enhance the current for field strengths close to half of the gap while lowering it at the gap resonance as compared to the purely electronic dissipation used by Murakami and Werner [Murakami and Werner, Phys. Rev. B 98, 075102 (2018)]. Once phonons are the only dissipation mechanism, the current in the metallic phase is almost one order of magnitude smaller than the typical values obtained by coupling to a fermionic bath. In this case, the transport regime is characterized by an accumulation of charge in the upper Hubbard band described by two effective chemical potentials.
We characterize the current-carrying nonequilibrium steady state (NESS) in a single-band Hubbard model confronted with a static electric field in the presence of quenched disorder. Beyond the linear response regime, the electric field amplitude must compensate for at least half of the band gap to have a non-negligible stationary current. As the disorder is not expected to dissipate the extra energy injected by the field, optical phonons assisted by a fermionic heat bath serve as dissipation channels for the current-induced Joule heat generated by the accelerated electrons. The NESS of the system is addressed employing the dynamical mean-field theory using the so-called auxiliary master equation approach as impurity solver. Disorder effects are treated locally via the coherent potential approximation (CPA) and the self-consistent Born (SCB) approach. In the regime in which the two schemes yield similar results, we employ the SCB as it is computationally cheaper than the CPA. We show that, in a purely electronic setup, the disorder-induced dephasing cannot contribute states within the gap but only smear out the edges of the Hubbard bands. When phonons are taken into account, the different nature of disorder-induced dephasing and phonon-related dissipation becomes clear. We show that although both disorder and electron-phonon interaction enhance the current at off-resonant fields, disorder effects play a marginal role since they cannot provide in-gap states which are instead brought about by phonons and represent the privileged relaxation pathway for excited electrons.
We study a model for photovoltaic energy collection consisting of a Mott-insulating layer in presence of acoustic phonons, coupled to two wide-band fermion leads at different chemical potentials and driven into a nonequilibrium steady state by a periodic electric field. We treat electron correlations with nonequilibrium dynamical mean-field theory using the so-called auxiliary master-equation approach as impurity solver and include dissipation by acoustic phonons via the Migdal approximation. For a small hybridization to the leads, we obtain a peak in the photocurrent as a function of the driving frequency which can be associated with impact ionization processes. For larger hybridizations the shallow peak suggests a suppression of impact ionization with respect to direct photovoltaic excitations. Acoustic phonons slightly enhance the photocurrent for small driving frequencies and suppress it at frequencies around the main peak at all considered hybridization strengths.
We present improvements of a recently introduced numerical method [E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)] to compute steady-state properties of strongly correlated electronic systems out of equilibrium. The method can be considered as a nonequilibrium generalization of exact diagonalization based dynamical mean-field theory (DMFT). The key modification for the nonequilibrium situation consists in addressing the DMFT impurity problem within an auxiliary system consisting of the correlated impurity, Nb{N}_{b}Nb​ uncorrelated bath sites, and two Markovian environments (sink and reservoir). Algorithmic improvements in the impurity solver allow to treat efficiently larger values of Nb{N}_{b}Nb​ than previously in DMFT. This increases the accuracy of the results and is crucial for a correct description of the physical behavior of the system in the relevant parameter range including a semiquantitative description of the Kondo regime. To illustrate the approach, we consider a monoatomic layer of correlated orbitals, described by the single-band Hubbard model, attached to two metallic leads. The nonequilibrium situation is driven by a bias voltage applied to the leads. For this system, we investigate the spectral function and the steady-state current-voltage characteristics in the weakly as well as in the strongly interacting limit. In particular, we investigate the nonequilibrium behavior of quasiparticle excitations within the Mott gap of the correlated layer. We find for low-bias voltage Kondo-type behavior in the vicinity of the insulating phase. In particular, we observe a splitting of the Kondo resonance as a function of the bias voltage.
Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics, dynamical constraints, and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady-state DC transport regime and the role of dissipation in it, and electric-field-driven phase transitions. Despite tremendous efforts over the past decade employing various numerical and analytical approaches, the manner in which a nonequilibrium steady state gets established has remained an unresolved problem. We develop here an effective large-N\mathcal{N}N Keldysh field theory for studying nonequilibrium transport in a regular one-dimensional dissipative Mott insulator system subjected to a uniform electric field. Upon abruptly turning on the electric field (a quench), a transient oscillatory current response reminiscent of Bloch oscillations is found. In the regime of small tunneling conductance the amplitude of these oscillations, over a large time window, decreases as an inverse square power law in time, ultimately going over to an exponential decay beyond a large characteristic time ${\ensuremath{\tau}}_{d}$ that increases with N.\mathcal{N}.N. Such a relaxation to a steady-state DC response is absent in the dissipation-free Hubbard chain at half filling. The steady-state current at small fields is governed by large-distance cotunneling, a process absent in the equilibrium counterpart. The low-field DC current has a Landau-Zener-Schwinger form but qualitatively differs from the expression for pair-production probability for the dissipation-free counterpart. The breakdown of perturbation theory in the Mott phase possibly signals a nonequilibrium phase transition to a metallic phase. Our study sheds light on the approach of a driven, dissipative strongly correlated system to a nonequilibrium steady state and also provides a general analytic microscopic framework for understanding other nonequilibrium phenomena in these systems.
The dynamical mean field theory is extended using the Keldysh Green's function formalism to study strongly correlated systems away from equilibrium. This technique has been applied to two different systems, whose insulating behavior is due to electronic correlation effects: excitonic insulators and Mott insulators. The real-time development of the electronic properties of excitonic insulators, such as the distribution function and the gap, after an ultrashort intense is studied. The appropriate self-consistency equations turned out to be matrix equations in frequency and Keldysh space. The self-consistency equations derived for the two-plane Hubbard model with a periodic time-dependent coupling between the two planes are matrix equations in energy sidebands due to quasi-energy conservation modulo the external frequency. Numerical results are shown for the local density of states and the nonequilibrium optical conductivity, both exhibiting a sideband structure, with the number and weight of the sidebands depending on the strength of the perpendicular coupling.