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Rectification by doped Mott-insulator junctions

Florian C. Sabou, Natalie Bodington-Rosen, John Bradley Marston

Published Aug 16, 2016• 2 citations
OpenAlex

Abstract

Abstract—Junctions of doped Mott insulators offer a route to rectification at frequencies beyond the terahertz range. Mott insulators have strong electronic correlations and therefore short timescales for electron-electron scattering. It is this short time scale that allows for the possibility of rectification at frequencies higher than those of semiconductor devices that are limited by the slow diffusion of charge carriers. We model a junc-tion by a one dimensional chain of electrons with p- and n-doping on the two halves of the chain. Two types of systems are investigated: spin polarized electrons with nearest-neighbor interaction, and spin-half electrons that interact via on-site repulsion (the Hubbard model). For short chains the many-body Schrödinger equation can be integrated numerically exactly, and when driven by an oscillating electromagnetic field such idealized junctions rectify, showing a preferred direction for charge transfer. Longer chains are studied by the time-dependent density-matrix renormalization-group method, and also shown to rectify. I.

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Ultra-fast photo-carrier relaxation in Mott insulators with short-range spin correlations

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Ultra-fast spectroscopy can reveal the interplay of charges with low energy degrees of freedom,which underlies the rich physics of correlated materials. As a potential glue for superconductivity,spin fluctuations in Mott insulators are of particular interest. A theoretical description of the coupledspin and charge degrees of freedom is challenging, because magnetic order is often only shortlivedand short-ranged. In this work we theoretically investigate how the spin-charge interactionsinfluence the relaxation of a two-dimensional Mott-Hubbard insulator after photo-excitation. We usea nonequilibrium variant of the dynamical cluster approximation, which, in contrast to single-sitedynamical mean-field theory, captures the effect of short-range correlations. The relaxation time isfound to scale with the strength of the nearest-neighbor spin correlations, and can be 10–20 fs in thecuprates. Increasing the temperature or excitation density decreases the spin correlations and thusimplies longer relaxation times. This may help to distinguish the effect of spin-fluctuations on thecharge relaxation from the influence of other bosonic modes in the solid.

•Jan 1, 2016•39 citations
Abstract—Junctions of doped Mott insulators offer a route to rectification at frequencies beyond the terahertz range. Mott insulators have strong electronic correlations and therefore short timescales for electron-electron scattering. It is this short time scale that allows for the possibility of rectification at frequencies higher than those of semiconductor devices that are limited by the slow diffusion of charge carriers. We model a junc-tion by a one dimensional chain of electrons with p- and n-doping on the two halves of the chain. Two types of systems are investigated: spin polarized electrons with nearest-neighbor interaction, and spin-half electrons that interact via on-site repulsion (the Hubbard model). For short chains the many-body Schrödinger equation can be integrated numerically exactly, and when driven by an oscillating electromagnetic field such idealized junctions rectify, showing a preferred direction for charge transfer. Longer chains are studied by the time-dependent density-matrix renormalization-group method, and also shown to rectify. I.
Junctions of doped Mott insulators offer a route to rectification at frequencies beyond the terahertz range. Mott insulators have strong electronic correlations and therefore short timescales for electron-electron scattering. It is this short time scale that allows for the possibility of rectification at frequencies well beyond those of semiconductor devices that are limited by the slow diffusion of charge carriers. We model a junction by a one dimensional chain of electrons with p- and n-doping on the two halves of the chain. Two types of systems are investigated: spin polarized electrons with nearest-neighbor interaction, and spin-half electrons that interact via on-site repulsion (the Hubbard model). For short chains the many-body Schrodinger equation can be integrated numerically exactly, and when driven by an oscillating electromagnetic field such idealized junctions rectify, showing a preferred direction for charge transfer. Longer chains are studied by the time-dependent density-matrix renormalization-group method, and also shown to rectify.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.
The real part of optical conductivity $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ on the on-site Coulomb interaction and next-nearest-neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ by modeling the electron-phonon coupling present in La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and Nd2CuO4{\mathrm{Nd}}_{2}{\mathrm{CuO}}_{4}Nd2​CuO4​, we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.
Local moment formation is ubiquitous in disordered semiconductors such as Si:P, where it is observed both in the metallic and the insulating regimes. Here, we focus on local moment behavior in disordered insulators, which arises from short-ranged, repulsive electron-electron interactions. Using density matrix renormalization group and strong-disorder renormalization group methods, we study paradigmatic models of interacting insulators: one-dimensional Hubbard chains with quenched randomness. In chains with either random fermion hoppings or random chemical potentials, both at and away from half-filling, we find exponential decay of disorder-averaged charge and fermion two-point correlations, but power-law decay of disorder-averaged spin correlations that are indicative of the random singlet phase. The numerical results can be understood qualitatively by appealing to the large-interaction limit of the Hubbard chain, in which a remarkably simple picture emerges.
Ultra-fast spectroscopy can reveal the interplay of charges with low energy degrees of freedom, which underlies the rich physics of correlated materials. As a potential glue for superconductivity, spin fluctuations in Mott insulators are of particular interest. A theoretical description of the coupled spin and charge degrees of freedom is challenging, because magnetic order is often only short-lived and short-ranged. In this work we theoretically investigate how the spin-charge interactions influence the relaxation of a two-dimensional Mott-Hubbard insulator after photo-excitation. We use a nonequilibrium variant of the dynamical cluster approximation, which, in contrast to single-site dynamical mean-field theory, captures the effect of short-range correlations. The relaxation time is found to scale with the strength of the nearest-neighbor spin correlations, and can be 10-20 fs in the cuprates. Increasing the temperature or excitation density decreases the spin correlations and thus implies longer relaxation times. This may help to distinguish the effect of spin-fluctuations on the charge relaxation from the influence of other bosonic modes in the solid.
Ultra-fast spectroscopy can reveal the interplay of charges with low energy degrees of freedom,which underlies the rich physics of correlated materials. As a potential glue for superconductivity,spin fluctuations in Mott insulators are of particular interest. A theoretical description of the coupledspin and charge degrees of freedom is challenging, because magnetic order is often only shortlivedand short-ranged. In this work we theoretically investigate how the spin-charge interactionsinfluence the relaxation of a two-dimensional Mott-Hubbard insulator after photo-excitation. We usea nonequilibrium variant of the dynamical cluster approximation, which, in contrast to single-sitedynamical mean-field theory, captures the effect of short-range correlations. The relaxation time isfound to scale with the strength of the nearest-neighbor spin correlations, and can be 10–20 fs in thecuprates. Increasing the temperature or excitation density decreases the spin correlations and thusimplies longer relaxation times. This may help to distinguish the effect of spin-fluctuations on thecharge relaxation from the influence of other bosonic modes in the solid.