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arXiv:0903.2707 · Physical Review B

Dielectric breakdown in a Mott insulator: Many-body Schwinger-Landau-Zener mechanism studied with a generalized Bethe ansatz

Takashi Oka, Hideo Aoki

Published Jan 14, 2010• 75 citations
arXivHTMLPDF

Abstract

The nonadiabatic quantum tunneling picture, which may be called the many-body Schwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a method due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density-matrix renormalization-group result is obtained.

DOI
10.1103/physrevb.81.033103

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The nonadiabatic quantum tunneling picture, which may be called the many-body Schwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a method due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density-matrix renormalization-group result is obtained.
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Nonlinear transport of electrons in strong electric fields, as typified by dielectric breakdown, is reformulated in terms of the ground-state decay rate originally studied by Schwinger in nonlinear QED. We discuss the effect of electron interaction on Zener tunneling by comparing the dielectric breakdown of the band insulator and the Mott insulator, where the latter is studied by the time-dependent density-matrix renormalization group. The relation with the Berry's phase theory of polarization is also established.
Doublon-hole pair production which takes place during dielectric breakdown in a Mott insulator subject to a strong laser or a static electric field is studied in the one-dimensional Hubbard model. Two nonlinear effects cause the excitation, i.e., multi-photon absorption and quantum tunneling. Keldysh crossover between the two mechanisms occurs as the field strength and photon energy is changed. The calculation is done analytically by the Landau-Dykhne method in combination with the Bethe ansatz solution and the results are compared with those of the time dependent density matrix renormalization group. Using this method, we calculate distribution function of the generated doublon-hole pairs and show that it drastically changes as we cross the Keldysh crossover line. After calculating the tunneling threshold for several representative one-dimensional Mott insulators, possible experimental tests of the theory is proposed such as angle resolved photoemission spectroscopy of the upper Hubbard band in the quantum tunneling regime. We also discuss the relation of the present theory with a many-body extension of electron-positron pair production in nonlinear quantum electrodynamics known as the Schwinger mechanism.
Application of a strong electric field to insulators induces a finite current. This phenomenon is called dielectric breakdown and is known as a fundamental nonequilibrium and nonlinear transport phenomenon in solids. Here, we study the dielectric breakdown of generic strongly correlated insulators in one dimension. Combining bosonization techniques with a quantum tunneling theory, we develop an effective field-theoretical description of dielectric breakdown using a non-Hermitian sine-Gordon theory. Then, we derive an analytic formula for the threshold field, which is a many-body generalization of the Landau-Zener formula. Importantly, we point out that the threshold field contains a previously overlooked factor originating from the charges of elementary excitations, which should be significant when a system has fractionalized excitations. We apply our results to integrable lattice models and confirm that our formula is valid in a broad range including the weak coupling regime, indicating its wide potential applicability. Our results unveil universal aspects of nonlinear and nonequilibrium transport phenomena in various strongly correlated insulators.
Time-dependent nonequilibrium properties of a strongly correlated electron system driven by large electric fields is obtained by means of solving the time-dependent Schrödinger equation for the many-body wave function numerically in one dimension. While the insulator-to-metal transition depends on the electric field and the interaction, the metallization is found to be described in terms of a universal Landau-Zener quantum tunneling among the many-body levels. These processes induce current oscillation for small systems, while giving rise to finite resistivity through dissipation for larger systems/on longer time scales.