[Paper Review] Strong field physics in condensed matter

Takashi Oka|arXiv (Cornell University)|Feb 12, 2011

Physics of Superconductivity and Magnetism1 references3 citations

TL;DR

This paper establishes deep theoretical connections between strong field quantum field theory in high-energy physics and non-equilibrium phenomena in condensed matter systems, showing that concepts like the Schwinger mechanism and Volkov states have direct analogs in condensed matter transport, such as the photovoltaic Hall effect and non-adiabatic geometric phases. The key contribution is a unified framework linking non-linear transport, dielectric breakdown, and topological responses in strongly correlated systems under strong electric and optical fields.

ABSTRACT

There are deep similarities between non-linear QFT studied in high-energy and non-equilibrium physics in condensed matter. Ideas such as the Schwinger mechanism and the Volkov state are deeply related to non-linear transport and photovoltaic Hall effect in condensed matter. Here, we give a review on these relations.

Motivation & Objective

• To identify and formalize deep analogies between non-linear quantum field theory in high-energy physics and non-equilibrium phenomena in condensed matter systems.
• To demonstrate that concepts like the Schwinger mechanism and Volkov states have direct counterparts in condensed matter transport, such as dielectric breakdown and the photovoltaic Hall effect.
• To extend the Berry phase theory of polarization to finite electric fields using a non-adiabatic effective Lagrangian formalism.
• To show how ac-fields, particularly circularly polarized light, can induce topological band structure changes and artificial gauge fields in Dirac materials like graphene.
• To provide a theoretical bridge between high-energy QFT concepts and experimental observables in strongly correlated and topological materials.

Proposed method

• Formalizing a condensed matter version of the Heisenberg-Euler effective Lagrangian to describe non-linear response in insulators under strong electric fields.
• Using the time-dependent gauge with phase-locked hopping terms to model time-varying electric fields in lattice models.
• Applying the imaginary time method and Landau-Zunder tunneling theory to compute decay rates and breakdown thresholds in Hubbard models.
• Employing the Floquet picture to describe electron dynamics under ac-fields, incorporating photon absorption and emission in the Green's function formalism.
• Extending the TKNN formula to ac-driven systems via the photo-induced Berry curvature and artificial gauge fields in momentum space.
• Combining Keldysh non-equilibrium Green's function techniques with Floquet theory to compute Hall current and conductance in driven graphene systems.

Experimental results

Research questions

• RQ1 How do the Schwinger mechanism and vacuum pair creation in QED relate to dielectric breakdown in band and Mott insulators?
• RQ2 To what extent can the non-adiabatic geometric phase and effective Lagrangian formalism describe non-linear transport in strong electric fields?
• RQ3 What is the role of electron correlation in modifying the dielectric breakdown threshold compared to non-interacting models?
• RQ4 How does circularly polarized light induce a topological phase transition and a photovoltaic Hall effect in Dirac materials?
• RQ5 Can the extended TKNN formula in the Floquet picture accurately predict the Hall conductivity in light-driven topological systems?

Key findings

• The imaginary part of the effective Lagrangian, Re ℒ(F), gives the decay rate of the insulating ground state under strong electric fields, with Γ(F)/L^d = 2 Im ℒ(F) describing tunneling-induced breakdown.
• In the non-interacting limit, the breakdown threshold F_th^LZ = (Δ/2)^2 / v from Landau-Zener theory agrees with the imaginary time method, but deviates significantly in the strong correlation regime.
• For strong Hubbard U, the breakdown threshold F_th^ITM ∝ U − const. deviates from the Landau-Zener prediction F_th^LZ ∝ U^2, indicating strong correlation effects.
• In graphene under circularly polarized light, a dynamical gap opens at the Dirac point, leading to a finite photo-induced Berry curvature and a measurable photovoltaic Hall current.
• The Hall conductivity σ_xy is given by a momentum-space integral of the photo-induced Berry curvature, consistent with the extended TKNN formula in the Floquet picture.
• Numerical simulations show that the Hall current increases with light intensity, confirming the photovoltaic Hall effect as a topological response to ac-driven gauge fields.