[Paper Review] Phonon-induced disorder in dynamics of optically pumped metals from non-linear electron-phonon coupling

John Sous, B. Kloss+3 more|arXiv (Cornell University)|Sep 1, 2020

Physics of Superconductivity and Magnetism56 references44 citations

TL;DR

This paper investigates non-equilibrium dynamics in optically pumped metals with quadratic electron-phonon coupling, demonstrating that coherent phonon excitation induces effective disorder through symmetry-protected phonon occupation conservation. The resulting loss of electronic phase coherence and rapid growth of local correlations—evidenced by flattened momentum-space correlations and enhanced double occupancy—leads to a correlated electron-phonon steady state, explaining the absence of transient superconductivity and revealing a pathway to dynamically induced strong coupling in out-of-equilibrium systems.

ABSTRACT

The non-equilibrium dynamics of matter excited by light may produce electronic phases that do not exist in equilibrium, such as laser-induced high-transition-temperature superconductivity. Here we simulate the dynamics of a metal driven at initial time $t=0$ by a spatially uniform pump that excites dipole-active vibrational modes which couple quadratically to electrons. We study in detail the evolution of electronic and vibrational observables and their coherences. We provide evidence for enhancement of local electronic correlations, including double occupancy, accompanied by rapid loss of spatial structure, which we interpret as a signature of emergent effective disorder in the dynamics. This effective disorder, which arises in absence of quenched randomness, dominates the electronic dynamics as the system evolves towards a correlated electron-phonon long-time state, possibly explaining why transient superconductivity is not observed. The pumped electron-phonon systems studied here, which are governed by non-linear coupling, exhibit a much more substantial dynamical response than linearly coupled models relevant in equilibrium, thus presenting a pathway to new modalities for out-of-equilibrium phases. Our results provide a basis within which to understand correlation dynamics in current pump-probe experiments of vibrationally coupled electrons, highlight the importance of the evolution of phase coherence, and demonstrate that pumped electron-phonon systems provide a means of approximately realizing recently proposed scenarios of dynamically induced disorder in translation-invariant systems.

Motivation & Objective

• To understand the non-equilibrium dynamics of metals driven by optical excitation of dipole-active phonons with quadratic coupling to electrons.
• To investigate how non-linear electron-phonon coupling leads to emergent electronic disorder without quenched randomness.
• To determine the role of initial coherent phonon states and conserved phonon occupations in inducing effective localization and loss of phase coherence.
• To compare the dynamical response of quadratic-coupling models with linear (Holstein) models, highlighting enhanced correlation effects.
• To provide a theoretical framework for interpreting pump-probe experiments involving vibrationally coupled electrons and identifying signatures of dynamically induced strong coupling.

Proposed method

• Simulates time evolution of an infinite one-dimensional system using the infinite-time-evolving block decimation (iTEBD) algorithm with tensor network methods.
• Employs direct Krylov subspace methods for finite-size systems (L = 3–6) with twisted boundary conditions to access long-time dynamics.
• Uses a squeezed basis transformation to derive an effective Hamiltonian that captures the qualitative dynamics of the quadratic electron-phonon model.
• Applies a fourth-order Trotterization scheme for time evolution with controlled time-step (dt) and truncation error (ϵTEBD) to ensure convergence.
• Converges results with respect to phonon Hilbert space dimension (dν = 10–14), bond dimension (χ ≤ 5000), and truncation error (ϵTEBD = 10−3.5).
• Compares the quadratic model to an effective Holstein-like model via an effective coupling λH derived from double occupancy and phonon number expectation values.

Experimental results

Research questions

• RQ1 How does quadratic electron-phonon coupling in a driven, non-equilibrium system lead to the emergence of effective disorder?
• RQ2 What is the role of conserved phonon occupation numbers in suppressing electronic phase coherence and inducing localization?
• RQ3 How does the dynamical response of the quadratic-coupling model differ from that of the linear Holstein model in terms of correlation growth and double occupancy?
• RQ4 What are the signatures of a long-time correlated electron-phonon steady state in momentum- and real-space observables?
• RQ5 Can the initial coherent phonon state lead to a self-averaging electronic response that mimics a disordered potential without quenched randomness?

Key findings

• A rapid loss of momentum-space structure in charge, spin, and pairing correlations—evidenced by flattening of momentum-dependent correlation functions—signals the emergence of effective disorder.
• The initial coherent phonon state, with approximately conserved phonon occupation, leads to electronic self-averaging across phonon sectors, destroying off-diagonal coherence and inducing localization.
• Double occupancy increases significantly in the quadratic model, with values exceeding those in the linear Holstein model, indicating a transition into a strong-coupling regime.
• The density-density correlation function becomes structureless behind a light-cone defined by the Fermi velocity, indicating spatially random correlations in the long-time limit.
• The electron-phonon interaction term’s expectation value increases over time, indicating evolution toward a strongly correlated long-time steady state.
• An effective coupling λH ≈ 0.1 is estimated for gq = 0.25 and ω = π/2, showing qualitative equivalence to a Holstein model with moderate electron-electron interaction, validating the effective theory approach.