Real-space microscopic description of laser-pulse induced melting of superconductivity

Technical Deep Dive: Microscopic Real-Space Description of Laser-Induced Melting of Superconductivity

Overview

This work presents a microscopic, real-space model of the dynamics of a superconductor subjected to a high-frequency laser pulse. The model uses self-consistent time-dependent Bogoliubov-de Gennes equations and Heisenberg equations within a tight-binding framework. This allows for a spatially resolved treatment of the superconducting order parameter and inclusion of the electromagnetic field. The key findings are:

• The model reproduces the experimentally observed critical slowing-down of the melting of the superconducting order parameter for laser fluences close to the condensation energy.
• The real-space resolution reveals:
  • Unusual current flow patterns with opposite phase and group velocity, resembling "backward waves"
  • Strong spatial fluctuations in the phase of the order parameter that suppress superconductivity

Problem & Context

• Ultrafast optical pump-probe experiments have enabled observation of superconductivity melting and recovery on picosecond timescales
• These experiments probe a regime far out of equilibrium where complex interplay of degrees of freedom determines observable phenomena
• However, a fully microscopic theoretical description connecting microscopic pairing physics to experimental signals under strong time-dependent fields, including spatial resolution of the order parameter, has been lacking

Methodology

• Modeled the superconductor using a mean-field Hamiltonian on a 2D lattice
• Employed Peierls substitution to include time-dependent electromagnetic field
• Solved self-consistent time-dependent Bogoliubov-de Gennes and Heisenberg equations to obtain spatially resolved dynamics of order parameter and currents
• Calculated internal energy absorbed from the laser pulse and compared to condensation energy to analyze melting dynamics

Results

Melting Dynamics without Phonons

• Reproduced experimental observation of critical slowing-down of order parameter melting near condensation energy
• Order parameter suppression initially increases with laser fluence, then changes sign around a critical value, leading to abrupt recovery
• Induced strong spatial variations in order parameter phase, generating counter-propagating current wavefronts

Melting Dynamics with Phonons

• Phonons modify current flow, introducing weak currents along the transverse direction
• Phonons also induce a constantly rotating phase in the order parameter
• Overall behavior of melting time vs absorbed energy qualitatively similar to no-phonon case

Current Textures

• Laser pulse induces transient bond-currents with unusual flow patterns
• Two counter-propagating wavefronts of currents moving at approximately 2 lattice sites per time unit
• Currents move in same direction as wavefronts, unlike typical wave propagation
• This "backward wave" behavior arises from spatial variations in the order parameter phase

Interpretation

• The microscopic real-space model provides a detailed understanding of how laser pulses melt and recover superconductivity
• Crucially, it captures spatiotemporal dynamics of order parameter and current flow, enabling direct experimental tests
• The critical slowing-down and unusual current textures arise from complex interplay between order parameter fluctuations and electromagnetic field

Limitations & Uncertainties

• Model does not include specific dissipation mechanisms, so system may persist in nonequilibrium state
• Incorporation of acoustic phonons or other modes could further enrich the dynamics

What Comes Next

• Explore role of additional degrees of freedom like acoustic phonons
• Apply the modeling framework to study ultrafast dynamics in superconducting heterostructures

Sources:

• Real-space microscopic description of laser-pulse induced melting of superconductivity