Density-matrix methods and time dependence of order parameter in superconductors

Ulrich Schollwöck

Oleg L. Berman, Shaul Mukamel

Equations of motion are derived for the normal and anomalous single-electron density matrices of a Fermi liquid using a time-dependent finite-temperature generalized coherent-state variational ansatz for the many-body density matrix. Self-consistent equations for the order parameter $\ensuremath{\Delta}$ allow us to investigate the interplay of the Coulomb repulsion and pairing attraction in homogeneous and inhomogeneous Fermi liquids with spontaneously broken symmetry such as high-temperature superconductors. The temperature of the Kosterlitz-Thouless transition to the two-dimensional superfluidity is calculated.

Jean G. Valatin

Allen M. Goldman

Medha Roy Choudhury, Sankha Subhra Bakshi, Pinaki Majumdar +1 more

We investigate the quantum dynamics of a conventional superconductor, described by the attrac- tive Hubbard model, driven far from equilibrium by quenching the Hubbard attraction. We evolve the full density matrix of the system in time using the Heisenberg equation of motion, tracking the spatiotemporal dynamics of the pairing and density fields. We use very weakly inhomogeneous initial conditions to probe the stability of the homogeneous dynamics to spatial perturbations. At initial times after the quench the pairing and density fields remain homogeneous in space while fluctuating in time. However, depending on the quench strength the spatially uniform dynamics can become unstable beyond a threshold time, with emergence of spatial textures. The onset time for the instability depends on the strength of the quench and the initial inhomogeneity. At long times the system evolves towards a state with significantly reduced spatial heterogeneity. The time dependence of the global superconducting order parameter suggests two broad categories of re- sponse to a quench. One of these involves strongly inhomogeneous pairing and bond currents in the nonequilibrium superconductor.

Thomas Papenkort, V. M. Axt, T. Kühn

The density matrix formalism is employed to calculate pump-probe spectra of BCS superconductors in the coherent regime. Two dynamical regimes, one adiabatic and one nonadiabatic, can be clearly distinguished. In the adiabatic regime, the modulus of the BCS order parameter can be identified with half the gap in the probe spectra. In the nonadiabatic regime, the order parameter oscillates in real time, whereas the gap observed in the spectra reflects its temporal average. The transition between these regimes is accompanied by a qualitative change of the intensity dependence of the dynamical gap renormalization. Furthermore, a hole-burning effect occurs if the spectral shape of the pump pulse is sufficiently sharp. A probe pulse preceding the pump pulse leads to spectral oscillations, and both the gap before and after the pump pulse are visible in the probe spectra.