Transient Dynamics ofd-Wave Superconductors after a Sudden Excitation

Abstract

Motivated by recent ultrafast pump-probe experiments on high-temperature superconductors, we discuss the transient dynamics of a d-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a decay channel which makes the dynamics much faster than in the conventional s-wave model. For every value of the quench parameter, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.PACS numbers: 74.20.Rp,74.40.Gh,05.70.Ln Introduction. -Recent advances in time-resolved spectroscopies have triggered a growing interest in the transient dynamical behavior of high-temperature superconductors optically excited far from equilibrium. By shining the sample with intense ultrafast pulses (pump) one can trigger nonequilibrium transient states, whose physical properties are then recorded by a second pulse (probe) which hits the sample with a given time delay. This approach opens up a wealth of information unavailable to conventional time-averaged spectroscopies [1][2][3][4][5][6][7][8][9]. When used in combination with angle-resolved photoemission spectroscopy (ARPES), these ultrafast methods allow us to track and follow in real time the evolution of quasiparticle modes in different momentum sectors, such as those close to the gap nodes and antinodes of d-wave cuprate superconductors [10][11][12]. In addition, when irradiation is sufficiently strong and optically tailored in such a way to selectively excite specific modes, one can even stabilize transient states with fundamentally different physical properties [13][14][15]. A spectacular example is given by recent experiments reporting signatures of light-induced metastable superconductivity in cuprates at much higher temperature than at equilibrium [16,17].

Damping of the collective amplitude mode in superconductors with strong electron-phonon coupling

“…The problem of how a superconducting (SC) state evolves in time after an external stimulation has attracted the interest of researchers for a long time [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. On the theoretical side, static mean-field analyses, which neglect inelastic collisions, have been widely employed to study the coherent dynamics.…”

Multiple amplitude modes in strongly coupled phonon-mediated superconductors

“…Before this experiment [15], the amplitude Higgs mode had been observed only in a special case, 2H -NbSe 2 , where SC coexists with a charge density wave [4][5][6]18,19]. Theoretical studies of the SC order parameter dynamics have so far primarily focused on the static mean-field dynamics [1][2][3][5][6][7][8][9][10][11][12][13]17,19,[22][23][24]. One important conclusion of these works is that the frequency of the Higgs amplitude mode (ω H ) should coincide with the SC gap (2 SC ) in the BCS regime [27], which is a threshold for quasiparticle excitations.…”

Quadratic band touching with long-range interactions in and out of equilibrium

“…2. The crucial difference with respect to previously considered quenches in superconductors [12,28] occurs, however, for small finite couplings. In this limit, the nematic order parameter does not vanish but approaches a finite, time independent stationary value.…”

“…Second, the equilibrium low-energy thermodynamics of 2D Dirac fermions is universal, no matter whether it is for graphene [30], d-wave superconductors [31] or the present nematic state. In sharp contrast, the dynamics after quench differs significantly from that of a d-wave BCS superconductor [28] where the order parameter vanishes identically for small quenches. We trace this difference back to the non-trivial non-interacting spectrum and its 2π Berry phase in Eq.…”