Density-matrix theory for time-resolved dynamics of superconductors in non-equilibrium

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1 Max Planck Institute for Solid State Research Density-matrix theory for time-resolved dynamics of superconductors in non-equilibrium co-workers and papers: (1) (2) (3) (4) Dirk Manske A. Knorr (TU Berlin), PRB 77, (R) (2008) A. Schnyder (MPI Stuttgart), A. Avella (Uni Salerno), PRB 84, (2011) Exp.: M. Rübhausen + team (Uni Hamburg), PRL 102, (2009) A. Schnyder, A. Akbari (MPI Stuttgart), I. Eremin (Uni Bochum), EPL 101, (2013) Hamburg, July 31st

2 3 types of non-equilibrium experiments optical control new transient ground state Thanks to: potential C. Giannetti (talk on Friday) D. Fausti et al., Science 331, 189 (2011) non-equilibrium spectroscopy recovery of the ground state coherent excitation coherent oscillation bandwidth

3 Content Motivation: how does the superconducting condensate response? Role of phonons? Theory: Equations of motion for coherent dynamics, quantum kinetic equations in the nonadiabatic regime Results: order parameter oscillations role of electron-phonon coupling coherent phonons vs. phonon bath multi-band effects

4 Motivation I: pump-probe spectroscopy Bi2212 Two kinds of information can be extracted: Time domain: conductivity change σ, depending on time delay t Energy domain: change in the conductivity spectra R.A. Kaindl et al., PRB 72, (R) (2005) Dirk Manske

5 Motivation II: time-resolved ARPES (1) Hot electrons dissipate on 2 distinct time scales: 110fs and 2ps Only % of the total lattice modes dominate the coupling strength (averaged) electron-phonon coupling λ < 0.25

6 Motivation III: time-resolved ARPES (2) Observation of coherent phonons in EuFe 2 As 2 PRL 108, (2012)

7 Motivation IV: glue of high-tc cuprates? Dirk Manske

8 Often used: effective theories Two different models for the description of time-resolved experiments:

9 Microscopic approach: with we consider: (a) tetragonal lattice (b) tight-binding band structure, e.g. from Kordyuk et al. ( 03) (c) s- or d-wave order parameter

10 DMT: Calculation of coherent dynamics Dirk Manske

11 Results Max Planck Institute for Solid State Research Case I: single band no phonons

12 Order parameter oscillations: 2 regimes lead: 2 0 = 2.7mev Non-adiabatic regime: gap continues to oscillate even when the pump pulse has been switched off long ago ( (t= ) = )

13 Analytic solution possible Yuzbashyan, Tsyplyatyev, Altshuler, PRL 2006

14 Intensity dependence Intensity

15 Probe spectra: no oscillations (well known) Pauli blocking Gap oscilllations cannot be perceived by means of a simple probe specrum See also: Papenkort, Axt, and Kuhn, PRB 07

16 Max Planck Institute for Solid State Research Case II: single band, coherent phonons <b> 0 Role of and τp τph... τ... pulse duration phonon period dynamical time scale ~h/(2 )?

17 Density-Matrix Formalism No bath approximation Cluster expansion: coupling of phonon-assisted quantities such as and solve numerically 6 Boltzmann-like equations Phonon equations for and

18 Adiabatic regime τ p > τ, τ ph pulse τ p = 20000fs = 1.35 Creation of coherent phonons possible for τ ph < τ < < τ p Inclusion of incoherent phonons would lead to damping

19 Crossover to non-adiabatic regime ω ph = 2.0 = 1.35 Occurence of Quantum beats:

20 Non-adiabatic regime τ p < τ τ p = 500fs = 1.35 = 0.85 Coherent phonons are resonantly enhanced

21 off-resonant: 2 = 1.7 and 2.3meV resonant: 2 = 2.0meV = ω ph tune the order parameter oscillations exactly to resonance by adjusting the integrated pump intensity PRB 84, (2011)

22 Order parameter oscillations: theory H. Krull, G. Uhrig, A. Schnyder, and D. Manske, preprint

23 Order parameter oscillations: Experiment PNAS 2012

24 Max Planck Institute for Solid State Research Case III: single band, phonons in equilibrium <b> = 0 (bath approximation) Motivation: time-resolved Raman scattering

25 Reminder: Conventional Raman scattering Raman intensity A 1g B 1g B 2g ω 2 0 same spectra for A 1g, B 1g and B 2g transferred energy B 1g (cos k x - cos k y ) ω 3 polarization dependence R. Hackl, D. Einzel et al. (1995) D. Manske et al. (PRB (RC)1997)

26 Exp.: Time-resolved Raman scattering (I) Bi2212, B 1g -polarization Phys. Rev. Lett. 102, (2009) t = 3ps

27 Exp.: Time-resolved Raman scattering (II) Bi2212, B 1g -polarization Phys. Rev. Lett. 102, (2009)

28 Comparison with experiment signatures of phonons Phys. Rev. Lett. 102, (2009)

29 Compare with YBCO, bonding band LDA calculation of the electron-phonon coupling strength K y K x widely used assumptions: buckling mode cos 2 (q x /2) + cos 2 (q y /2) breathing mode sin 2 (q x /2) + sin 2 (q y /2) R. Heid, K.-P- Bohnen, R. Zeyher, and D. Manske, Phys. Rev. Lett. 100, (2009)

30 Momentum- and frequency-resolved coupling Dirk Manske

31 Max Planck Institute for Solid State Research Case IV: 2 bands, no phonons

32 Density-Matrix Formalism solve numerically 8 Boltzmann-like equations (still no phonons)

33 Multiband effects Calculation for pnictides: g 11 = 0 = g 22 and g 12 < 0

34 Order parameter oscillations (1): MgB 2 Characteristic changes due to inter-band scattering: 2 coupled harmonic oscillators A. Akbari et al., EPL (2013)

35 Order parameter oscillations (2): Quantum beats are possible

36 Summary Micoscopic theory for ultrafast dynamics in superconductors employing Density Matrix Theory: What happens after the pump pulse? case 1: no phonons, single band OP oscillations in the non-adiabatic regime if τ p < τ case 2: coherent phonons, single band Quantum Beats and resonance effects if case 3: incoherent (bath) phonons, single band Comparison with time-resolved Raman scattering case 4: no phonons, two bands 2 damped oscillators, quantum beats

37 Outlook consideration of non-centrosymmetric superconductors (E. Bauer and M. Sigrist (Eds.), Non-centrosymmetric superconductors, Lecture Notes in Physics 847, Springer 2012) Interdependence of singlet- and triplet-pairing light-induced superconductivity (see work by A. Cavalleri, MPI) Pumping pre-formed pairs (within Density-Matrix Theory) consideration of strong electron-electron interaction

38 END OF TALK Max Planck Institute for Solid State Research Thank you!