Relaxation of Hot Quasiparticles in a d -Wave Superconductor A. Rosch (Cologne), P. Howell (Karlsruhe) P. Hirschfeld (Florida) • pump-probe experiments in high-temperature superconductors • relaxation of high-energy quasi-particles • momentum conservation and diffusion in momentum space
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Relaxation of Hot Quasiparticles in a d-WaveSuperconductor
A. Rosch (Cologne), P. Howell (Karlsruhe)
P. Hirschfeld (Florida)
• pump-probe experiments in high-temperature superconductors
• relaxation of high-energy quasi-particles
• momentum conservation and diffusion in momentum space
Phase Diagram of the Cuprates
Fermi liquid?
T
AF
M in
sulato
r
pseudogap
strange metal
hole concentration
superconductor
best understood (??): physics within superconducting phase
Scenario 1: Quasiparticles in superconducting phase
Microwave conductivity σ(ω) in
YBa2Cu3O6−δ Hosseini et al. (1999)
well fitted by thermal QPs
Agreement with λ−2(T).
τ−1tr decreases fast below Tc
Umklapp scattering of QPs
Walker & Smith, PRB 61, 11285 (2000)
Scenario 2: Quantum Critical Scaling
σ(ω) in Bi2Sr2CaCu2O8 requires more complicated model
phonons equilibrated with hot QP transport energy out of system
Step 0: excitation of QP (1 eV)
Step 1 ( < 1ps):
Step 2 (1−10ps):
Step 3 (ns − s):
This talk !
µ
Rothwarf, Taylor (1967)
Pump–Probe Reflectivity on YBa2Cu3O6.5
time-resolved reflectivity δR ∝ ∫
dω ω2δσ(ω) after pumping
Segre, Gedik, Orenstein, Bonn, Liang, Hardy et al., PRL 88, 137001 (2002)
QPs relax very fast down ∼∆0, then slowly with τ−1 ∝ T3
Mystery:QP energy ∼∆0 ≫ T so expect τ independent of T.
More experiments...
in general: very different time-scales measured in pump-probe experi-ments in HTc depending on doping, sample quality, frequency, inten-sity, temperature
some recent experiments:
• Diffusion of nonequilibrium quasi-particles in a cuprate superconductor, (Gedik et
al. Science 2003):writing a interference pattern on crystal to obtain diffusion
• Dynamics of Cooper pair formation in Bi2Sr2CaCu2O8−δ (Kaindl et al.,Science 2003,
PRB, 2005):time-dependence of σ(4meV < ω < 11meV )
• Nonequilibrium quasiparticle relaxation in the vortex state
of La2−xSrxCuO4, (Bianchi et al. PRL 2005)
• Abrupt transition in quasiparticle dynamics at op-
timal doping in a cuprate superconductor system
(Gedik, et al. PRL 2005): different sign and differ-ent density dependence for under- and overdopedsamples!
underdoping vs. overdoping (Gedik, et al. PRL 2005)
need other hot QP to free trapped excitations for underdoped system?
Fermi Liquid Interpretation
Photoinduced QPs create cascade of QPs, i.e. excite pairs out of
condensate.
Some QPs end up near gap antinodes with energy ∆0.
How do these ‘hot’ QPs relax?
E and k conservation ⇒bottleneck for pair-breaking