Violation of Matthiessen’s rule in pump/probe TRARPES

Jim Freericks Georgetown University
Thomas Devereaux (Stanford/SLAC), Alexander Kemper (North Carolina State),
Brian Moritz (SLAC), Sona Najafi (Georgetown), and Michael Sentef (Hamburg)
Georgetown work supported by DOE, BES, DE-FG02-08ER46542 and McDevitt bequest

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

PRL 102, 136401 (2009)
PRL 111, 077401 (2013)
PRX 3, 041033 (2013)
PRB 87, 235139 (2013)
PRB 90, 075126 (2014)
Adv. Imag. Elect. Phys (2015)
PRB 92, 224517 (2015)
Entropy 18, 180 (2016)
Fort. Phys. 64 (2017).

Nonequilibrium many-body theory
Lesser Green function:

ij1eqG (t , t) = iZ Tr[e  Heq †jc (t)ci (t )]Include the effects of a strong driving field via the Peierls’ substitution –for a spatially uniform but time-dependent electric fieldW
S=g…and about its history
System knows about its
thermal initial state…
Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017k  k  eA(t )Electron-phonon
coupling included viaperturbation theory
invoking Migdal’s
theoremElectron-electron
coupling via secondorder perturbation
theoryTime-resolved ARPES

Image source: FHI Berlin
Freericks, et al., PRL 102, 136401 (2009); Freericks, et al., Physica Scripta 2015 T165
014012 (2015); Freericks and Krishnamurthy, Photonics 3 58 (2016)
Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

Five myths about excitation and relaxation
1.
2.
3.
4.

5.

Changes in spectral functions arise from changes in the
instantaneous eigenvalues
Once excited, a many-body system must relaxIf it relaxes, the self-energy governs the relaxation rate
Electrons thermalize amongst themselves to form a hot thermal
state that subsequently relaxes energy to the phonon bath (hotelectron model)
Relaxation times are automatically separated in the time
domain.
Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

Five realities about excitation andrelaxation
1.
2.
3.
4.
5.

Systems without dipolar coupling matrix elements do notchange their instantaneous eigenvalues
Excited systems can only relax if energy can be removed fromthem
The rate of relaxation is related to the self-energy, but in acomplex fashion
It is the deviations from hot-electron behavior that determine
the relaxation
Relaxation times separate in the time domain because ofenergy bottlenecks and the violation of Mathiessen’s rule
Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

Clear difference between relaxation and line-widths?
Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

Three Types of Interactions

Impurity

Electron-phonon

Electron-electron

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017Electron phonon versus impurity
Electron-phonon

Impurity

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017Electron-phonon and impurity

Equilibrium: quasiparticle

Non-equilibrium: population

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017Electron-phonon and impurity

Equilibrium: quasiparticle

Non-equilibrium: population

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

Violation of Matthiessen’srule comes from energy
transfer bottlenecks
Electrons

Energytransferdetermines
population
dynamics

Heat bath

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017Electron-electron interaction
Electronelectron

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017Electron phonon vs electron-electron
Change in total electronic energy
Electronphonon

Electronelectron

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017Electron-phonon and electron-electron
Step in lifetimes remains visible
Competition between e-p and e-escatteringMatthiessen’s rule appears not tohold.

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

TR-ARPES experiment showing thisTime-resolved ARPES experiment by J.D. Rameau,
S. Freutel, I. Avigo, M. Ligges, L. Rettig, P.D.
Johnson, U. Bovensiepen

Population decay time in Bi2201
as a function of binding energy
Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

Decay rates depend on fluence300-2

 (Jcm )short (fs)25035105165
315200150

Decay rates areprimarily reflective ofenergy transfer
processes

100500ab5075

E100125-E (meV)

binF

150

5075

100125150

E-E (meV)F

Population dynamics can be understood with a strongly coupled boson at approximately
75 meV and.
Quantitative agreement between experiment and theory
Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

Relaxation is complicated—not just hot electrons
Holst.Hubb.

Holst.

GΣ

Relaxation rate not given
just by self-energy…
(Entropy 18 2016)...
Different distributionfunction for G and Σ …
(Fort. Phys. 64 2017)

ratio

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017Conclusions
Relaxation is not always determined by equilibrium
relaxation rates.
Energy dissipation bottleneck governs the relaxation
process. If a boson dissipates energy, you canmeasure its effective relaxation rate.
Using equilibrium concepts in nonequilibrium can befraught with peril.
Still need to figure out precisely how relaxation rate isdetermined. We are making progress, but not thereyet.
Violation of Matthiessen’s rule in pump/probe TR-ARPESCORPES, July 6, 2017

Thanks toLex Kemper

Tom Devereaux

Brian Moritz

Sona Najafi

Violation of Matthiessen’s rule in pump/probe TR-ARPES
CORPES, July 6, 2017

Michael Sentef