Optical signatures for strong coupling in graphene

Bright excitonic signatures in theabsorption spectrum indicates a strongly Coulomb correlated, gapped state.

no Coulomb, shows band edge

full calculation,excitons below

band edge

frequency

abso

rption

0

0

momentum

ener

gy

quasiparticleconduction bandin strong-coupling

phase

brightexcitons

quasiparticlevalence band

Spectrum has clustered peaks. Clustering comes from coupling between two degenerate p states.

Coupling is caused by Auger processes in the Coulomb interaction.

Auger processes,antisymmetric

particles-per-band preserved, symmetric

Graphene in the strong-coupling phase has a broken sublattice symmetry, and a non-zero band gap.

Calculated with gap equations,see poster \Strong coupling in graphene - conditions" by T.S.,J.H.G., and S.W.K.

intrabandinterband

antisymmetric p states superimposed on ground

state populations

excite

Light creates p states because of the symmetry of the light-matter coup-ling at the Dirac point.

+ similar terms

light-matter matrix element

Strong-coupling

can be viewed either as populated Dirac bands, or quasiparticles with gapped bands.

J. H. Gronqvist, T. Stroucken, and S.W. Koch

1. Department of Physics and Material Sciences Center, Philipps University Marburg, Germany2. Department of Physics, Abo Akademi University, Finland

11,2 1

0

couplin

g stren

gth

c o n t i n u u m

frequency

Excite ground state p-like excitons at the Dirac point.

Ground state

Optical excitation

Auger splitting

band edge

gap

Excitons in absorption spectrum

isotropic (Dirac band) populations in strong-coupling

ground state

Swicthing off the Auger terms gives degenerate exciton peaks.

0

Auger

strength

frequency

3/4

fullAuger

noAuger

1/41/2

Gradually turning the Auger terms back on lifts the degeneracy.

Size of gapdepends on coupling strength. Coupling smaller gap smaller excitons squeeze together.

T. Stroucken, J. H. Gronqvist, and S. W. Koch, \Excitonic resonances as fingerprint of strong Coulomb coupling in graphene," J. Opt. Soc. Am. B 29, A86 (2012)\Optical response and ground state of graphene," Phys. Rev. B 84, 205445 (2011).