Jörg Schmalian. Population inversion and stimulated emission of dense Dirac fermions in graphene.

Transcription

1 Population inverion and timulated emiion of dene Dirac fermion in graphene Jörg Schmalian (TKM), Center for Functional Nanotructure (CFN), Karlruhe Intitute of Technology (KIT) KIT Univerity of the State of Baden-Wuerttemberg and National eearch Center of the Helmholtz Aociation

2 collaborator: DOE-Ame Laboratory +Iowa State Univerity Tianqi Li Liang Luo Miron Hupalo Michael Tringide Jigang Wang Junhua Zhang T. Li, L. Luo, M. Hupalo, J. Zhang, M. C. Tringide, J. Schmalian, and J. Wang, Phy. ev. Lett. 108, (01)

3 ummary SiC (graphene on a ubtrate) experiment: pump-probe at high pump fluence theoretical argument 4παQED / 1.458% c n 1 critical pule induced reflectence change where conductivity change ign Concluion: pule induced population inverion and broad band gain population inverion tabilized by Dirac pectrum 3

4 The role of Coulomb interaction in graphene H v velocity renormalization i σ p + e 1 i 4πε ri r i j ( α 1+ log ( D k) ) 4 v v / finite denity: croover caling argument ( + α log ( n n) ) v v / j e. α v ε ε J. Gonzalez, F. Guinea, M. A.H. Vozmediano, Nucl. Phy. B 44, (1994). D. Sheehy, J. Schmalian Phy. ev. Lett. 99, 6803 (007). 4

5 The role of Coulomb interaction in graphene H v velocity renormalization i σ p + e 1 i 4πε ri r i j ( α 1+ log ( D k) ) 4 v v / finite denity: croover caling argument ( + α log ( n n) ) v v / j e. α v ε ε J. Gonzalez, F. Guinea, M. A.H. Vozmediano, Nucl. Phy. B 44, (1994). D. Sheehy, J. Schmalian Phy. ev. Lett. 99, 6803 (007). detailed experimental verification D. C. Elia, et al. Nature Phyic 7, 701 (011) 5

6 further evidence for e-e interaction optic APES Z. Q. Li et al. Nat. Phy., 4 (008) D. A Siegel. et al. PNAS 1, (011) 6

7 Life time due to e-e cattering: Fermi golden rule allowed procee conerve hole and electron number individually h h h + h e + e e + e e h h + e 7

8 implication for d.c. tranport d.c. conductivity E electron hole j σ E σ. ( ) ln e T0 d c. T h T L. Fritz, J. Schmalian, M. Müller, S. Sachdev, PB (008). hear vicoity y u x T xy η u y x velocity field of the fluid momentum flux η ( k ) B T e M. Müller, J. Schmalian, L. Fritz, Phy. ev. Lett. 103, (009) 8

9 longitudinal conductivity No interaction A. Ludwig et al. PB 50, 756 (1994) σ ( ω) e / h T 0 π σ e π 0( ω, T 0) h ω / k B T 9

10 longitudinal conductivity No interaction A. Ludwig et al. PB 50, 756 (1994) σ ( ω) e / h T 0 π σ e π 0( ω, T 0) h tranmiion coefficient (upended graphene) T ω / k B T ( ) ( ) ( ω) 1+ π σ ω c T 0 ( ) 1+ πα QED / 1 πα QED Nair et al. Science, 30 (008) 10

11 longitudinal conductivity No interaction A. Ludwig et al. PB 50, 756 (1994) σ ( ω) e / h T 0 π σ e π 0( ω, T 0) h Coulomb interaction ( ω >> k B T ) ω / k B T σ ( ω) (1 + e π e h C vε +...) C π E. G. Mihchenko, EPL 83, (008) D. Sheehy, J. Schmalian, Phy. ev. B 80, (009) Iue under debate: V Juričić et al., Phy. ev B 8, 3540 (010) interaction yield negligible correction to the univeral opt. conductivity 11

12 reflection coefficient (graphene on a ubtrate) ( ω) 1 n 1+ n 4πσ + 4πσ ( ω ) ( ω ) / c / c reflection change due to graphene free Dirac fermion k B T << ω << D + g n 1.458% 4 1 4π c 4π α 1 σ ( ) ( ) ω n QED + O [ n α QED 1.458%.7 (SiC)] ( ) / + g differential reflection 1

13 ultrafat fat optic in graphene pule induced change in the reflectance Laer pule nonlinear dependence on the pump fluence 13

14 number of photo-excited carrier tate filling (coherent abi ocillation of the excited tate) n ex 13 ( / ) ε cm ρ ω ωn ex A 0 I 0 include change in aborption due to change in reflectivity photoexcitation go beyond tate filling 14

15 band filling + thermalization (during the pule) thermalization via electron-electron Coulomb cattering h conervation of hole and electron population inverion h h + h e + e e + e e h h + e tabilized by conervation of hole + electron 15

16 Decribing the non-equilibrium tranient tate µ + tranient tate ditribution function f ± ( k) exp ( β ( ± vk µ )) e 1 ± µ electron temperature and chemical potential 16

17 Decribing the non-equilibrium tranient tate electron temperature chemical potential µ µ µ + max n max ex 0.15nex 9 ω ω n << nex µ ω ex 16π v k T B el ω v dilute claical ga of e-h pair degenerate quantum ytem 17

18 Decribing the non-equilibrium tranient tate electron temperature chemical potential include SiC induced Fermi energy µ 0 400meV dilute claical ga of e-h pair degenerate quantum ytem 18

19 Optical propertie of the non-equilibrium tate µ + tranient tate ditribution function f ± ( k) exp ( β ( ± vk µ )) e 1 ± µ optical gain σ ( ω) < 0 σ ( ω) If ω < µ µ + ω 19

20 0 ( ) ( ) QED c g O n α ω σ π + + ( ) ( ) ( ) ) ( ) ( / t t n t t c g g σ σ π critical reflectence change where conductivity change ign 1.458% 1 4 / QED c n πα Pule induced reflectence change

21 Pule induced reflectence change (%).0 / peak ev pump 1.55 ev probe 1.16 ev probe σ ( ω) pump pule probe pule 1.0 ω 0.5 σ ( ω, ) ω pump I pump pump fluence ( µ J/cm ) I pump T 1 elf induced tranparency 1

22 Pule induced reflectence change (%).0 / peak ev pump 1.55 ev probe 1.16 ev probe pump fluence ( µ J/cm ) I pump

23 Condition for optical gain photoexcited carrier denity hould be larger than the the initial background denity gating the ytem or uing upended graphene photoexcited carrier denity hould be of the order of n max ex 9 16π ω v uing lower frequencie require lower pump fluence a direct meaurement in the tranmiion regime remain to be done more photon out than in: T ( ω ω ) > 1 < pump 3 Jörg Schmalian

24 ummary SiC (graphene on a ubtrate) experiment: pump-probe at high pump fluence theoretical argument 4παQED / 1.458% c n 1 critical pule induced reflectence change where conductivity change ign Concluion: pule induced population inverion and broad band gain 4