Infrared phonon activity and quantum Fano interference in multilayer graphenes

1. Lara Benfatto ISC, CNR, Rome, Italy Alexey B. Kuzmenko Dept. Physics Uni. Geneve, Switzerland Workshop on Quantum Fielt Theory aspects of Condensed Matter Physics, LNF, Frascati, 7 September 2011 Infrared phonon activity and quantum Fano interference in multilayer graphenes Emmanuele Cappelluti Instituto de Ciencia de Materiales de Madrid (ICMM) , CSIC, Madrid, Spain Institute of Complex Systems (ISC), CNR, Rome, Italy, and: Z.Q. Li, C.H. Lui, T. Heinz (Columbia, NY, USA)

2. Outline motivations (limits of Raman spectroscopy) experimental measurements (intensity and Fano asymmetry modulation) theoretical approach unified theory for phonon intensity (charged phonon) and Fano asymmetry tunable phonon switching effect comparison with experiments conclusions

3. Probing interactions (and characterization) in graphenes electronic states ARPES - dispersion anomalies - renormalization - linewidth A Bostwick et al., NJP 9, 385 (2007) DC Elias et al., Nat Phys 7, 701 (2011)

4. Probing interactions (and characterization) in graphenes electronic states optical conductivity ZQ Li et al., Nat. Phys. 4, 532 (2008) • doping dependence • electronic interband features - possible to extract bandgap  KF Mak et al, PRL 102, 256405 (2009)

5. Probing interactions (and characterization) in graphenes lattice dynamics optical transitions single layer in-plane in-plane E2g (G) out-of-plane bilayer Eg Eu Raman IR

6. Raman spectroscopy phonon intensity I Calizo et al, JAP 106, 043509 (2009) C Casiraghi, PRB 80, 233407 (2009) difficult access to absolute phonon intensity relative intensity between different peaks instead used

7. Raman spectroscopy focus on: ph. frequency ph. linewidth J Yan et al, PRL 98, 166802 (2007)

8. Raman spectroscopy - not only characterization, also fundamental physics doping dependence of phonon frequency and linewidth: evidence of nonadiabatic breakdown of Born-Oppenheimer S Pisana et al, Nat Mat 6, 198 (2007)

9. Raman spectroscopy investigation tools: peak frequency peak linewidth relative (non absolute) peak intensity but no modulation of intensity no asymmetric peak lineshape J Yan et al, PRL 98, 166802 (2007)

10. IR phonon spectroscopy suitable tool???

11. IR phonon spectroscopy IR phonon peak best resolved in ionic systems -Z +Z Z: dipole effective charge (related to oscillator strength S, f) ex. Na+ Cl- Z = 1 integrated area VG Baonza, SSC 130, 383 (2004)

12. IR phonon spectroscopy bilayer graphene one allowed in-plane IR mode: antisymmetric (A) Eu homo-atomic compound first approximation: all the C atoms equal charge equally distributed no net dipole q q q q no IR activity

13. IR phonon spectroscopy taking into account the slight difference between atomic sites small charge disproportion however finite dipole Z ≈ (q1-q2) q1, q2 < n limited by the total amount of doped charge n q2 q1 q2 q1 Z ≈ 10-3 (static dipole) no hope, thus..... but.....

14. Exp. results: Geneve group tunable phonon peak intensity Zmax ~ 1.2!! huge! as large as 1 electron over N=4 (sp3) !! AB Kuzmenko et al, PRL 103, 116804 (2009)

15. Exp. results: Geneve group tunable phonon peak intensity neutrality point (NP) n=0 also problem: negative peak area… Z not defined…? AB Kuzmenko et al, PRL 103, 116804 (2009)

16. Negative peak: Fano effect and quantum interference arising from quantum interference (coupling) between a discrete state (phonon) with continuum spectrum (electronic) asymmetry Fano parameter non coupled phonon weakly coupled strongly coupled asymmetric lineshape negative peak symmetric lineshape |q| ≈  |q| ≈ 1 |q| ≈ 0

17. Exp. results: Geneve group four independent parameter fit p : related to intensity q : Fano asymmetry 0 : phonon frequency  : phonon linewidth “bare” intensity (in the absence of Fano) AB Kuzmenko et al, PRL 103, 116804 (2009)

18. Exp. results: Geneve group phonon softening with doping: ok with LDA and TB theory Eg (S) mode Eu (A) mode T Ando, JPSJ 76, 104711 (2007) AB Kuzmenko et al, PRL 103, 116804 (2009)

19. Exp. results: Geneve group phonon linewidth: strong increase at NP: why?? Eu (A) mode? T Ando, JPSJ 76, 104711 (2007) AB Kuzmenko et al, PRL 103, 116804 (2009)

20. Exp. results: Geneve group linear dependence of bare intensity with doping: where from? why so huge Z? NB: tight-binding calculations AB Kuzmenko et al, PRL 103, 116804 (2009)

21. Exp. results: Geneve group linear dependence of bare intensity with doping: where from? why so huge Z? Fano asymmetry: where from? related to el. optical background? points out finite intensity at n=0…! AB Kuzmenko et al, PRL 103, 116804 (2009)

22. KxC60 Charge-phonon effect doped insulators: organic and C60 systems doping huge intensity increase of selected IR modes upon electron doping x SC Erwin, in Backminsterfullerenes (1993) K-J Fu et al, PRB 46, 1937 (1992)

23. Charge-phonon effect : el. polarizability (interband transitions) direct light-phonon coupling electronical background of optical conductivity but these no polar materials:....

24. Charge-phonon effect : el. polarizability (interband transitions) direct light-phonon coupling electronical background of optical conductivity but these no polar materials:.... no intrinsic dipole further channels to be considered

25. Rice (Michael) theory electronic polarizability provides finite IR intensity to phonon modes allowed but otherwise not active : el. polarizability (interband transitions) irreducible diagrams phonon mediated contribution electronical background of optical conductivity giving rise to resonance at phonon energy no phonon resonance

26. Rice (Michael) theory fundamental ingredients: phonon resonance

27. Rice (Michael) theory fundamental ingredients: current/ electron-phonon response function intensity ruled by the current/electron-phonon response function

28. Rice theory in bilayer graphene : real function (α doping) tuning the phonon intensity

29. Rice theory in bilayer graphene : real function (α doping) tuning the phonon intensity Rice theory: in its original application: semiconductors effective theory: interesting peculiarities of bilayer graphene: zero gap semiconductor: low energy interband transitions : complex quantity Fano asymmetry tunable charged-phonon effects controlled by external voltage biases (doping and gap)

30. Microscopic Rice theory in bilayer graphene three different response functions: jj (el.background) AA (ph. self-energy) jA (charged-phonon effect) we can compute microscopically each of them

31. Fano-Rice theory in bilayer graphene interband transitions at low energy: jA = RejA +iImjA jA complex quantity!!! (in gapped systems: ImjA = 0) Fano formula! Fano and charged-phonon effects same origin! it permits a microscopical identification

32. Peak parameters in Fano systems Fano fit -integrated area not good |qA| ≈ 0 (RejA=0)  negative peak but WA=0 not good |qA| ≈ 1 (RejA = ImjA)  asymmetric peak but W’A=0 phonon strength

33. 4 3 2 1 Phonon intensity in bilayer graphene Step by step analysis: gating induces doping but not Ez  in this case low-energy transitions between 2 and 3 system like a gapped semiconductor Im = 0 no Fano effect doping depedence of -integrated area W’ perfectly reproduced what about WA? negative area? E Cappelluti et al, PRB 82, 041402 (2010)

34. Exp. results: Berkeley group n = 0 double-gated device possible tuning doping and  in independent way n = 0 and   0: negative peak like us Fano effect as a function of  they attribute origin of negative peak at n = 0 to Eg (S) (Raman-active) mode (S allowed by symmetry in IR when   0) T-Ta Tang et al, Nat Nanotechn 5, 32 (2010)

35. Different phonon channels in optical conductivity  > 0 gating induces z-axis asymmetry Ez Eg (S) mode also IR active! two main IR channels present probes DAA ph. propagator probes DSS ph. propagator relative “intensity” ruled by pA and pS total spectra dependent on the relative dominance of one channel vs. the other one

36. Optical channels and phonon switching in optical conductivity - phase diagram Berkeley Eu-A and Eg-S modes dominant in different regions of phase diagram: possible switching of intensity from one mode to other one Geneve E Cappelluti et al, PRB 82, 041402 (2010)

37. Phonon switching in optical conductivity Geneve group Eu (A) Eg (S) Eu (A) E Cappelluti et al, PRB 82, 041402 (2010) experimental integrated area and Fano asymmetry interpolates and switches from A to S mode AB Kuzmenko et al, PRL 103, 116804 (2009)

38. Trilayer graphenes and stacking order ABA and ABC deeply different stacking revealed phonon intensity and phonon frequency strongly doping dependent in ABC but not in ABA good agreement with theory CH Lui et al, submitted to PRL (2011)

39. Trilayer graphenes and stacking order fundamental ingredient: electronic band structure reminder: phonon activity is triggered by electronic particle-hole excitations upon doping, el. transitions at ω = √2 γ1 ≈ 0.55 eV in ABA, at ω ≤ γ1 ≈ 0.39 eV in ABC ABC closer to ω0 ≈ 0.2 eV phonon activity amplified CH Lui et al, submitted to PRL (2011)

40. Raman spectroscopy in bilayer graphene remarkable features: |q| ≈  no Fano asymmetry !!! (in IR S mode had q ≈ 0) unlike IR probes! why? intensity does not depend on doping !!! J Yan et al, PRL 98, 166802 (2007) C Casiraghi, PRB 80, 233407 (2009)

41. Fano-Rice theory for Raman spectroscopy effective mass approximation Raman vertex electronic Raman background Rice theory Raman active S mode

42. Fano-Rice theory for Raman spectroscopy IR Raman EC RejA ~ const. ImjA ~ const. ReS ~ EC ImS ~ const. ReS scaling with UV dispersion cut-off Ec ReS >> ImS weakly dependent on band-structure details (doping, ) W’S ≈ WS  Ec2 no Fano profile

43. Conclusions source of microscopic IR phonon intensity unified theory of IR intensity and Fano profile more information encoded in phonon intensity and Fano factor phonon mode switching predicted (and observed) differences between IR and Raman spectroscopy accounted for alternative and powerful tool to characterize ML graphenes

44. Additional slides

45. Raman spectroscopy in bilayer graphene focus on Eg symmetric mode Raman active present also in single-layer graphene J Yan et al, PRL 101, 136804 (2008) T Ando, JPSJ 76, 104711 (2007) frequency and linewidth OK with theoretical calculations

46. Fano-Rice theory for Raman spectroscopy ex.: isotropic Raman scattering two main quantities: S, A EC scaling with UV dispersion cut-off Ec ReS ~ EC, ImS ~ const. ReA ~ const., ImA ~ const. pS » pA dominant DSS channel no Fano profile weakly dependent on band-structure details (doping, ) W’S ≈ WS  Ec2

47. Fano-Rice theory for Raman spectroscopy effective mass approximation Raman vertex electronic Raman background Rice theory = 0 only S mode coupled

48. Fano-Rice theory for Raman spectroscopy effective mass approximation Raman vertex electronic Raman background Rice theory   0 phonon switching possible (in principle)

49. Fano-Rice theory for Raman spectroscopy ex.: isotropic Raman scattering two main quantities: S, A EC scaling with UV dispersion cut-off Ec ReS ~ EC, ImS ~ const. ReA ~ const., ImA ~ const. pS » pA dominant DSS channel no Fano profile weakly dependent on band-structure details (doping, ) W’S ≈ WS  Ec2

50. Probing electronic spectrum: optical conductivity bilayer (BL) AB Kuzmenko et al, PRB 80, 165406 (2009) possible to extract gap  and doping n vs. gate voltage Vg KF Mak et al, PRL 102, 256405 (2009)