2. Organic Conductors and Superconductors: signatures of electronic correlations Martin Dressel 1. Physikalisches Institut der Universit ä t Stuttgart Outline 1.Organic Conductors basics and development 2.Optical Properties metallic conductivity vs electronic localization 3.Mott Transition at Half Filling filling control vs bandwidth control  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x 4.Outlook M. Dumm, N. Drichko, D. Faltermeier 1. Physikalisches Institut Universit ä t Stuttgart C. Meziere, P. Batail CNRS, Universite d ’ Angers, France J. Merino Universidad Autonoma, Madrid, Spain R. McKenzie UQ, Brisbane, Australia

3. Organic Conductors radical cation salts b a c (BEDT-TTF) 2 X The structure consists of BEDT-TTF layers as electron donors, separated by sheets of inorganic acceptors. anisotropy within the plane  c /  a ~ 0.5 perpendicular to the plane  b /  a ~ 10000

4. Organic Conductors radical cation salts (BEDT-TTF) 2 X The layered arrangement of the organic molecules, separated by anions, leads to a two-dimensional electronic system. The bandwidth depends on the overlap integral between neighboring molecules W = 8t  1 eV for these compounds. The bandfilling depends on the stoichiometry. The on-site (U) and intersite (V) Coulomb interaction depends on the molecule U eff = 0.5 eV strong influence of electron-electron correlations

5. Optical Properties of Organic Conductors and Superconductors What are the optical properties of two-dimensional organic conductors? Do they behave like conventional metals? What is the influence of the reduced dimension and narrow bands? Are there fingerprints of electronic correlations? What are the indications of charge order? Can we see the superconducting gap?

6. Optical Reflection Measurements experimental setup Fourier transform infrared spectrometer Bruker IFS 113v Bruker IFS 66v Infrared microscope Bruker Hyperion Frequency range: 15 cm -1 – 25 000 cm -1 (2 meV – 3 eV) Temperature range: 5 K ≤ T ≤ 300 K Absolute values of reflectivity by Au evaporation method. size of the surfaces: (0.5 – 1 mm) 2 with IR microscope: (150  m) 2

7. Quasi-Two-Dimensional Organic Conductors optical properties Small in-plane anisotropy: reflectivity is higher in the direction of larger overlap. Deviations from a simple metallic behavior. R max R min  -(BEDT-TTF) 2 NH 4 Hg(SCN) 4 T = 300 K c a The width of the conductance band is typically 0.8-1 eV (overlap integrals t about 0.1 eV). This is comparable to Coulomb interaction U. The spectral weight is defined as where the plasma frequency is given by

8. Molecular Vibtrations in BEDT-TTF salts The intra-molecular vibrations are a measure of the localized charge. The phonon frequency shifts down when electrons are taken off. M. Dressel and N. Drichko, Chemical Reviews 104, 5689 (2004) electrons on molecule IR active molecular vibrations are intense only for polarization E  conducting layers 3 ( A ) 4 ( A ) 27 (B 1u )

9. Electron-Molecular Vibtrational Coupling theory symmetry break (dimerization) charge transfer within the molecules change of the molecular geometry due to charge modulation on the HOMO The totally symmetric intra-molecular vibrations become infrared active by coupling to the localized charge: electron-molecular vibrational (emv) coupled phonons. charge transfer band Conductivity 1200 cm -1 ~3000 cm -1 Frequency emv-coupled feature

10. Electron-Molecular Vibtrational Coupling experimental evidence slightly dimerized system strongly dimerized system R max R min  -(BEDT-TTF) 2 NH 4 Hg(SCN) 4 T = 300 K

11. Quasi-Two-Dimensional Organic Conductors electronic correlations  -(BEDT-TTF) 2 X 2:1 stoichiometry: insulator, metal, superconductor 1/4-filled system: hole carriers 0 -  /a E k +  /a 0 -  /a E k +  /a +  /2a -  /2a  -(BEDT-TTF) 2 X 2:1 stoichiometry, dimerized: metal, superconductor 1/2-filled upper band: hole carriers

12. Quasi-Two-Dimensional Organic Conductors (BEDT-TTF) 2 X salts Proposed Phase Diagrams ¼ filled compounds½ filled compounds U / W Tuning parameters: electronic correlations (on-site U, inter-site V) _____________________________________ bandwidth W V / W

13. Half-Filled System strongly dimerized  -phase salts The organic molecules are arranged in pairs (dimers). The conduction band is split. Interband transitions intraband transitions or intradimer transitions (localized) interdimer transitions (itinerant) 0 -  /a E k +  /a +  /2a -  /2a

14. Half-Filled System localized carriers The localized carriers on the dimer: charge transfer between the molecules activates intramolecular vibrations of BEDT-TTF molecules the charge transfer and the intra-moleuclar vibrations are described by cluster model The cluster model describes well the temperature- and doping- dependence of the electronic charge-transfer band and the coupled vibrations. D. Faltermeier et al., Phys. Rev. B 76, 165113 (2007)

15. Half-Filled System itinerant carriers The itinerant carriers can be described by the Hubbard model on a frustrated square lattice: t1t1 t2t2 t2t2 t 1 =0.8 t 2 Mott metal-insulator transition at U c  1.66 W. close to the metal-insulator transition a ‚bad‘ metallic behavior occurs: a crossover from coherent exhitations at low temperatures to ‚bad‘ metallic behavior at high temperatures.

16. Half-Filled System  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x in-plane dc resistivitylow-T phase diagram t2t2 t2t2 t2t2 t2t2 t1t1 tAtA tAtA tAtA tAtA ClBr p  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x AFM Mott insulator Super- conductor Fermi liquid Semiconductor Bad metal

17. Antiferromagnet Mott insulator Super- conductor Fermi liquid Semiconductor Bad metal in-plane dc resistivitylow-T phase diagram t2t2 t2t2 t2t2 t2t2 t1t1 tAtA tAtA tAtA tAtA ClBr p  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x Half-Filled System  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x

18. Metal-Insulator Transition bandwidth control by anion substitution in-plane dc resistivity ClBr p What are the dynamical properties close to the metal-insulator transition? We investigated the temperature dependent optical conductivity of  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x with x = 0%, 40%, 73%, 85%, and 90%. Changing size of the anions changes the overlap integral t : ‘chemical pressure’  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Cl is a semiconductor at room temperature which becomes a Mott insulator below 100 K. At low temperature it orders magnetically, under slight pressure it superconducts.  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br is metallic for T  T*  50 K. Organic superconductor with maximum T c = 12 K.  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x

19. Optical Properties of  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x Br content

20. Metal-Insulator Transition in  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x temperature rises When the temperature rises, the gap shifts to lower frequencies, like a mean-field behavior. When Br content increases, i.e. U/t decreases, spectral weight starts to fill the gap, finally a Drude-like component develops.

21. Intra-molecular vibrations: 4 emv coupling Electronic Excitations Drude-Lorentz fit Intra-dimer excitations Inter-dimer excitations Optical Properties different contributions The optical conductivity contains different contributions which can be disentangled: tAtA tAtA tAtA tAtA t2t2 t2t2 t2t2 t2t2 t1t1 tAtA tAtA tAtA tAtA

22. Optical Properties itinerant charge carriers Inter-dimer excitations localized charge carriers due to the on-site (dimer) Coulomb repulsion; excitations across a Mott-Hubbard gap delocalized charge carriers Hubbard model on frustrated square lattice t2t2 t2t2 t2t2 t2t2 t1t1 tAtA tAtA tAtA tAtA U ≈ 0.3 eV t 2 ≈ 0.03 eV t 2 : nearest neighbor hopping amplitude t 1 = 0.8 t 2 : next-nearest neighbour hopping amplitude U: on-dimer Coulomb repulsion

23. Dynamics of Correlated Charge Carriers theoretical model Hubbard model on frustrated square lattice U ≈ 0.3 eV t 2 ≈ 0.03 eV t 2 : nearest neighbor hopping amplitude t 1 = 0.8 t 2 : next-nearest neighbour hopping amplitude U: on-dimer Coulomb repulsion U 2W 0 h  ( ) U-W W U/2-U/20 E DOS Insulating state (U/t 2 > 10) 0 U U/2 W h  ( ) U/2-U/20 E DOS Metallic state (U/t 2 < 10) M. Rozenberg, G. Kotliar and H. Kajueter, Phys. Rev. B 54, 8452 (1996); J. Merino, M.Dumm, M. Dressel, N. Drichko, R. McKenzie, Phys. Rev. Lett. (2008).

24. Metal-Insulator Transition bandwidth control U/t U on dimer 0 U U/2 W h  ( ) Metallic state E U/2-U/2 0 DOS W Drude-like feature due to the coherent quasiparticles (Fermi liquid) band of width W centered around U/2 broad band at U of width 2W. U-W W U/2-U/20 E DOS U 2W 0 h  ( ) Insulating state gap of  Mott = U-W broad band of width 2W centered around U M. Rozenberg, G. Kotliar and H. Kajueter, Phys. Rev. B 54, 8452 (1996)

25. Dynamics of Correlated Charge Carriers optical conductivity Temperature dependent optical conductivity J. Merino, M. Dumm, N. Drichko, M. Dressel, R. McKenzie, Phys. Rev. Lett. 100, 086404 (2008). DMFT calculations for the Hubbard model optical conductivity of correlated charge carriers for E||c Number of holes per dimer Band at U/2 suppressed in experimental data Gradual destruction of quasiparticles above T*  = 3300 Å 3 m b = 2.5 m e

26. Dynamics of Correlated Charge Carriers effective charge carrier number Effective carrier number per BEDT-TTF dimer t 2 = 0.03 eV With increasing correlations U/t: spectral weight is transferred to higher frequencies effective charge-carrier number is supressed J. Merino, M. Dumm, N. Drichko, M. Dressel, R. McKenzie, Phys. Rev. Lett. 100, 086404 (2008).

27. Dynamics of Correlated Charge Carriers frequency dependent scattering rate and mass Extended Drude analysis from experiments from DMFT calculations When approaching the metal-insulator transition from the metallic side, the effective mass increases, because correlations increase. (Brinkman-Rice) The prefactor A becomes larger as the metal- insulator transition is approached, because correlations increase. (Kadowaki-Woods-plot) The scattering rate indicates a Fermi-liquid behavior: J. Merino, M. Dumm, N. Drichko, M. Dressel, R. McKenzie, Phys. Rev. Lett. 100, 086404 (2008).

28. Drude Weight at the Metal-Insulator Transition density of states The Mott transition can be visualized as a reduction in the density of states at the Fermi energy. At the transition D(E F ) is zero. Since the metal-insulator transition is first order, there is an abrupt jump with (D c /D 0 ) = 0.1... 0.3. EFEF D(E) E D/D 0 t/U (t/U) c D c /D 0 Mott insulator metal For large x > 70% we find a dramatic increase of the spectral weight as the temperature is reduced below T* = 50 K. This clearly separates the Mott insulating from the metallic state at x c  70%.

29. Summary: ½ Filling  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x The two-dimensional organic conductor  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x is a half-filled correlated electron system which serves as a model of a bandwidth controlled Mott insulator. For the metallic compounds a coherent carrier response appears below 90 K. When the Mott transition is approached by increasing U/t, the Drude spectral weight decreases. The Drude response disappears on crossing the phase border to the Mott insulator. D. Faltermeier et al., Phys. Rev. B 76, 165113 (2007)

30. 1/2-filled 1/4-filled 1/5-filled T=300 K 1/2-filled 1/4-filled 1/5-filled T=50 K Overlap integrals: t = 0.1 eV for 1/2-filled t = 0.07 eV for 1/4-filled t = 0.07 eV for 1/5 filled Coherent Response for Different Filling of BEDT-TTF-based conductors

31. 1/5-filled 1/4-filled 1/2-filled Changing the filling from 1/2 to 1/4 to 1/5 increases the Drude weight of the coherent carriers and makes it less temperature dependent. U/t is the same Spectral Weight of the coherent carriers response Overlap integrals: t = 0.1 eV for 1/2-filled t = 0.07 eV for 1/4-filled t = 0.07 eV for 1/5 filled Drichko et al., Physica C 460-462, 125 (2007)

32. Summary two-dimensional organic conductors unconventional metal SC ordered state temperature band filling electronic correlations In the half-filled compounds  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Br x Cl 1-x a bandwidth-controlled Mott transition was explored. The dependence of coherent carriers response for different band-fillings was studied; it increases on doping from ½ filling. For metallic compounds with the same U/t ratio, a coherent carriers response is present only at low temperatures for 1/2-filled compound, - it increases slightly on cooling for 1/4-filled compound - it stays constant for 1/5-filled compound. Dressel and Drichko, Chem. Rev. 104, 5689 (2004)