1. Mott physics in organic charge-transfer salts Michael Lang J.W. Goethe-Universität Frankfurt Temperature Pressure Mott insulator AF order superconductor anomalous metal  -(BEDT-TTF) 2 X Fermi-liquid

2. Collaborations Experiment:Mariano de Souza*Phys. Institute, Goethe-Univ., FFM Rudra S. Manna* State Univ. Sao Paulo, Brazil Andreas Brühl Christian Strack Sebastian Köhler Ulrich Tutsch Jens MüllerPhys. Institute, Goethe-Univ., FFM Gerd SchönhensePhys. Institute, Gutenberg-Univ., Mainz Katja Medjanik Hans J. Elmers Theory:Lorenz BartoschInstitute f. Theor. Phys., Goethe-Univ., FFM Harald Jeschke Roser Valent ί Samples:Dieter SchweitzerUniversity Stuttgart John SchlueterArgonne Nat. Lab. SFB/TR49 (Frankfurt-Kaiserslautern-Mainz) “Condensend Matter Systems with Variable Many-Body Interactions “

3. Materials on the verge of the Mott transition fundamental aspects : - universality of the Mott transition (order parameter, analogy to liquid-gas trans.?) - role of lattice degrees of freedom in the Mott transition - anomalous states next to the Mott transition (V 1-x Cr x ) 2 O 3 AFM insulator param. insulator param. metal T (K) McWham et al., PRB 7, 1920 (’73) Limelette et al., Science 302, 89 (‘03) Georges et al., J. Phys. 114, 165 (’04) P ~ 20 kbar (P 0,T 0 ) metal superconductor param. insulator T MI TNTN AFM insulator superconductor  -(ET) 2 Cu[N(CN) 2 ]Cl Kino, Fukuyama, JPSJ 65, 2158 (’96) Kanoda, Hyperfine Int. 104, 235 (’97) Lefebvre et al., PRL 85, 5420 (’00) Limelette et al., PRL 91, 016401 (‘03) Fournier et al., PRL 90, 127002 (‘03) Kagawa et al., Nature 436, 534 (’05) P ~ 200 bar anomalous metal T*T*

4. C. Castellani et al., PRL 43, 1957 (1979) gasliquid solid p T Analogy to liquid-gas transition !? Insulator doublon holon Metal high density (“liquid“) low density of doublons (“gas“) double occupancy (n = 1)  order parameter  Ising universality class !? W. F. Brinkman, T. M. Rice, PRB 7, 1508 (1973)

5. outline 1)Lattice effects at the Mott transition 2) Mott criticality 3)Probing the anomalous metallic state by Hard X-ray photoemission spectroscopy

6.  -(BEDT-TTF) 2 X X-X- [(BEDT-TTF) 2 ] + X = Cu[N(CN) 2 ]Br, Cu[N(CN) 2 ]Cl: - strong dimerization: one hole/dimer - U  W : strong-correlation regime - triangular dimer structure t‘~ t EFEF

7. t‘t‘ tt  -(BEDT-TTF) 2 X frustrating interactions X t‘/t Cu[N(CN) 2 ]Br0.68 0.42 Cu[N(CN) 2 ]Cl0.72 0.44 Cu(NCS) 2 0.84 0.58 Cu 2 (CN) 3 1.06 ~ 0.83 ext. Hückel ab initio Kandpal et al., PRL 103, 067004 (’09) Nakamura et al., JPSC 78, 083710 (‘09). T. Mori et al., Chem. Soc. Jpn 72, 179 (’99) Komatsu et al., JPSJ 65, 1340 (’96) spin liquid

8. Minimal model for  -(BEDT-TTF) 2 X Kandpal et al., PRL 103, 067004 (2009) metal d-wave superconductor antiferromagnet 2D frustrated Hubbard model Cellular dynamical mean-field theory: Kyung, Tremblay PRL 97, 046402 (2006) Ab initio-derived U/t and t‘/t values: spin liquid U/t t‘/t X = Cu 2 (CN) 3 spin liquid X = Cu[N(CN) 2 ]Br (superconductor) X = Cu[N(CN) 2 ]Cl (afm) X = Cu(NCS) 2 (superconductor) Kino, Fukuyama, JPSJ 65, 2158 (1996)

9. Effect of (chemical) pressure X = Cu[N(CN) 2 ]Cl (P 0,T 0 ) metal superconductor param. insulator T MI TNTN AFM insulator superconductor Cu[N(CN) 2 ]Br  -(BEDT-TTF) 2 X W/U T*T* anomalous metal Pressure: increase the bandwidth W  bandwidth-controlled Mott transition Cu[N(CN) 2 ]Cl Cu[N(CN) 2 ]Br

10. X = Cu[N(CN) 2 ]Cl (P 0,T 0 ) metal superconductor param. insulator T MI TNTN AFM insulator superconductor Cu[N(CN) 2 ]Br  -(BEDT-TTF) 2 X W/U T*T* “D8-Br“ anomalous metal Effect of (chemical) pressure CH2  CD2CH2  CD2  -(D8-ET) 2 Cu[N(CN) 2 ]Br (“D8-Br“): crossing T MI at ambient pressure ! A. Kawamoto et al., PRB 55, 14140 (‘97)

11. #3 #1 T MI  ~ 16 K #3 #1  -(D8-ET) 2 Cu[N(CN) 2 ]Br #2 - M-I transition T MI  16 K - percolative (not bulk) superconductivity resistivity

12. High-resolution dilatometrie resolution:  L  1/100 Å (  L/L  10 -10 for L = 10 mm) 30 mm

13. Thermal expansion on  -(D8-ET) 2 Cu[N(CN) 2 ]Br #1 - - glass-like transition at T g  77 K J. Müller et al., PRB 65, 144521 (02) A.U.B. Wolter et al., PRB 75, 104512 (07) - - peak anomaly at T* = 30 K (indicative of 2 nd -order transition)  a/a - - phase transition at T MI  14 K (1 st -order) #1 T* Sweep rate: ±1.5 K/h  L a /L a  T MI T*T* TgTg M. de Souza et al., PRL 99, 037003 (07) D8-Br #1 (T 0, P 0 ) literature T* T MI afm insulator sc afm insulator

14. 1) Directional-dependent lattice effects D8-Br A2907#1 - volume expansion  V/V ~ 0.04 % below T MI M. de Souza et al., PRL 99, 037003 (07) - striking in-plane anisotropy! - unexpected out-of-plane expansion!  Intricate coupling of  -electrons to lattice degrees of freedom  intra-dimer degrees of freedom !? T*T*

15. 2) Critical fluctuations close to (P 0, T 0 ) preliminary analysis based on the assumption:   C (  =  /C = const.) M. de Souza, et al., PRL 99, 037003 (07) D8-Br  = 0.5  = 0.3 #1 #3 M. de Souza et al., PRL 99, 037003 (07) D8-Br #1 (T 0, P 0 ) literature T* T MI afm insulator sc afm insulator -“unusual (large) critical exponent“  = (0.8  0.15) ?! -“inhomogeneous broadening“  T 0  1.7 K ?! ~

16. Criticality at 2 nd -order end-point (P 0, T 0 ) Finite-T critical end point:T dependent ! T p p, T : independent variables p T c = T c (p):   = const. T

17. Criticality at 2 nd -order end-point (P 0, T 0 ) Scaling form for the Gibbs free energy for the 2D Ising universality class: ss (T 0,p 0 )  large  (T) anomaly + sign change expected 

18. Scaling for 2D Ising universality class L. Bartosch, M. de Souza, M.L., PRL 104, 245701 (10) - Expansitity data consistent with 2D Ising universality class Thermodynamics:  large lattice deformations accompany the Mott critical end point #1 #3 - “D8-Br“ crystals are situated 20-30 bar off P 0 - For P = P 0 :  4 times bigger  (T) anomaly expected !

19. Literature results - (V 1-x Cr x ) 2 O 3 “universality of liquid-gas transition“ (3D Ising) (P. Limelette et al., Science 302, 89 (03)) -  (T) =  ( , energy density ) (S. Papanikolaou et al., Phys. Rev. Lett. 100, 026408 (2008)) for dominant coupling to energy density:  conductivity data on  -(ET) 2 Cu[N(CN) 2 ]Cl consistent with 2D Ising universality class -  -(ET) 2 Cu[N(CN) 2 ]Cl Ass.: conductivity  (T)     t   “unconventional Mott criticality“: ( , ,  ) = ( 2, 1, 1) (F. Kagawa et al.,Nature 436, 534 (05); Nature Phys. 5, 880 (09)) cf. 2D Ising:(15,1/8, 1.75)

20. Summary  -(BEDT-TTF) 2 X W/U (P 0,T 0 ) metal supercondu ctor param. insulator T MI TNTN AFM insulator superconductor T*T* anomalous metal 1) Lattice effects at the Mott transition: - strongly anisotropic lattice effects which do not match the dimer-dimer electronic structure  intricate role of the lattice degrees of freedom (intra-dimer effects !?) 2) Mott criticality : - strongly T-dependent Grüneisen parameter incl. sign change at the 2 nd -order critical end point  large lattice deformations around (P 0, T 0 )! - Thermal expansion data are consistent with a 2D Ising universality class

21. Hard X-ray photoemission spectroscopy 1.6 nm UPS 0.5 nm information depth HAXPES > 10 nm escape depth bulk sensitivity

22. Core-level spectroscopy Sulphur 2s HAXPES: local spectroscopic probe in the BEDT-TTF layers idea: use interactions of core hole with “local electronic environment“ via (“shake-up processes“) to gain access to the electronic states in the valence shell

23. metal superconductor param. insulator T MI TNTN AFM insulator superconductor  -(ET) 2 Cu[N(CN) 2 ]Br U/W T*T* anomalous metal T < T* : single-line spectrum Core-level spectroscopy T  T*: occurrence of satellites A, B, B‘ at higher binding energies

24. Core-level spectroscopy -sudden decrease of main line intensity to 84% -accompanied by satellites A, B, B‘, C with T-dependent intensities T  T * “T* anomalies“

25. (i) Correlated metal regime consistent with a “correlated metal“ state all three valence electrons per dimer are itinerant (“coherent band state“) EFEF T  40 K: single-line spectrum “(cf. simple metals) Intensity (itinerant electrons do not couple to the core hole)

26. (ii) Anomalous metal regime main line satellites B A T  T*: core-level satellites (cf. open d-shell systems) EFEF HOMO-1 “partial localization of electrons on dimer sites“ opens new excitations channels: (shake up into empty states) HOMO-1 HOMO Ligand state B A Instanteneous rearrangements of electrons in HOMO and HOMO-1 (incl. ligand) states required energy  lowering of the electrons‘ kinetic energy

27. (ii) Anomalous metal regime  formation of a superstructure!? Drop in main-line intensity: 100%  84% speculation: (  3x  3)-R30°  reduction of 1/3 of 50 %  16 % expected S i (  50% of all S) SiSi SoSo C C HOMOs

28. Acoustic anomaly sound velocity Fournier et al., PRL 90, 127002 (03) - large softening of c 22 (  planes) upon approaching ( P 0, T 0 ) “diverging electronic compressibility!“ P > P 0 P0P0 P < P 0 (P 0,T 0 )  -Cl metal superconductor param. insulator T MI TNTN AFM insulator superconductor Hassan et al., PRL 94, 036402 (05) - predicted by theory (compressional Hubbard model) as response to the lattice expansion through the Mott transition T0T0 “crossovers“

29. Background contribution background: non-critical electronic + phonon contributions D8-BrH8-Br

30. T MI ~ 13.5K T* = 30.1K Evolution of T* anomaly with chemical pressure D8-Br A2907#1D8-Br A2995#3 T c = 11K T* = 37 K J. Müller, M.L. et al., PRB 65, 144521 (2002) H8-Br T MI ~ 14.1K T* = 29.6K M. de Souza, et al., PRL 99, 037003 (07) T * = 37 K (H8-Br) coincides with “pseudogap“ phenomena Mayaffre et al. ’94, Kawamoto et al. ’95, DeSoto et al. ‘95 (T 1 T) -1 T*T*