Strongly Correlated Superconductivity Close to Mott Transitions in - PowerPoint PPT Presentation

Strongly Correlated Superconductivity Close to Mott Transitions in Orbitally Degenerate Molecular Conductors E.Tosatti SISSA, ICTP, Democritos Trieste, Italy HVAR, October 3, 2005

THE TRIESTE MIRAMARE CAMPUS: ICTP SISSA UNIV. TRIESTE DEMOCRITOS

Collaborators M. Capone (Rome) C. Castellani (Rome) M. Fabrizio (Trieste) G.E. Santoro (Trieste) J. Tobik (Trieste) M. Capone et al, PRL 93, 047001 (2004) E. Tosatti et al., PRL 93, 117002 (2004) M. Capone et al, Science 296, 2364 (2002) M. Capone et al, PRL 86, 5361 (2001)

MOLECULAR CONDUCTORS WITH ORBITAL DEGENERACY: ALKALI FULLERIDES A3C60 A4C60 A = K, Rb, (Cs)

MOTIVATIONS d=3 d=5

ALKALI FULLERIDE SOLIDS: NARROW BANDS

Alkali Doped Fullerenes ● C60 molecular crystal with a 3-fold degenerate LUMO ● AnC60: alkali metal atoms donate n electrons to LUMO ● Expect ordinary metals, but... ● n=4 Mott insulator (unconvent.) n=3 Superconductor

CAN ALSO BE MADE CONDUCTING BY ALKALI DOPING M. F. Craciun, S. Rogge, M. J. L. den Boer, T. M. Klapwijk, A. F. Morpurgo,cond-mat/0401036

LUMO (d = 2) 0 – 4 electrons HOMO (d = 1) M.S. Liao and S. Scheiner, J. Chem. Phys. 114, 9780 (2001)

DFT CALCULATED NARROW BANDS OF ALKALI DOPED PHTHALOCYANINES W = 0.3 eV! EF LUMO MgPc a- PHASE HOMO E. Tosatti et al., PRL 93, 117002 (2004)

~2 ~4 M. F. Craciun, S. Rogge, M. J. L. den Boer, T. M. Klapwijk, A. F. Morpurgo,cond- mat/0401036

<n>=3 FULLERIDE SUPERCONDUCTORS INCREASE OF Tc WITH VOLUME A3C60 BCS-LIKE? WHAT NEXT? Low spin (S=1/2) Mott insulator

MARGADONNA et al. , JACS (1999) MOTT TRANSITION! K NH C 3 3 60 Low spin (S=1/2) Mott insulator

Dubitskii Tc DURAND et al (2003) U/W

MAIN ACTORS -- NARROW BANDS, WIDTH W, DEGENERACY d >1 -- LARGE ON-SITE REPULSION U>W -- ORB. DEGEN.(1) : HUND'S RULE J -- ORB. DEGEN.(2) : JAHN TELLER EJT

Example : d=2 <n> = 2 Hund's rule: favor Triplet Jahn-Teller: favor Singlet |a> |a> b a b a EH= - 4| J | E= - EJT |b> |b> ~ 0.06 eV in MgPc Energy difference: LIAO et al (2001)

MOLECULAR CONDUCTION IN ORB. DEGENERATE MODEL SYSTEM t ___ ___ ___ ___ ___ ___ ___ ___ <n> ___ ___ ___ ___ Deg. d U, J , E JT H = T + H + H Jeff U Jeff = J - (3/4) EJT < 0! (BUT NEARLY 0)

HAMILTONIAN (d=3) W ~ 0.5 eV H = U ~ 1 eV _ J_eff ~ -0.02 eV Retardation effects neglected near Mott transition, where ZW <<hw, and J_eff =J -(3/4)E_JT should be adequate

MULTIPLET STATES FOR 2 OR 4 ELECTRONS IN t1u ORBITAL (d=3) S=0 S=1

MULTIPLET STATES FOR 3 ELECTRONS IN t1u ORBITAL, (d=3) S=3/2 S=1/2

U/W MOTT INSULATORS _ 2 METAL HALF FILLING 1 2 3 4 <n>

Jeff < 0: “MOTT- JAHN TELLER” INSULATOR M. FABRIZIO, E. T. , PRB 55, 13465 (1997) F F F 1 _ 2 _ _ 3 _ _ _ t12 H = (dFi/dt)^2 + cos(Fi - Fj )|tij tji |/U U > Ucrit : QUANTUM MELTING

DYNAMICAL MEAN FIELD THEORY (M. CAPONE) ____ ____ ____ t A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)

The Mott-Hubbard (ONE BAND Transition MODEL) ● Coexistence of Metallic e Insulating features U Z ● Metallic Peak (Kondo Resonance) at 0 the Fermi level of width Z, energy decreasing with U ● High-energy

U/W MOTT INSULATORS _ 2 “A4C60” METAL HALF FILLING 1 2 3 4 <n> M. Capone, M. Fabrizio, C. Castellani, E. T., Science 296, 2364 (2002)] d=3,<n>=4

M. Capone, et al Science 296, 2364 (2002)] MOTT TRANSITION FOR d=3 BANDS AT <n>=4 (or 2) QUASIPARTICLE WEIGHT Jeff /U = - 0.02 METAL MOTT INSULATOR (SINGLET)

QUASIPARTICLE PAIR SINGLET SCATTERING AMPLITUDE A ? CHARGE SECTOR RENORMALIZED BY Z ----> 0! SPIN SECTOR UNRENORMALIZED!

STRONGLY CORRELATED SUPERCONDUCTIVITY M. Capone, M. Fabrizio, C. Castellani, E. T., Science 296, 2364 (2002)]

FROM BCS TO STR. CORREL. SUPERC. l=2|Jeff|N(EF) <n> =4 BCS SCS MIT

HAN GUNNARSSON CRESPI (2003)

P(n)

U/W MOTT INSULATORS _ 2 “A3C60” METAL 1 2 3 4 n HALF FILLING M. Capone, M. Fabrizio, et al. in preparation, d=3,<n>=3

d =3 <n> =3 FULLERIDE MODEL PRELIM. DMFT RESULTS (CAPONE) AFI SC SC “U/W” 1.5 1.0 0.8 0.4 SC METAL SC MOTT INSULATOR (S=1/2)

DRUDE WEIGHT : SC STATE GAINS KINETIC ENERGY CAPONE et al, to be published 1 BAND MOTT 3 BAND METAL INS. METAL

CAPONE et al, to be published NORMAL STATE SUSCEPTIBILITY STONER 1 BAND (3 BANDS) EF EF

J. ROBERT et al. (1998)

WHY SUPERCONDUCTIVITY WILL ARISE NEAR LOW-SPIN MOTT INSULATOR PHASES 1. CLOSE TO MOTT, Z ----> 0, Q-P. BAND NARROWS 2. CLOSE TO MOTT, QUASIPARTICLES CEASE TO REPEL ONE ANOTHER (CHARGE FREEZING) 3. PAIRING ATTRACTION J<0 BETWEEN Q-P.'s IN SPIN CHANNEL UNAFFECTED BY MOTT 4. MAX PAIRING GAP AT STRONG CPL, WHEN -J= ZW 5. EXPECT MAX Tc ~ 5% |J| M. CAPONE, M. FABRIZIO, C. CASTELLANI, E. TOSATTI c SCIENCE 296, 2364 (2002); PRL 93, 047001 (2004).

ALKALI DOPED PHTHALOCYANINES: ARE THERE (STOICHIOMETRIC) MOTT INSULATORS? ARE THERE SUPERCONDUCTORS?

CAN ALSO BE MADE CONDUCTING BY ALKALI DOPING M. F. Craciun, S. Rogge, M. J. L. den Boer, T. M. Klapwijk, A. F. Morpurgo,cond-mat/0401036

MOLECULAR CONDUCTION IN d=2 DEGENERATE MODEL t ____ ____ ____ ____ ____ ____ ____ ____ U, J , E JT Capone, Fabrizio, Castellani, Tosatti, PRL 93, 047001 (2004)

HAMILTONIAN (deg. = 2) S=1, T=0 __ __ __ 0 U~ 1 eV Jeff ~ - 0.07 eV S=0, T=1, |Tz|=1 __ __ Jeff/2 W~ 0.3 eV S=0, T=1, Tz =0 __ Jeff Dynamical Mean Field Theory (nel=2)

U/W MOTT INSULATORS _ 1 “K2MPc” METAL 1 2 3 n HALF FILLING

DYNAMICAL MEAN FIELD THEORY ____ ____ t IMPURITY SOLVER = LANCZOS (M. CAPONE)

. U.F.P FULL DMFT PHASE DIAGRAM M. CAPONE et al, PRL 93, 047001 (2004);cond-mat/0401090

DOPED MOTT- JAHN TELLER” INSULATOR: AN ON-SITE RVB F F F 1 _ 2 _ _ 3 _ _ _ t12

The Pseudogap Phase “NORMAL METAL” PHASE NEAR MOTT INSULATOR HAS PSEUDOGAP

From Normal Superconductivity to SCS • Large Uncompensated Attractive J (or E JT ): usual Migdal- Eliashberg reduction of Tc • Small , Compensated Attractive J: SCS - Tc enhanced by U Capone, Fabrizio, Castellani, Tosatti, PRL 93, 047001 (2004) • (see also J.E. Han, PRB 70, 054513 (2004))

Drude Weight Gain in the Superconducting Phase

Two Energy Scales T+ : high energy “band dispersion” T- : low energy q.p. weight minus plus Obtained by fitting form FABRIZIO et al, PRL 91, 246402 (2003); PRB (2004)

K3C60 T+ GOLDONI et al, 2005

PSEUDOGAP STATE IN FULLERIDES? 1) NO VISIBLE KONDO RESONANCE, POOR ELECTRONIC SPEC HEAT 2) VERY HIGH H_c2 AS IN CUPRATES (BUNTAR 1996). NERNST EFFECT? 3) OPTICAL ABS. SHOULD CONFIRM KINETIC ENERGY GAIN IN SC STATE 4) ARPES: PSEUDOGAP? (BUT: VIBRONIC EFFECTS)

CONCLUSIONS STRONGLY CORREL. SUPERCONDUCTIVITY SHOULD BE UBIQUITOUS IN MOLECULAR CONDUCTORS NEAR MOTT JAHN TELLER INSULATOR PHASE s-WAVE, PHONON DRIVEN, YET RELATED TO HIGH-Tc IN CUPRATES (ON SITE RVB) PROB. REALIZED IN ALKALI FULLERIDES. NOVEL REALIZATIONS MAY BE POSSIBLE IN ELECTR. DOPED M-PHTHALOCYANINES, PRESSURIZED HOLE DOPED C60, ....