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 A = K, Rb, (Cs) A4C60

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

• M. F. Craciun, S. Rogge, M. J. L. den Boer, T. M. Klapwijk, A. F.

Morpurgo,cond-mat/0401036 CAN ALSO BE MADE CONDUCTING BY ALKALI DOPING

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

MgPc a- PHASE W = 0.3 eV!

• E. Tosatti et al., PRL 93, 117002 (2004)

HOMO LUMO EF DFT CALCULATED NARROW BANDS OF ALKALI DOPED PHTHALOCYANINES

• M. F. Craciun, S. Rogge, M. J. L. den Boer, T. M. Klapwijk, A. F. Morpurgo,cond-

mat/0401036 ~2 ~4

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

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

Dubitskii DURAND et al (2003) U/W Tc

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

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

MOLECULAR CONDUCTION IN

• ORB. DEGENERATE MODEL SYSTEM

___ ___ ___ t U, J , E JT ___ ___ ___ ___ ___ ___ ___ ___ ___ H = T + H + H Jeff = J - (3/4) EJT < 0! (BUT NEARLY 0) U Jeff

• Deg. d

<n>

HAMILTONIAN H = W ~ 0.5 eV 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 (d=3)

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

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

Jeff < 0: “MOTT- JAHN TELLER” INSULATOR

• M. FABRIZIO, E. T. , PRB 55, 13465 (1997)

_ _ _ _ _ _ F F F 1 2 3 H = (dFi/dt)^2 + cos(Fi - Fj )|tij tji |/U U > Ucrit : QUANTUM MELTING t12

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 Transition

• Coexistence of

Metallic e Insulating features

• Metallic Peak

(Kondo Resonance) at the Fermi level

• f width Z,

decreasing with U

• High-energy

U (ONE BAND MODEL) energy Z

<n> U/W 1 2 3 4 2 METAL MOTT INSULATORS HALF FILLING _ “A4C60”

• M. Capone, M. Fabrizio, C. Castellani, E. T.,

Science 296, 2364 (2002)] d=3,<n>=4

MOTT TRANSITION FOR d=3 BANDS AT <n>=4 (or 2)

• M. Capone, et al Science 296, 2364 (2002)]

METAL MOTT INSULATOR (SINGLET) QUASIPARTICLE WEIGHT Jeff /U = - 0.02

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)]

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

HAN GUNNARSSON CRESPI (2003)

P(n)

n U/W 1 2 3 4 2 METAL MOTT INSULATORS HALF FILLING _ “A3C60”

• M. Capone, M. Fabrizio, et al. in preparation,

d=3,<n>=3

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

• PRELIM. DMFT RESULTS (CAPONE)

SC

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

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

• 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|

c

• M. CAPONE, M. FABRIZIO, C. CASTELLANI, E. TOSATTI

SCIENCE 296, 2364 (2002); PRL 93, 047001 (2004).

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

• M. F. Craciun, S. Rogge, M. J. L. den Boer, T. M. Klapwijk, A. F.

Morpurgo,cond-mat/0401036 CAN ALSO BE MADE CONDUCTING BY ALKALI DOPING

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

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

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

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

U.F.P

• M. CAPONE et al, PRL 93, 047001 (2004);cond-mat/0401090

FULL DMFT PHASE DIAGRAM .

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 EJT): 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

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

K3C60 GOLDONI et al, 2005 T+

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, ....