Organic Conductors and Superconductors: signatures of electronic correlations Martin Dressel 1. Physikalisches Institut der Universität Stuttgart

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2 Organic Conductors and Superconductors: signatures of electronic correlations Martin Dressel 1. Physikalisches Institut der Universität 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 κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br x Cl 1-x 4. Outlook M. Dumm, N. Drichko, D. Faltermeier 1. Physikalisches Institut Universität Stuttgart C. Meziere, P. Batail CNRS, Universite d Angers, France J. Merino Universidad Autonoma, Madrid, Spain R. McKenzie UQ, Brisbane, Australia

3 (BEDT-TTF) 2 X Organic Conductors radical cation salts The structure consists of BEDT-TTF layers as electron donors, separated by sheets of inorganic acceptors. Bis(ethylene-dithio)tetrathiofulvalene S S S S C C C C C C C C C C S S S S BEDT-TTF b a anisotropy within the plane σ c / σ a ~.5 perpendicular to the plane σ b / σ a ~ 1 c

4 (BEDT-TTF) 2 X Organic Conductors radical cation salts The layered arrangement of the organic molecules, separated by anions, leads to a two-dimensional electronic system. Thebandwidth 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 =.5 ev strong influence of electron-electron correlations

5 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. The spectral weight is defined as 2 ω p I = σ 1( ω) dω 8 = σ where the plasma frequency is given by ω td e π = sin p ρ hv 2 m The width of the conductance band is typically.8-1 ev (overlap integrals t about.1 ev). This is comparable to Coulomb interaction U. Conductivity (Ω -1 cm -1 ) Reflectivity 1,,8,6,4,2, R min c R max α-(bedt-ttf) 2 NH 4 Hg(SCN) 4 T = 3 K Wavenumber (cm -1 ) a

6 Molecular Vibtrations in BEDT-TTF salts The intra-molecular vibrations are a measure of the localized charge ν 2 (A g ) ν 2 = cm 1 ν 3 = cm 1 ν 3 (A) ν 4 (A) Vibrational frequency (cm -1 ) ν 3 (A g ) ν 27 (B 1u ) ν 6 (A g ) Average charge per BEDT-TTF molecule (+e) The phonon frequency shifts down when electrons are taken off. electrons on molecule 1 ν 27 (B 1u ) IR active molecular vibrations are intense only for polarization E conducting layers M. Dressel and N. Drichko, Chemical Reviews 14, 5689 (24)

7 Electron-Molecular Vibtrational Coupling theory The totally symmetric intra-molecular vibrations become infrared active by coupling to the localized charge: electron-molecular vibrational (emv) coupled phonons. Conductivity emv-coupled feature charge transfer band 12 cm -1 ~3 cm -1 Frequency ν 3 = cm 1 symmetry break (dimerization) charge transfer within the molecules change of the molecular geometry due to charge modulation on the HOMO

8 Electron-Molecular Vibtrational Coupling experimental evidence slightly dimerized system strongly dimerized system 1. q b1 Reflectivity R min R max c b1 p p q b2.2 a Conductivity (cm -1 ) α-(bedt-ttf) 2 NH 4 Hg(SCN) 4 T = 3 K Conductivity (Ω -1 cm -1 ) 4 2 κ-(bedt-ttf) 2 Cu(N(CN) 2 )Br.85 Cl.15 T=2 K E//c Experimental data Dimer model with emv coupling itinerant electrons Wavenumber (cm -1 ) Wavenumber (cm -1 )

9 Quasi-Two-Dimensional Organic Conductors electronic correlations α-(bedt-ttf) 2 X 2:1 stoichiometry: insulator, metal, superconductor 1/4-filled system: hole carriers E -π/a +π/a k κ-(bedt-ttf) 2 X 2:1 stoichiometry, dimerized: metal, superconductor 1/2-filled upper band: hole carriers E -π/a -π/2a +π/2a +π/a k

10 Quasi-Two-Dimensional Organic Conductors (BEDT-TTF) 2 X salts ¼ filled compounds Proposed Phase Diagrams ½ filled compounds V / W U / W Tuning parameters: electronic correlations (on-site U, inter-site V) bandwidth W

11 Half-Filled System strongly dimerized κ-phase salts The organic molecules are arranged in pairs (dimers). The conduction band is split. (a) q p b1 (b) E c b1 b2 t 1 p q t 1 a k -π/a -π/2a +π/2a +π/a Interband transitions intraband transitions or intradimer transitions (localized) interdimer transitions (itinerant)

12 Half-Filled System localized carriers The localized carriers on the dimer: (a) (b) charge transfer between the molecules activates intramolecular vibrations of BEDT-TTF molecules q b1 p c b1 b2 t 1 p q t 1 the charge transfer and the intra-moleuclar vibrations are described by cluster model a 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, (27) Conductivity (Ω -1 cm -1 ) 4 2 κ-(bedt-ttf) 2 Cu[N(CN) 2 Br.85 Cl.15 T = 2 K) E//c Wavenumber (cm -1 ) experimental data itinerant electrons dimer model with emv coupling

13 Half-Filled System itinerant carriers The itinerant carriers can be described by the Hubbard model on a frustrated square lattice: H = t ( c c + c c ) t ( c c + c c ) 2 iσ jσ jσ iσ 1 iσ jσ jσ iσ ij σ ij σ + U n n μ c c i i i iσ iσ iσ t 1 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. Conductivity (Ω -1 cm -1 ) 4 2 t 1 =.8 κ-(bedt-ttf) 2 Cu[N(CN) 2 Br.85 Cl.15 T = 2 K) E//c Wavenumber (cm -1 ) experimental data itinerant electrons dimer model with emv coupling

14 What are the dynamical properties close to the metal-insulator transition? Metal-Insulator Transition bandwidth control by anion substitution We investigated the temperature dependent optical conductivity of κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br x Cl 1-x with x = %, 4%, 73%, 85%, and 9%. Changing size of the anions changes the overlap integral t : chemical pressure κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Cl is a semiconductor at room temperature which becomes a Mott insulator below 1 K. At low temperature it orders magnetically, under slight pressure it superconducts. κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br is metallic for T T* 5 K. Organic superconductor with maximum T c = 12 K. ρ/ρ 3K E-3 1E-4 1E-5 Cl Br p in-plane dc resistivity κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br x Cl 1-x 2% Br 4% Br 7% Br 8% Br 85% Br 9% Br 1E T (K)

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16 Metal-Insulator Transition in κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br x Cl 1-x When the temperature rises, the gap shifts to lower frequencies, like a mean-field behavior. Conductivity (Ω -1 cm -1 ) % Br c axis 5 K 35 K 2 K Wave numbers (cm -1 ) When Br content increases, i.e. U/t decreases, spectral weight starts to fill the gap, finally a Drude-like component develops. Conductivity (Ω -1 cm -1 ) % Br T = 2 K c axis 73% Br 1 % Br Wave numbers (cm -1 )

17 Optical Properties different contributions The optical conductivity contains different contributions which can be disentangled: Intra-molecular vibrations: σ 1 (Ω -1 cm -1 ) κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br.85 Cl.15 c axis T = 2 K Drude-Lorentz fit ν 4 emv coupling Frequency (cm -1 ) Electronic Excitations Intra-dimer excitations Inter-dimer excitations t A t A t 1 t A t A σ 1 (Ω -1 cm -1 ) κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br.85 Cl.15 4 c axis 3 T = 2 K Frequency (cm -1 )

18 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 σ 1 (Ω -1 cm -1 ) κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br.85 Cl.15 c axis T = 2 K Hubbard model on frustrated square lattice : nearest neighbor hopping amplitude t 1 =.8 : next-nearest neighbour hopping amplitude U: on-dimer Coulomb repulsion U.3 ev.3 ev t A Frequency (cm -1 ) H = t ( c c + c c ) t ( c c + c c ) + U n n μ c c 2 iσ jσ jσ iσ 1 iσ jσ jσ iσ i i iσ iσ ij σ ij σ i iσ t A t 1 t A t A

19 Metallic state DOS W σ(ν) Metal-Insulator Transition bandwidth control U/t U U/2 -U/2 U/2 E hν Drude-like feature due to the coherent quasiparticles (Fermi liquid) band of width W centered around U/2 W broad band at U of width 2W. Insulating state DOS U-W W -U/2 U/2 E gap of Δ Mott = U-W σ(ν) 2W U hν Conductivity (Ω -1 cm -1 ) broad band of width 2W centered around U % Br 4 % Br % Br E c 2 K 5 K 9 K 15 K 3 K Wavenumber (cm -1 ) M. Rozenberg, G. Kotliar and H. Kajueter, Phys. Rev. B 54, 8452 (1996) U on dimer

20 Dynamics of Correlated Charge Carriers optical conductivity Temperature dependent optical conductivity DMFT calculations for the Hubbard model optical conductivity of correlated charge carriers for E c σ 1 (Ω -1 cm -1 ) U =.3 ev U/ = 1 N eff K 62 K.2 72 K 12 K 132 K Freq. (cm -1 ) σ 1 (Ω -1 cm -1 ) κ-(et) 2 Cu[N(CN) 2 ]Br.73 Cl.27.4 c axis 5 K 2 K.2 5 K 9 K 15 K ν(cm -1 ) N eff Frequency (cm -1 ) Number of holes per dimer ω m b 2 eff 2 1 e π Band at U/2 suppressed in experimental data Gradual destruction of quasiparticles above T* N Frequency (cm -1 ) ( ω) =Ω σ ( ω )dω Ω = 33 Å 3 m b = 2.5 m e J. Merino, M. Dumm, N. Drichko, M. Dressel, R. McKenzie, Phys. Rev. Lett. 1, 8644 (28).

21 Dynamics of Correlated Charge Carriers effective charge carrier number Effective carrier number per BEDT-TTF dimer N =.3 ev 2 ω 2D Ωh M ( ω) = σ ( ω )dω π ed E eff kin N eff U =.6 ev U =.24 ev U =.3 ev U =.36 ev Frequency (cm -1 ) N ω 2 Ωm eff = b 2 1 π e ( ω) σ ( ω )dω (BEDT-TTF) 2 - Cu[N(CN) 2 ]Br x Cl 1-x T = 2 K c axis x = 73 % x = 85 % Frequency (cm -1 ) Neff 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. 1, 8644 (28).

22 Extended Drude analysis Dynamics of Correlated Charge Carriers frequency dependent scattering rate and mass 2 1 ne σ1( ω) = τω ( ) m σ1( ω) + σ2( ω) from DMFT calculations [ ] [ ] 2 2 τ -1 (1 3 cm -1 ) τ -1 (1 3 cm -1 ) 3 (a) U/t2 = 1 m 2 *( ω ) ne 2( ) = σ ω 2 2 mb mω [ σ1( ω) ] + [ σ2( ω) ] U =.3 ev 6 The scattering rate indicates a Fermi-liquid behavior: = A ( 2πkBT) ( ω) τ + h The prefactor A becomes larger as the metalinsulator transition is approached, because correlations increase. (Kadowaki-Woods-plot) from experiments (c) κ-(bedt-ttf) 2 - x = 73 % Cu[N(CN) x = 85 % 2 ]Br x Cl 1-x (b) (d) Frequency (cm -1 ) U/ = 8 U/ = m*/m b m* /m b When approaching the metal-insulator transition from the metallic side, the effective mass increases, because correlations increase. (Brinkman-Rice) J. Merino, M. Dumm, N. Drichko, M. Dressel, R. McKenzie, Phys. Rev. Lett. 1, 8644 (28).

23 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 ) = D(E) D/D D c /D E F E For large x > 7% we find a dramatic increase of the spectral weight as the temperature is reduced below T* = 5 K. This clearly separates the Mott insulating from the metallic state at x c 7%. Spectral Weight (1 4 Ω -1 cm -1 ) (t/u) c Mott insulator metal Br concentration (%) t/u Relative Drude weight D/D

24 Summary: ½ Filling κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br x Cl 1-x The two-dimensional organic conductor κ-(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 9 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, (27)

25 Coherent Response for Different Filling of BEDT-TTF-based conductors Overlap integrals: Reflectivity T=3 K /2-filled 1/4-filled 1/5-filled t =.1 ev for 1/2-filled t =.7 ev for 1/4-filled t =.7 ev for 1/5 filled Reflectivity 1..5 T=5 K 1/2-filled 1/4-filled 1/5-filled Conductivity (Ω -1 cm -1 ) Wavenumber (cm -1 ) Conductivity (Ω -1 cm -1 ) Wavenumber (cm -1 )

26 Spectral Weight of the coherent carriers response 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 Overlap integrals: t =.1 ev for 1/2-filled t =.7 ev for 1/4-filled t =.7 ev for 1/5 filled. Bandfilling /5-filled 1/4-filled /2-filled.2 1. Temperature (K) Drude-part of the spectral weight Drichko et al., Physica C , 125 (27)

27 Summary two-dimensional organic conductors In the half-filled compounds κ-(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. temperature Dressel and Drichko, Chem. Rev. 14, 5689 (24) electronic correlations unconventional metal SC ordered state unconventional metal SC band filling

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