Tailoring Matter on the Molecular Level: organic solids as models to - - PowerPoint PPT Presentation

Tailoring Matter on the Molecular Level:

• rganic solids as models to study physics in reduced dimensions

Martin Dressel

• 1. Physikalisches Institut der Universität Stuttgart, Germany

Outline

• 1. Organic Conductors

basics and development

• 2. Competing Interactions

charge order charge fluctuations, superconductivity

• 3. Electronic Correlations

localization Mott transition, charge dynamics

• 4. Outlook
• N. Drichko, M. Dumm,
• D. Faltermeier, S. Kaiser,
• Y. Sun, S. Yasin

Universität Stuttgart, Germany

• C. Meziere, P. Batail

CNRS, Universite d’Angers, France

• J. Schlueter

Argonne National Laboratory, U.S.A.

• R. Lyubovskaya

RUS, Chernogolovka, Russia

• J. Merino

Universidad Autonoma, Madrid, Spain

• R. McKenzie

UQ, Brisbane, Australia

• A. Greco

Rosario, Argentina

Organic Conductors

basics

Organic materials: 19 Mio. compounds containing carbon Aromatic rings: delocalized π-orbitals e.g. benzene . . .

naphthalene

Organic Conductors

basics

Organic solids are in general insulators because the bonds are saturated, the electronic bands are filled Requirements for electrical conductivity:

• overlap of orbitals:

band formation

• add or extract electrons:

partially filled bands

• electrical field effect
• charge transfer salts

Organic Conductors

charge transfer salts

TTF-TCNQ The structure consists of TTF and TCNQ stacks. TTF is a strong electron donor, TCNQ is an electron acceptor. Along the stacks the π-orbitals overlap leading to one-dimensional conductivity.

C

TCNQ Tetracyanoquinodimethane

C C N N C C C C C C C C C N N

S

Tetrathiofulvalene TTF

C C C C C C

S S S

Organic Conductors

charge transfer salts

(TMTTF)2PF6 The structure consists of TMTTF stacks as electron donors, separated by inorganic acceptors. Along the stacks the π-orbitals overlap leading to one-dimensional conductivity. a c

Tetrametyl-tetraselenafulvalene TMTSF

C C C C C C C C C C

Se Se Se Se

c b

Organic Conductors

crystal growth

Growth of single crystals by electro-crystallization from solution. typical size: 1 to 5 mm

(TMTSF)2PF6

5 mm

Organic Conductors

development

Ishiguro, Yamaji, Saito, 1998

Starting point: 1964 W.A. Little predicts excitonic superconductivity in organic polymer chains 1979 K. Bechgaard, D. Jerome 1 dim organic superconductor (TMTSF)2ClO4 1984 E.B. Yagubskii 2 dim organic superconductor (BEDT-TTF)2X

S

C

TCNQ Tetracyanoquinodimethane Tetrathiofulvalene TTF

C C N N C C C C C C C C C N N C C C C C C

S S S

1973 F. Wudl, A. Heeger 1dim organic conductor TTF-TCNQ

Tetrametyl-tetraselenafulvalene TMTSF

C C C C C C C C C C

Se Se Se Se

Bis(ethylene-dithio)tetrathiofulvalene BEDT-TTF

C C C C C C C C C C

S S S S S S S S

Organic Conductors

radical cation salts

Bis(ethylene-dithio)tetrathiofulvalene BEDT-TTF

C C C C C C C C C C

S S S S S S S S

b a c (BEDT-TTF)2X The structure consists of BEDT-TTF layers as electron donors, separated by sheets of inorganic acceptors. anisotropy within the plane σc / σa ~ 0.5 perpendicular to the plane σb / σa ~ 10000

Organic Conductors

radical cation salts

(BEDT-TTF)2X 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 band-filling depends on the stoichiometry.
• The on-site (U) and inter-site (V) Coulomb interactions

depend on the molecule Ueff = 0.5 eV strong influence of electron-electron correlations

Ordering Phenomena

low-dimensional systems

Ordering patterns in low-dimensional systems k-space phenomena: Fermi-surface instabilities: CDW, SDW real space phenomena: spin-Peierls, spin order, charge order, Wigner crystal Competing interactions: lattice degree of freedom charge degree of freedom spin degree of freedom

• rbital degree of freedom

electron-electron interaction electron-phonon interaction spin-phonon interaction spin-spin interaction … Localization, metal-insulator transition, antiferromagnetic ordering, …

Ordering Phenomena

low-dimensional systems

Charge order in two dimensions 1/4-filled systems

homogeneous charge distribution horizontal stripes vertical stripes diagonal stripes checker board homogeneous charge distribution charge order frustration charge order fluctuations 1/5 filling

Ordering Phenomena

low-dimensional systems

Charge order in two dimensions 1/4-filled systems

homogeneous charge distribution horizontal stripes vertical stripes diagonal stripes checker board homogeneous charge distribution charge order frustration charge order fluctuations 1/5 filling

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: 1 K ≤ T ≤ 300 K Magnetic field: Hydrostatic pressure: B ≤ 12 Tesla p < 7 GPa Absolute values of reflectivity by Au evaporation method. size of the surfaces: (0.5 – 1 mm)2 with IR microscope: (150 μm)2

Quasi-Two-Dimensional Organic Conductors

• ptical properties

Small in-plane anisotropy: reflectivity is higher in the direction of larger overlap. Deviations from a simple metallic behavior.

0,0 0,2 0,4 0,6 0,8 1,0 1000 2000 3000 4000 5000 6000 200 400 600

Conductivity (Ω

• 1cm
• 1)

Wavenumber (cm

• 1)

Reflectivity Rmax Rmin

α-(BEDT-TTF)2NH4Hg(SCN)4 T = 300 K

c a 8 ) (

2 1 p

d

I

ω ω ω σ

σ

= = ∫

∞

2 2 2

16 sin 2

p m

td e V π ρ

ω

⎧ ⎫ = ⎨ ⎬ ⎩ ⎭ h

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 is given by

• M. Dressel and N. Drichko, Chem. Rev. 104, 5689 (2004)
• N. Drichko et al., Phys. Rev. B 74, 235121 (2006)

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.

1350 1400 1450 1500 1550 ν27(B1u) ν3(Ag) ν6(Ag) ν2(Ag) Vibrational frequency (cm-1) 0.0 0.5 1.0 1.5 2.0 900 950 1000 Average charge per BEDT-TTF molecule (+e)

electrons on molecule ν2 = 1554.2 cm−1

ν3 (Ag)

Raman shift in α-(BEDT-TTF)2NH4Hg(SCN)4 three vibrational peaks indicates three different sites.

1350 1400 1450 1500 1550 1600

intensity (a.u.)

Raman shift (cm-1)

1462 1486 1510

horizontal stripes

Molecular Vibtrations

in BEDT-TTF salts

1350 1400 1450 1500 1550 ν27(B1u) ν3(Ag) ν6(Ag) ν2(Ag) Vibrational frequency (cm-1) 0.0 0.5 1.0 1.5 2.0 900 950 1000 Average charge per BEDT-TTF molecule (+e)

electrons on molecule

IR mode in β″-(BEDT-TTF)2SF5CH2CF2SO3 splitting below 150 K indicates charge order Δρ = 0.2e

1400 1420 1440 1460 1480 1500 20 40 60

004K 050K 100K 150K 200K 300K

σ(Ω−1cm-1)

Wavenumber (cm-1)

vertical stripes

The intra-molecular vibrations are a measure of the localized charge.

1

IR active molecular vibrations are intense

• nly for polarization E ⊥ conducting layers

ν27 (B1u)

• S. Kaiser et al., arXiv:0812.3732

Collective Modes

in charged ordered systems

Collective CO mode in β″-(BEDT-TTF)2SF5CH2CF2SO3 appears below 150 K.

The inter-molecular vibrations are lattice vibrations, which become IR active due to charge order: collective excitations.

• S. Kaiser et al., arXiv:0812.3732

Quasi-Two-Dimensional Organic Conductors

electronic correlations

• α-(BEDT-TTF)2X

2:1 stoichiometry: insulator, metal, superconductor 1/4-filled system: hole carriers

• π/a

E k +π/a

• π/a

E k +π/a +π/2a

• π/2a
• κ-(BEDT-TTF)2X

2:1 stoichiometry, dimerized: metal, superconductor 1/2-filled upper band: hole carriers

Quasi-Two-Dimensional Organic Conductors

(BEDT-TTF)2X salts

Proposed Phase Diagrams ¼ filled compounds ½ filled compounds U / W Tuning parameters: electronic correlations (on-site U, inter-site V) _____________________________________ bandwidth W V / W

Metal-Insulator Transition

bandwidth control by anion substitution

Cl Br p What are the dynamical properties close to the metal-insulator transition? We investigated the temperature dependent

• ptical conductivity of

κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-x with x = 0%, 40%, 73%, 85%, and 90%. Changing size of the anions changes the

• verlap integral t : ‘chemical pressure’

κ-(BEDT-TTF)2Cu[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. κ-(BEDT-TTF)2Cu[N(CN)2]Br is metallic for T ≤ T* ≈ 50 K. Organic superconductor with maximum Tc = 12 K. in-plane dc resistivity

50 100 150 200 250 300 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 10 100 1000 10000 100000 20% Br 40% Br 70% Br 80% Br 85% Br 90% Br

ρ/ρ300K

T (K)

κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-x

• D. Faltermeier et al., Phys. Rev. B 76, 165113 (2007); M. Dumm et al. Phys. Rev B (2009)

Optical Properties

• f κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-x

Br content

Metal-Insulator Transition

in κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-x

When the temperature temperature rises 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.

500 1000 1500 100 200 300

50 K 20 K

Conductivity (Ω-1cm-1) Wave numbers (cm-1)

0% Br c axis

35 K

500 1000 1500 100 200 300 400 500 600 700

Wave numbers (cm-1) Conductivity (Ω-1cm-1)

90% Br 73% Br

T = 20 K c axis

0% Br

• M. Dumm et al., Phys. Rev. B (2009)

2000 4000 6000 100 200 300 400 500

T = 20 K

κ-(BEDT-TTF)2Cu[N(CN)2]Br0.85Cl0.15

σ1 (Ω-1cm-1)

Frequency (cm-1)

c axis

Intra-molecular vibrations:

ν4

emv coupling Electronic Excitations

2000 4000 6000 100 200 300 400 500

T = 20 K

κ-(BEDT-TTF)2Cu[N(CN)2]Br0.85Cl0.15

σ1 (Ω

• 1cm
• 1)

Frequency (cm

• 1)

c axis

Drude-Lorentz fit

Intra-dimer excitations Inter-dimer excitations

Optical Properties

different contributions

The optical conductivity contains different contributions which can be disentangled:

tA tA tA tA t2 t2 t2 t2 t1 tA tA tA tA

• M. Dressel, et al., Physica B (2008)

Optical Properties

itinerant charge carriers

1000 2000 3000 100 200 300 400 500

T = 20 K

κ-(BEDT-TTF)2Cu[N(CN)2]Br0.85Cl0.15

σ1 (Ω

• 1cm
• 1)

Frequency (cm

• 1)

c axis

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

t2 t2 t2 t2 t1 tA tA tA tA

U ≈ 0.3 eV t2 ≈ 0.03 eV

t2: nearest neighbor hopping amplitude t1 = 0.8t2: next-nearest neighbour hopping amplitude U:

• n-dimer Coulomb repulsion

† † † † † 2 1

( ) ( )

i j j i i j j i i i i i ij ij i i

H t c c c c t c c c c U n n c c

σ σ σ σ σ σ σ σ σ σ σ σ σ

μ

↑ ↓

= − + − + + −

∑ ∑ ∑ ∑

• M. Dressel, et al., Physica B (2008)

Metal-Insulator Transition

bandwidth control U/t

400

40 % Br

400 800

Conductivity (Ω

• 1cm
• 1)

20 K 50 K 90 K 150 K 300 K

E ⎢⎢c

90% Br

1000 2000 3000 4000 400

Wavenumber (cm

• 1)

0 % Br

Uon dimer

U U/2 W

hν σ(ν)

Metallic state

E

U/2

• U/2

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/2

E DOS

U 2W

hν σ(ν)

Insulating state

• gap of ΔMott = U-W
• broad band of width 2W centered around U
• M. Rozenberg, G. Kotliar and H. Kajueter, Phys. Rev. B 54, 8452 (1996); M. Dumm et al. Phys. Rev. B (2009)

Dynamics of Correlated Charge Carriers

• ptical conductivity

Temperature dependent optical conductivity

• J. Merino, M. Dumm, N. Drichko, M. Dressel, R. McKenzie, Phys. Rev. Lett. 100, 086404 (2008).

1000 2000 3000 200 400 600 800 1000

σ1 (Ω

• 1cm
• 1)

Frequency (cm

• 1)

c axis

1000 2000 3000 0.0 0.2 0.4 0.6

κ-(ET)2Cu[N(CN)2]Br0.73Cl0.27

Neff

5 K 20 K 50 K 90 K 150 K

ν(cm

• 1)

1000 2000 3000 200 400 600 800 1000

1000 2000 3000 0.0 0.2 0.4 0.6

50 K 62 K 72 K 102 K 132 K

σ1 (Ω

• 1cm
• 1)

Frequency (cm

• 1)

U = 0.3 eV U/t2 = 10

Neff

• Freq. (cm
• 1)

DMFT calculations for the Hubbard model

• ptical 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*

eff 1 2

2 ( ) ( )d

b

m N e

ω

ω σ ω ω π ′ ′ = Ω

∫

Ω = 3300 Å3 mb = 2.5 me

Dynamics of Correlated Charge Carriers

effective charge carrier number

Effective carrier number per BEDT-TTF dimer

1000 2000 3000 0.0 0.2 0.4 0.6 0.8 1.0 (BEDT-TTF)2- Cu[N(CN)2]BrxCl1-x

Neff

T = 20 K

x = 73 % x = 85 %

Frequency (cm

• 1)

c axis 1000 2000 3000 0.0 0.2 0.4 0.6 0.8 1.0

Frequency (cm

• 1)

Neff

U = 0.3 eV U = 0.36 eV U = 0.06 eV U = 0.24 eV

t2 = 0.03 eV

With increasing correlations U/t:

• spectral weight is transferred to higher frequencies
• effective charge-carrier number is supressed

eff 1 2

2 ( ) ( )d

b

m N e

ω

ω σ ω ω π Ω ′ ′ =

∫

2 eff 1 2 2 kin

2 ( ) ( )d D M N e d E

ω

ω σ ω ω π Ω ′ ′ = −

∫

h

• J. Merino, M. Dumm, N. Drichko, M. Dressel, R. McKenzie, Phys. Rev. Lett. 100, 086404 (2008).

Dynamics of Correlated Charge Carriers

frequency dependent scattering rate and mass

Extended Drude analysis

1000 2000 3000 1 2 3 (c)

x = 73 % x = 85 %

τ

• 1 (10

3cm

• 1)

κ-(BEDT-TTF)2-

Cu[N(CN)2]BrxCl1-x 1000 2000 3000 2 4 6 (d)

m* /mb Frequency (cm

• 1)

1 2 3 (a)

U/t2 = 10 U/t2 = 8 U/t2 = 7

τ

• 1 (10

3cm

• 1)

2 4 6

U = 0.3 eV

m*/mb

(b)

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:

( ) ( )

2 2

1 2

B

A k T π ω τ ⎡ ⎤ = + ⎣ ⎦ h

[ ] [ ]

2 2 2 2 1 2

*( ) ( ) ( ) ( )

b

m ne m m ω σ ω ω σ ω σ ω = +

[ ] [ ]

2 1 2 2 1 2

1 ( ) ( ) ( ) ( ) ne m σ ω τ ω σ ω σ ω = +

• J. Merino, M. Dumm, N. Drichko, M. Dressel, R. McKenzie, Phys. Rev. Lett. 100, 086404 (2008).

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(EF) is zero. Since the metal-insulator transition is first order, there is an abrupt jump with (Dc/D0) = 0.1 ... 0.3.

EF D(E) E D/D0 t/U (t/U)c Dc/D0 Mott insulator metal

0.0 0.5 1.0 50 100 20 40 60 Spectral Weight (10

4 Ω

• 1cm
• 1)

Br concentration (%) Relative Drude weight D/D0

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 xc ≈ 70%.

Summary: ½ Filling

κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-x The two-dimensional organic conductor κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-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
• n crossing the phase border

to the Mott insulator.

• D. Faltermeier et al., Phys. Rev. B 76, 165113 (2007); M. Dumm et al. Phys. Rev. B (2009)

Summary

two-dimensional organic conductors

unconventional metal unconventional metal SC SC

• rdered

state

temperature band filling electronic correlations

• In the half-filled compounds κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-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 1/2 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)