united nationseducational, scientific

and culturalorganization

theiinternational centre for theoretical physics

international atomicenergy agency

SMR.1320 - 13

SUMMER SCHOOLon

LOW-DIMENSIONAL QUANTUM SYSTEMS:Theory and Experiment

(16 - 27 JULY 2001)

PLUS

PRE-TUTORIAL SESSIONS(11 - 13 JULY 2001)

TRANSPORT AND DIMENSIONAL CROSSOVERIN QUASI-ONE DIMENSIONAL CONDUCTORS

T. GIAMARCHIUniversite de Paris XI (Paris-Sud)

Laboratoire de Physique des SolidesBatiment 510, Centre Universitaire

F-91405 Cedex OrsayFrance

These are preliminary lecture notes, intended only for distribution to participants

strada costiera, I I - 34014 trieste italy - tel. +39 04022401 I I fax +39 040224163 - sci_info@ictp.trieste.it - www.ictp.trieste.it

Transport and dimensionacrossover in quasi-one

ensional conductors

G. Gruner, L. De1

A. Schwarz, V. Vesc<

A. Georges, N. Sandier

S. Biermann, A. Lichtenste

.. Dressel

S8ffiS

• Organic Superconductors: quasi-onedimensional systems (Bechgaard salts)

• TMTTF and TMTSF molecules

• Remarquable properties :

• Non Fermi liquid behavior• Quantum Hall effect• Superconductivity and Frohlichconductivity

TMTSF2(X)

Propagation of electrons along the chains

Commensurate filling (1/4 filling)

kb3000^,300^,20^

High Energy (T,co): ID

Low Energy (T,co): 2D,3D

a

W 1

10

1 !>••

<TMTTP>2Br i TMTTFJ2PF61.

X

\

•* i * * * $

V. Vescoli et al.EuroPhysJB 13503 (2000)

,,-<J" **

102

T «K>

100 200 300 O

Temperature (K) O

Cb) 50 100 150 200 2S0 300

Temperature (K)

D. Jerome in "Organicsuperconductors", ed. J.P.Farges

Questions

• Are TMTSF strongly correlated systems ?

• What is the strength of interactions ?

• What causes the difference between TF and SF(weak vs strong dimerization ?) ?

• At what scale does the dimensional crossovertakes place ? tb renormalized by interactions (CBourbonnais). 300K vs 20 K !

Luttinger liquid

Spin charge separation

Fermion

Spinon Holon

No fermionic quasiparticlesPower law decay of correlation functions

+K.• •

Kp contains all information about interactions

Transport in a LL

TG PRB 44 2905 (91); Physica B 230 975 (97)

ff

I

D=2uK 2A

4nK-5

CO

• Mott insulator for _filling also !

• Power law in a(co)determines Kp

• Deviations from IDlaw gives Ec

Jo1 OX)

0

3000

2000

1000 -

X=PFfi (T=20K)

X=AsF6 (T=20K)

X=C104 (T=1OK)

(TMTSF)^EII a "

2 3co/co

10 10 10* 10

0.1

b"

0.01

(TMTSF),X

EII a "

X=PF6 (T=20K)

X=AsF(j (T=20K)

X=C10;| (T-10K)

10co/co

peak

A. Schwartz et al. PRB 58 1261(1998)

Frequency (cm")

f

f

Consequences

• Luttinger Liquid !

• Kp = 0.23 very strong interactions

• Dimerization not important (1/4 filled Mottinsulator) [confirmed in new non-dimerized compound]

• TF vs SF likely to be due to change ofinteractions (quantum critical point)

•Dimensional crossover at E=100K !

Puzzle from NMR

(TMTSF)2ClP = 1bar

10 20 30T(K)

/

: 2\. o

o o n c o

2 t 6 8 10 T£K1

40

F. Creuzet et al., J. Phys.Lett 45 L755 (84)

Non fermi liquidbelow Ec ?

100

1 i r

-•"i i i I i i i I i i r

(TMTTF)2PF6

10

0 4

P(GPa)

6

After D. Jerome

8

Dimensional Crossover

A. Georges, TG, N. Sandlers PRB 61 16393 (00)

d = oo + 1 (cDMFT)

Effective one dimensional theory

3

+

3+3

3

X

• Self consistent theory for

• Feedback of t± in S (a prioriimportant for deconfinement)

•Different from RPA

G(k, k±, icon) =7/7") — F —

• Difficult to solve the equationsanalytically

Transverse transport

2a -1

a u0.6

ropt

100

80

60

£Q

CL 40

20 -

0 .-

0 50 100 150 200 250 300 350 400

T(K)

J. Moser et al. Euro Phys.J.B 139 (1998)

2000

K'OC

10

0.1

Ejf/b1

= E//cvalue a: 10 K

dc vaUe al '00 Ki i

10" icr icrFrequency {cm""}

• 1 0 K

• 100 K• 200 K•3OTK

A I TL-m^era".jrc-s (10-3C0 <)

V. Vescoli et al. Euro Phys J B 11365 (1999)

Numerical Solution

S. Biermann, A. Georges, A. Liehtenstein, TG

Hubbard Model

QMC (16-32 sites)

32 time slices (T/W = 1/50)

ncommensurate case

FLT

LLT

0.02 0.03 J_W

0.04

FIG. 2: Effective Kp vs. temperature in the doped case (fillingn ~ 0.8) for U/W = 1.0, i±/W = 0.14.

T

T

n

1-0

Commensurate case

MI , FL

TABLE 11: Effective Kp at half-iilling, as a function of t±/Wfor l'/W = 0.G5 and T/\Y = 1/10.

l_/W 0,00 0.04 0.07 0.11 0.14 0.16 0.18Ko 0.00 0.02 1.01 1.09 1.07 1.06 1.

to

o

ooCDCO

CD

COcCO

o

Fermi Surface

t

0.5 A 1.0-1.0

Z k_/n 0.28 0.38 0.50 0.62 0.77Z(k±) 0.78 0.77 0.76 0.77 0.79

Conclusions

Transport proves LL nature of high enery phase

• K=0.23, _ filled Mott insulators

• Ec = 100K much higher than expected

• Nature of the 2D phase ? 2D non Fermi liquid ?

• cDMFT Good method to tackle the dimensionalcrossover

_ Filling with cDMFT

Other physical quantities : Hall effect

Ordered phases (superconductivity)