Thermoelectrics in strongly-correlated metals:Towards the nano-scale energy conversion in self-organized systems

Ichiro TerasakiDepartment of Applied Physics,

Waseda UniversityTokyo

Outline

• Brief introduction to thermoelectrics

• Layered cobalt oxide NaxCoO2

– Large thermopower due to large entropy at lattice sites

• Layered rhodium oxide CuRhO2

– Self-organization of doped carriers

• Towards the nano-scale energy conversion

What is Thermoelectrics?

• ThermoelectricsConversion between heat

and electricity via ther-moelectric phenomena

• Thermoelectric Devices– long life,no maintenance

– no waste matter

– power from waste heat

• A key to Energy and Ecological issues

Thermoelectric Material

• Thermoelectric figure of merit Z

Z = STEP2 / ZT >1 is a goal

• high thermo(electric)power STEP large voltage

• low resistivity low internal resistance

• low thermal conductivity large T

Strongly correlated system

• A strongly correlated electron system is a system in which each electron moves with the other electrons in a correlated way owing to strong electron-electron Coulomb repulsion.

• Electrons are nearly localized, and show intermediate properties between metal and insulator.

• Typical examples are conducting transition-metal oxides.

Intermediate between metal and insulator

Metal Mott insulatorElectric ConductionHeat ConductionThermoelectric EffectsSpecific HeatMagnetismPressure EffectsOptical Properties

goodgoodsmallsmallnonmagneticsmallluster

insulatingmostly badlargelargemagnetic

?transparent

We need large themopower like an insulator and low resistivity like a metal

Layered cobalt oxide NaxCoO2

O

Co

O

Co

Co

a

a

c

Thermoelectric properties of NaxCoO2

Resistivity: In-plane 200 cm at 300 K Out-of-plane 8 mcm at 300 K

Themopower: In-plane 100 V/K at 300 K

(I. T. : PRB56 (1997) R12685)

Thermal conductivity:(Data are scattered from sample to sample) In-plane 40 mW/cmK at 300 K

(Satake: JAP 96 (2004) 931)

S TE

P

ZT of the layered Co oxides

The Boltzmann equation for electrons

TVST

TSV

Q

TEP

TEP

j

j

Electric field（ = E）

Temperature gradient

Electric current density(particle flow)

Thermal current density(Heat flow)

Physical meaning of thermopower

.

or ,

Then .0 Suppose

TEP

TEP

jST

j

jTSj

dxdT

Q

Q

Entropy current density

Electric current density

Thermopower is the ratio of the entropy current to the electric current, i.e. Entropy per carrier.

Co3+ Co3+ Co3+Co3+Co3+ Co4+ Co3+

t2g

eg

t2g

eg

Degeneracy 6Entropy kBln6

Charge of e flows with an entropy of kBln6

Degeneracy 1Entropy 0

Origin of large thermopower

K/V1501

6ln

||TEP e

kS B Koshibae et al.

PRB 62(2000)6869

NaxCoO2

x~0.5

Co3+:Co4+

=1:1

Layered rhodium oxide CuRhO2

•Rh is located below Co in the periodic table

•CuRhO2 has the hexagonal RhO2 layer that is isomorphic to the hexagonal CoO2 layer in NaxCoO2

•Kuriyama et al. found that the substitution of Mg for Rh supplies carries.

CuRh1-yMgyO2

Shibasaki, Kobayashi, IT

S TE

P

eST

EP

Doping-independent thermopower

• The thermopower S is roughly written as

• If the thermopower is independent of carrier concentration, then we get

• This implies /n=0, and the compressibility of the electron system diverges a sign for phase separation

TeNe

S

j

TjS Q

1/

TEP

01 2

TEP

Tnen

S

Electronic Phase Separation

Phys. Rev. B61 (2000) 15515

cond-mat/0011293

nV

1

Self-organization of carrier and spin

Stripe order in high-Tc Cu oxides

Bi-stripe order in Mn oxides

Towards nano-scale energy conversion

• Strongly correlated systems are at the verge of electronic phase separation (nano-scale self-organization of carriers)– This is a nature-made modulation d

oping– The mobility of CuRh2-xMgxO2 is in

dependent of Mg content for x<0.2

• Each Co4+ (Rh4+) cite includes a large entropy kBlog6. – The large thermopower from Co4+ s

hould be in principle effective at nano scale

Co3+Co3+Co3+ Co4+