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


                  Ichiro Terasaki
             Department of Applied Physics,
                   Waseda University
                        Tokyo
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?

                           • Thermoelectrics
                             Conversion 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




    We need large themopower like an
    insulator and low resistivity like a metal
Layered cobalt oxide NaxCoO2
 Thermoelectric properties of NaxCoO2

                                Resistivity:
                                 In-plane 200 cm at 300 K
                                 Out-of-plane 8 mcm at 300 K



                                Themopower:
                                 In-plane 100 V/K at 300 K
                                 (I. T. : PRB56 (1997) R12685)
STEP




                                Thermal conductivity:
                                (Data are scattered from sample to
                                sample) In-plane 40 mW/cmK at
                                300 K
                                 (Satake: JAP 96 (2004) 931)
ZT of the layered Co oxides
The Boltzmann equation for electrons

Electric current density
    (particle flow)




 Thermal current density   Electric field   Temperature
      (Heat flow)             (= E)           gradient
Physical meaning of thermopower




  Entropy current                Electric current
      density                        density


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

             Degeneracy 6                      Degeneracy 1
             Entropy kBln6                     Entropy 0
NaxCoO2            eg                          eg
x~0.5
                   t2g                         t2g
Co3+:Co4+
=1:1
               Co3+      Co3+   Co3+   Co4+   Co3+   Co3+   Co3+


        Charge of e flows
        with an entropy of kBln6


                                                      Koshibae et al.
                                                      PRB 62(2000)6869
Layered rhodium oxide CuRhO 2

•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
STEP




               eSTEP


                Shibasaki, Kobayashi, IT
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
Electronic Phase Separation


       cond-mat/0011293




                              Phys. Rev. B61 (2000) 15515
Self-organization of carrier and spin




Stripe order in high-            Bi-stripe order in
Tc Cu oxides                     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
     doping
   – The mobility of CuRh2-xMgxO2 is
     independent of Mg content for
     x<0.2
• Each Co4+ (Rh4+) cite includes a
  large entropy kBlog6.
                                           Co3+   Co4+   Co3+   Co3+
   – The large thermopower from    Co4+
     should be in principle effective at
     nano scale