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

1. Thermoelectrics in strongly-correlated metals:Towards the nano-scale energy conversion in self-organized systems Ichiro Terasaki Department of Applied Physics, Waseda UniversityTokyo

2. 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

3. 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

4. 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

5. 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.

6. Intermediate between metal and insulator We need large themopower like an insulator and low resistivity like a metal

7. Layered cobalt oxide NaxCoO2

8. 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) Thermal conductivity:(Data are scattered from sample to sample) In-plane 40 mW/cmK at 300 K (Satake: JAP 96 (2004) 931) STEP

9. ZT of the layered Co oxides

10. The Boltzmann equation for electrons Electric current density (particle flow) Temperature gradient Thermal current density (Heat flow) Electric field（= E）

11. Physical meaning of thermopower Entropy current density Electric current density Thermopower is the ratio of the entropy current to the electric current, i.e. Entropy per carrier.

12. eg t2g Co4+ Co3+ Co3+ Co3+ Co3+ Co3+ Co3+ eg t2g Origin of large thermopower Degeneracy 6Entropy kBln6 Degeneracy 1Entropy 0 NaxCoO2 x~0.5 Co3+:Co4+=1:1 Charge of e flows with an entropy of kBln6 Koshibae et al.PRB 62(2000)6869

13. 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.

14. CuRh1-yMgyO2 STEP eSTEP Shibasaki, Kobayashi, IT

15. 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

16. Electronic Phase Separation cond-mat/0011293 Phys. Rev. B61 (2000) 15515

17. Self-organization of carrier and spin Bi-stripe order in Mn oxides Stripe order in high-Tc Cu oxides

18. Co4+ Co3+ Co3+ Co3+ 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. • The large thermopower from Co4+ should be in principle effective at nano scale