THE SEEBECK COEFFICIENT Anthony Rice MTRL 286K 12/15/14

Outline The Seebeck coefficient is a property dependent on the electronic structure near the fermi-level and is sensitive to things including effective mass, carrier concentration, and band shape Seebeck measurements may be used to further elucidate basic electronic properties through a transition NaCo 2 O 4 is a high-Seebeck metal, with possible explanations including configurational entropy and peculiar band shape

“Power Factor” The Seebeck Effect A. Shakouri. Annu. Rev. Mater. Res :399–431 -Direct E g, Parabolic bands J. Solyom. Fundamentals of the Physics of Solids

Typical Metallic Values Sign determines whether dominant conduction occurs below or above fermi level J. Solyom. Fundamentals of the Physics of Solids

“Mott Formula” τ-carrier lifetime v-group velocity ε-band dispersion For a Metal/degenerate-semiconductor: Generalized For a Semiconductor: A- material dependent constant H. Fritzsche,Solid State Commun.9, 1813 (1971) J. Solyom. Fundamentals of the Physics of Solids M. Cutler, N.F. Mott. Phys. Rev. 181, 1336 (1969)

Pisarenko Plots B. Jalan, S. Stemmer. Appl. Phys. Lett. 97, (2010)

PbTe:Tl J.P. Heremans. V. Jovovic. E.S. Toberer. A. Saramat. K. Kurosaki. A. Charoenphakdee. S. Yamanak, G.J. Snyder. Science 25 July 2008: Vol. 321 no pp Solid line-calculated/published to date Dots-Current study

V 1-X W x O 2 : T MI vs. T s T. Katase, K. Endo, and H. Ohta. Phys. Rev. B 90, (R) (2014)

V 1-X W x O 2 :Parabolic Bands? T. Katase, K. Endo, and H. Ohta. Phys. Rev. B 90, (R) (2014)

Magnetite at the Verwey Transition -Provides a probe of carrier type without B-field Oxidation varied-A least oxidized, E most Above ~120K-independent of oxidation A.J.M. Kuipers and V.A. Brabers. Phys. Rev. B. 14, 1401 (1976)

Thermopower in the Correlated Hoping Regime Seebeck governed by entropy change due to addition of one more carrier in cases of interacting carriers at high temperatures P.M. Chaikin, G. Beni. Phys. Rev. B. 13, 647 (1975) “Heikes formula”

NaCo 2 O 4 I. Terasaki, Y. Sasago and K. Uchinokura. Phys. Rev. B 56, R (1997) Na/CoO 2 Layered Structure At stoichiometry, Co valence +3.5

Initial explanation- Hopping due to degeneracy Degeneracy, plus 3d correlation effects causes large S W. Koshibae, K. Tsutsui, S. Maekawa. Phys. Rev. B. 62, 6869 (2000) g 3, g 4.-# of configurations for each valence x-ratio of 3+/4+ states (depends on x na )

ARPES Results M. Z. Hasan et at. Phys. Rev. Lett. 92, (2004) D.J. Singh. Phys. Rev. B (2000) H.-B. Yang et al. Phys. Rev. Lett. 92, (2004) Missing crossings near K point Na 0.7 CoO 2 Na 0.6 CoO 2

“Pudding mold” Bands K. Kuroki, R. Arita. J. Phys. Soc. Jpn. 76, (2007)

Fe(As 1-x Se x ) 2 H. Usui, K. Suzuki, K. Kuroki, S. Nakano, K. Kudo, M. Nohara. Phys. Rev. B. 88, (2013) Pnnm (no. 58)

Summary The Seebeck coefficient provides useful information beyond resistivity for basic electronic studies Metal-insulator studies may be further enhanced by using thermopower measurements A number of materials with unique band-structure may be potential candidates for further thermoelectric study

CuAlO 2 -Proposed Hole-doped TE K. Mori, H. Sakakibara, H. Usui, K. Kuroki. Phys. Rev. B. 88, (2013)