chap9 - Chapter 9: Electronic Transport Onsager April 23,...

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Unformatted text preview: Chapter 9: Electronic Transport Onsager April 23, 2001 Contents 1 Quasiparticle Propagation 2 1.1 Quasiparticle Equation of Motion and Effective Mass . . . . . . . . . 5 2 Currents in Bands 8 2.1 Current in an Insulator . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Currents in a Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Scattering of Electrons in Bands 13 4 The Boltzmann Equation 18 4.1 Relaxation Time Approximation . . . . . . . . . . . . . . . . . . . . . 21 4.2 Linear Boltzmann Equation . . . . . . . . . . . . . . . . . . . . . . . 22 5 Conductivity of Metals 24 5.1 Drude Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.2 Conductivity Using the Linear Boltzmann Equation . . . . . . . . . . 25 6 Thermoelectric Effects 30 6.1 Linearized Boltzmann Equation . . . . . . . . . . . . . . . . . . . . . 31 1 6.2 Electric Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 6.3 Thermal and Energy Currents . . . . . . . . . . . . . . . . . . . . . . 34 6.4 Seebeck Effect, Thermocouples . . . . . . . . . . . . . . . . . . . . . 39 6.5 Peltier Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 7 The Wiedemann-Franz Law (for good metals) 42 2 As we have seen, transport in insulators (of heat mostly) is dominated by phonons. The thermal conductivity of some insulators can be quite large (cf. diamond). However most insulators have small and uninteresting transport properties. Metals, on the other hand, with transport dominated by elec- trons generally conduct both heat and charge quite well. In addition the ability to conduct thermal, charge, and entropy currents leads to interesting phenomena such as thermoelectric effects. 1 Quasiparticle Propagation In order to understand the transport of metals, we must un- derstand how the metallic state propagates electrons: ie., we must know the electronic dispersion ( k ). The dispersion is ob- tained from band structure E ( k ) = h ( k ) in which the metal is approximated as an almost free gas of electrons interacting weakly with a lattice potential V ( r ), but not with each other. 3 e f8e5 V V(r) Figure 1: The dispersion is obtained from band structure E ( k ) = h ( k ) in which the metal is approximated as an almost free gas of electrons interacting weakly with a lattice potential V ( r ) , but not with each other. The Bloch states of this system k ( r ) = U k ( r ) e i k r , U k ( r ) = U k ( r + r n ) (1) may be approximated as plane waves U k ( r ) = U k . Then, the state describing a single quasiparticle may be expanded. ( x, t ) = 1 2 Z - d k U ( k ) e i ( k x- ( k ) t ) (2) If U ( k ) = c ( k- k ) then ( x, t ) e i ( k x- t ) and the quasi- particle is delocalized. On the other hand, if U ( k ) = constant then ( x, t ) ( x ) and the quasiparticle is perfectly localized....
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This note was uploaded on 01/10/2012 for the course PHYSICS 707 taught by Professor Electrodynamics during the Fall '11 term at LSU.

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chap9 - Chapter 9: Electronic Transport Onsager April 23,...

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