What is thermoelectricity?

I noticed I'd never written up anything about thermoelectricity, and while the wikipedia entry is rather good, it couldn't hurt to have another take on the concept.   Thermoelectricity is the mutual interaction of the flow of heat and the flow of charge - this includes creating a voltage gradient by applying a temperature gradient (the Seebeck Effect) and driving a heating or cooling thermal flow by pushing an electrical current (the Peltier Effect).  Recently there have been new generalizations, like using a temperature gradient to drive a net accumulation of electronic spin (the spin Seebeck effect).

First, the basic physics.  To grossly oversimplify, all other things being equal, particles tend to diffuse from hot locations to cold locations.  (This is not entirely obvious in generality, at least not to me, from our definitions of temperature or chemical potential, and clearly in some situations there are still research questions about this.  There is certainly a hand-waving argument that hotter particles, be they molecules in a gas or electrons in a solid, tend to have higher kinetic energies, and therefore tend to diffuse more rapidly.  That's basically the argument made here.)

Let's take a bar of a conductor and force there to be a temperature gradient across it.  The mobile charge carriers will tend to diffuse away from the hot end.  Moreover, there will be a net flux of lattice vibrations (phonons) away from the hot end.  Those phonons can also tend to scatter charge carriers - an effect called phonon drag.   For an isolated bar, though, there can't be any net current, so a voltage gradient develops such that the drift current balances out the diffusion tendency.  This is the Seebeck effect, and the Seebeck coefficient is the constant of proportionality between the temperature gradient and the voltage gradient.   If you hook up two materials with different (known) Seebeck coefficients as shown, you make a thermocouple and can use the thermoelectric voltage generated as thermometer.

Ignoring the phonon drag bit, the Seebeck coefficient depends on particular material properties - the sign of the charge carriers (thermoelectric measurements are one way to tell if your system is conducting via electrons or holes, leading to some dramatic effects in quantum dots), and the energy dependence of their conductivity (which has wrapped up in it the band structure of the material and extrinsic factors like the mean free path for scattering off impurities and boundaries).

Because of this dependence on extrinsic factors, it is possible to manipulate the Seebeck coefficient through nanoscale structuring or alteration of materials.  Using boundary scattering as a tuning parameter for the mean free path is enough to let you make thermocouples just by controlling the geometry of a single metal.  This has been pointed out here and here, and in our own group we have seen those effects here.   Hopefully I'll have time to write more on this later....

(By the way, as I write this, Amazon is having some kind of sale on my book, at $19 below publisher list price.  No idea why or how long that will last, but I thought I'd point it out.  I'll delete this text when that expires.)