Transport in AMO Systems

Questions

• How can cold atoms be used to measure the thermoelectric transport properties of strongly-correlated model systems?
• What is the “expected” transport behavior in these AMO systems? What are the reliable indicators of strong correlations (i.e. “exotic” physics) in this context?
• What are the necessary ingredients to observe superconductivity in repulsively-interacting cold atom systems?

Background

In a nutshell, transport properties describe how easily some quantity (most often charge, spin or energy) can move through a material. In a conventional metal, for example, conduction electrons are not bound to atomic nuclei and therefore are free to move around. If I were to put a chunk of metal in a DC (constant) electric field, \(E\), the electrons should feel a force and begin to move. After waiting a bit, we’ll find that there is an electric current \(J\) in the metal. The DC (charge) conductivity, \(\sigma\), is the constant that relates these two quantities: \(J=\sigma E\). If \(\sigma=0\), then the system is an insulator: no current flows in the steady-state regime, no matter the electric field applied. If \(\sigma>0\), then the system allows charge transport. When someone says they’re studying the “transport properties” of a material, that most likely means that they are measuring or computing either a conductivity or a closely-related quantity.

These properties are tricky to calculate. Here I actually calculate the resistivity, \(\rho\), which is just the reciprocal of the conductivity: \(\rho=1/\sigma\). You can think of resistivity somewhat like air resistance, but applied to a metal. A battery accelerates electrons in a wire (as gravity accelerates objects on Earth), but after a while those electrons will run into things (e.g. impurities, other electrons). When they run into things, they transfer momentum to the material and slow down. This means that electrons end up taking a very circuitous path through a wire, bumping into a bunch of things and “drifting” slowly in the direction that the battery pulls it. This drift velocity is akin to the terminal velocity of something falling through air.

As should be clear, resistivity is sort of an average over many different physical processes – in other words, the electron is only “drifting” at a constant speed if you squint your eyes and ignore how it bumps into things. The fact that it can depend on so many things means that resistivity can be quite challenging to calculate from first principles.

Relevant Article(s)

Transport in the 2D Fermi-Hubbard Model: Lessons from Weak Coupling, Thomas G. Kiely and Erich J. Mueller, Phys. Rev. B 104, 165143 (2021)

High temperature Transport in the One Dimensional Mass-Imbalanced Fermi-Hubbard model, Thomas G. Kiely and Erich J. Mueller, in preparation