## Sunday, September 30, 2007

### This week in cond-mat

Two recent papers in cond-mat this time, both rather thermodynamics-related. That's appropriate, since I'm teaching undergrad stat mech these days.

arxiv:0709.4181 - Kubala et al., Violation of Wiedemann-Franz law in a single-electron transistor
The Wiedemann-Franz law is one of those things taught in nearly every undergraduate solid-state physics class. It also happens to be extremely useful for doing cryogenic engineering, as I learned during my grad school days. The idea is simple: simple kinetic theory arguments (and dimensional analysis) imply that the conductivity of some parameter via some excitations is given by the product (carrying capacity of that parameter per excitation)*(speed of excitation carrying that parameter)*(mean free path of that excitation), with some geometric factor out in front (e.g., 1/3 for three dimensional diffusive motion of the excitation). For example, the electrical conductivity in a 3d, diffusive, ordinary metal is (1/3)(e)(v_F)(\ell), where e is the electronic charge, v_F is the Fermi velocity for conduction electrons, and \ell is the mean free path for those electrons (at low T, \ell is set by impurity scattering or boundary scattering). However, in a normal metal electrons can also carry thermal energy with some heat capacity c_v per electron that scales like T, while the speed and mean free path of the electrons are as above. This implies the Wiedemann-Franz law, that the ratio of the thermal conductivity to the (electrical conductivity*T) in an ordinary metal should be a constant (the Lorenz number, ~25 nanoOhms W/K^2). Deviations from the W-F law are indicators of interesting physics - basically that simple metal electrons either aren't the dominant carriers of the electrical current, or that the charge carriers don't carry thermal energy as normal. This paper is a theory piece by the Helsinki group showing that the W-F law fails badly for single-electron transistors. In particular, in the co-tunneling regime, when current is carried via quantum coherent processes, the Lorenz number is predicted to be renormalized upward by a factor of 9/5. This will be challenging to measure in experiments, but exquisite thermal conductivity measurements have been performed in similar systems in the past.

arxiv:0709.4125 - Allahverdyan et al., Work extremum principle: structure and function of quantum heat engines
Marlan Scully (also here) caused a bit of a flurry of excitement a few years ago by proposing a form of heat engine that uses quantum coherence and its destruction to do work, in addition to the conventional approach of using two thermal baths at different temperatures. This paper is a theoretical analysis of some such quantum heat engines. Carnot can sleep easy - in the end you can't violate the Carnot efficiency even with quantum heat engines, if you dot all the "i"s and cross all the "t"s. Neat to think about, though, and of some experimental relevance to the cold atom community, who can prepare highly coherent atomic gases at very low temperatures. This paper is long and detailed and I don't claim to have read it in depth, but it looks interesting.

Unknown said...

I am not sure that it is appropriate to discuss too many details in this public blog, please let me know if it is not.

I took a brief look and have some comments about their experimental scheme.

In the scheme, they considered diffusion through SET and e-ph relaxation but not photon radiation. In fact, they publish result on photon radiation last year: Meschke, M., Guichard, W. & Pekola, J.P. Single-mode heat conduction by photons. Nature 444, 187-190 (2006).

Besides, when the normal metal source is in proximity with superconducting electrodes, there exsits a Josephson junction for the NIS configuration, which may radiate when a bias is applied.

So, the story sounds ok, but the realization seems tricky, especially at the lowest temperature.

Pet Care Rx Reviews said...

This paper is long and detailed and I don't claim to have read it in depth, but it looks interesting.