Two interesting papers relating to mesoscopic physics on the arxiv this past week:

cond-mat/0606486 - Jakobs et al., Temperature-induced phase averaging vs. addition of resistances in mesoscopic systems

Classically, electrical conduction is well described by Ohm's Law. Take two resistors and put them in series, and the total resistance is just the sum of the two individual resistances. In the quantum world things are more complicated. Imagine an electron incident on a tunneling barrier, such that there is some tunneling amplitude t for transmission, leading to a transmission probability of |t|^2. Now consider two such barriers in series. Classical expectations would lead you to expect a transmission probability for the two-barrier system to be (|t|^2)^2. In fact, depending on the details of the system (the incident energy of the particle, the barrier heights and widths, the separation between the barriers), the full quantum treatment can give transmission probabilities ranging from zero to one (!), because of interference effects. These can be constructive or destructive, depending on just how the multiply reflecting waves bouncing back and forth between the two barriers sort themselves out, in terms of phase differences racked up. On the macroscale, inelastic interactions with the environment act to randomize the relative phases of those waves, washing out interference effects and restoring the classical Ohm's Law result. This is treated really well by Datta in one of his books. Anyway, this paper considers just what happens at finite temperature, even in the absence of true decoherence. Because electrons that dominate conduction have a spread in energy of around kT, they have a spread in wavelengths, and effectively a spread in their phase accumulation as they bounce around between scatterers. This paper looks at the effect of that averaging on the addition of resistances.

cond-mat/0606473 - Gao et al., Cotunneling and one-dimensional localization in individual single-walled carbon nanotubes

This paper is related, in the sense that it actually looks at the temperature dependence of conduction through a one-dimensional system containing randomly distributed scatterers. In this case the system is a single-walled nanotube, which really has 1d band structure because of its geometry. The scatterers are defects or disorder, and the tubes in question are around a micron in length. Gao et al. find that the tubes exhibit activated transport (becoming exponentially more resistive as T approaches 0), though the activation energies can change as temperature is reduced. At the low temperature end they find that the tubes effectively have broken up into a 1d array of quantum dots. They argue that the varying activation energies happen as the effective dot size changes with T. As temperature is decreased, coherence is increased, and higher order tunneling processes ("cotunneling") can enhance interdot conduction. A neat result and a nice idea, though their Fig. 1 raises a common issue that comes up in many such measurements. They take a log-linear plot of resistance vs. 1/T, and have "guide to the eye" lines indicating regimes of different activation energy. Are there really clear multiple regimes, or is the effective activation energy smoothly varying over the whole range? Lines to "guide the eye" should be used with caution....

## 2 comments:

Doug,

I enjoy these TWiCM write-ups. Keep up the good work!

and...go White Sox!

Electrical conduction is well described by Ohm's Law. Take two resistors and put them in series, and the total resistance is just the sum of the two individual resistances.

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