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Thermoelectric transport in disordered mesoscopic systems

Abstract : Landau theory of Fermi liquids foresees that the charge and heat are tranported by the same objects: the fermionic Landau quasi-particles. In a very general way, it is true if the screening among particles is quite strong to can consider the system as composed yet by independent particles. This is the case for the electron sea in an ordinary bulk metal. The existance of just one responsible for charge and heat transport is expressed by the Wiedemann-Franz (WF) law. It states that the ratio between the thermal and electrical conductivity depends on temperature by a constant which is more or less the same for several metals. The constant of proportionality is called the Lorenz number.
What happens if the above-mentioned condition on screening is no longer satisfied, as for example in low-dimensional systems or electronic low-density systems?
The thesis is diveded into two parts. In the first one, we studied the thermal and electrical transport in a disordered quantum wire; in the second one, the influence of superconducting fluctuations on thermal conductivity in granular metals.

-) Quantum Wires:

Generally, one calls quantum wire a uni-dimensional conductor. Today, it is possible to make conductors with very strong confining potentials along one or two linear dimensions. Particularly, quantum wires really behave as electron wave-guides since they have a diameter which is comparable to the Fermi wave-length.
Because of the low dimensionality, such systems are studied in the context of Luttinger liquids theory which can take into account the interactions among electrons.
For a clean quantum wire connected to two reservoirs, electrical conductance is not renormalised by interactions, while the thermal one is because of the presence
of the connection to reservoirs. The presence of weak desorder renormalises the thermal conductance too. This was already known.
We evaluated the renormalization due to impurities for thermal conductance. Then, we could evaluate the correction, due to disorder, to Lorenz number.
At very low temperatures, the correction vanishes, while at high temperatures does not. We can states that a quantum wire with weak desorder is not in a Fermi liquid state.

-) Granular Metals:

In a normal metal, in presence of BCS interaction, electrons can form Cooper pairs even at temperatures larger then critical temperature. In this case, the transport properties of normal state mix with the properties of superconducting state. This gives rise to some particular contributions determining the charge and heat transport.
There are three different terms: the Aslamazov-Larkin contribution, the Maki-Thomson contribution, and the density of State contribution.
The first one takes into account the facility of electrons forming a Cooper pair to propagate through the system. This contribution is also called paraconductivity. Electrons forming a Cooper pair are no longer available for one particle transport. This is taken into account by DOS contribution. The last term, the MT one, takes into account the coherent scattering of electrons forming a Cooper pair on the same impurity.
For a bulk metal, it has been shown that the DOS and MT contribution compensate exactly. There is just the AL term which is not singular in the temperature.
A granular metal can be seen as a D-dimensional array of metallic grains embedded in an insulating matrix. The grains communicate among them by tunneling effect.
It is reasonable imagining that the presence of tunneling effect renormalises the transport properties. In fact, a temperature depending behaviour appear. The AL and MT contributions are of higher order with respect to the DOS term.
Two regimes are present: close and far to critical temperature. Far from critical temperature, the tunneling is not effective, and the granular structure prevails; a suppression of correction to thermal conductivity is found.
Close to critical temperature, the tunneling is effective and the bulk behaviour is found. The sign of correction is not defined univocally. It depends on the barrier transparency and on the competions among the different contributions.
In both regimes, the WF law is violated.
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Contributor : Raffaello Ferone <>
Submitted on : Friday, June 15, 2007 - 10:05:39 PM
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  • HAL Id : tel-00155222, version 1




Raffaello Ferone. Thermoelectric transport in disordered mesoscopic systems. Condensed Matter [cond-mat]. Université Joseph-Fourier - Grenoble I, 2006. English. ⟨tel-00155222⟩



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