Kondo effect and mesoscopic fluctuations
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2011-11-01
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Abstract
Two important themes in nanoscale physics in the last two decades are correlations between electrons and mesoscopic fluctuations. Here we review our recent work on the intersection of these two themes. The setting is the Kondo effect, a paradigmatic example of correlated electron physics, in a nanoscale system with mesoscopic fluctuations; in particular, we consider a small quantum dot coupled to a finite reservoir (which itself may be a large quantum dot). We discuss three aspects of this problem. First, in the high-temperature regime, we argue that a Kondo temperature TK which takes into account the mesoscopic fluctuations is a relevant concept: for instance, physical properties are universal functions of T/TK. Secondly, when the temperature is much less than the mean level spacing due to confinement, we characterize a natural cross-over from weak to strong coupling. This strong coupling regime is itself characterized by well-defined single-particle levels, as one can see from a Nozières Fermi-liquid theory argument. Finally, using a mean-field technique, we connect the mesoscopic fluctuations of the quasiparticles in the weak coupling regime to those at strong coupling. © Indian Academy of Sciences.
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Ullmo, D, S Burdin, DE Liu and HU Baranger (2011). Kondo effect and mesoscopic fluctuations. Pramana - Journal of Physics, 77(5). pp. 769–779. 10.1007/s12043-011-0191-3 Retrieved from https://hdl.handle.net/10161/26476.
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Harold U. Baranger
The broad focus of Prof. Baranger's group is quantum open systems at the nanoscale, particularly the generation of correlation between particles in such systems. Fundamental interest in nanophysics-- the physics of small, nanometer scale, bits of solid-- stems from the ability to control and probe systems on length scales larger than atoms but small enough that the averaging inherent in bulk properties has not yet occurred. Using this ability, entirely unanticipated phenomena can be uncovered on the one hand, and the microscopic basis of bulk phenomena can be probed on the other. Additional interest comes from the many links between nanophysics and nanotechnology. Within this thematic area, our work ranges from projects trying to nail down realistic behavior in well-characterized systems, to more speculative projects reaching beyond regimes investigated experimentally to date.
Correlations between particles are a central issue in many areas of condensed matter physics, from emergent many-body phenomena in complex materials, to strong matter-light interactions in quantum information contexts, to transport properties of single molecules. Such correlations, for either electrons or bosons (photons, plasmons, phonons,…), underlie key phenomena in nanostructures. Using the exquisite control of nanostructures now possible, experimentalists will be able to engineer correlations in nanosystems in the near future. Of particular interest are cases in which one can tune the competition between different types of correlation, or in which correlation can be tunably enhanced or suppressed by other effects (such as confinement or interference), potentially causing a quantum phase transition-- a sudden, qualitative change in the correlations in the system.
My recent work has addressed correlations in both electronic systems (quantum wires and dots) and photonic systems (photon waveguides). We have focused on 3 different systems: (1) qubits coupled to a photonic waveguide, (2) quantum dots in a dissipative environment, and (3) interfaces between graphene and a superconductor, particularly when graphene is in the quantum Hall state. The methods used are both analytical and numerical, and are closely linked to experiments.
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