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## Electronic transport in nanostructures

The technological revolution of the last 30 years has been based on the continuous miniaturization of electronic and optical components. This miniaturization is rapidly reaching the point where a rich variety of quantum effects start playing a major role. Many such quantum effects are not yet well understood, and leave some fundamental questions unanswered.

In particular, one can now make low-dimensional and nanometre-sized structures from combinations of various solid-state systems, be they metals, superconductors, magnetic material, or two-dimensional materials such as graphene. Such systems have rich and varied behaviours, which are not easily understood in terms of either the physics of bulk materials (macroscopic systems) or of single atoms (microscopic systems) ; consequently, they are often called "mesoscopic systems".

A large part of our activity involves studying the properties of electrical currents, heat, or spin currents in these structures. Some of the most interesting cases are when one such current induces another, for example thermoelectric effects for which heat flows induce electrical currents and vice-versa. One interesting question is how normal metals (N) and ferromagnets (F) behave when coupled to superconductors (S) which induce a proximity effect. Charge transfer is possible at low energies through a multi-particle process known as Andreev reflexion. We work to understand how this affects the properties of N-S, S-N-S or S-F sandwiches, often combined with other structures such as quantum dots and Aharonov-Bohm rings.

Specific activities at the LPMMC are :

## - THERMOELECTRIC EFFECTS IN NANOSTRUCTURES.

Thermoelectric effects such as the Seebeck effect (voltage difference induced by a temperature difference) and Peltier effect (heat flow induced by current flow) can be significant in low-temperatures nanostructures. For room-temperature devices (unusual semiconductors) these effects are due occur due to band-structure, however in low-temperatures nanostructures they can also be due to interference effects or superconductive (Cooper pairing). We are currently investigating the thermoelectric properties of such systems. We are particularly interested in thermoelectric refrigeration effects that work below 1Kelvin, with a long-term aim of proposing methods of cooling nanostructures to previously un-achieved temperatures (i.e. cooling to a milliKelvin or below).

## - EFFECT OF SYMMETRIES ON QUANTUM CHAOTIC TRANSPORT.

Quantum chaos is the study of quantum mechanics in systems which would be chaotic in classical physics, it is particularly relevant to electron transport through quantum-dots. While it is clear that the quantum mechanic in such chaotic systems is different from in regular (non-chaotic) one, one of the central questions to address is how "chaotic" the quantum mechanics of such systems really is. Here we study how symmetries affect the quantum mechanics of transport through such systems (their conductance, etc). In particular, we study the effect of spatial symmetry in the chaotic system (such as a mirror-symmetric quantum dot), or electron-hole symmetry (induced by Andreev reflection from a superconductor). The presence of such symmetries typically give the system properties which are between those of chaotic and regular (non-chaotic) systems, we study how this affects electron flow though such systems.

## - HYBRID SUPERCONDUCTING NANOSTRUCTURES.

In hybrid nanostructures involving superconductors, some superconducting properties can be transferred to the normal or magnetic materials composing the structure via the proximity effect. Conversely, the properties of the superconductors get affected by the close proximity of non-superconducting materials. Such a coupling gives rise for instance to the Josephson effect between two spaced superconductors, which is used in the development of functional nanostructures, including superconducting electronics and quantum computing. In the presence of a magnetic material, nontrivial superconducting correlations are generically created close to the interfaces. At LPMMC, we study the mechanism at play both for single and for double interfaces (Josephson junctions), with a particular accent on the influence of magnetic inhomogeneities.