Date de publication : Apr 30, 2013 4:44:0 PM
When a nanoscale conductor is connected in series with an electrical resistance R, the latter induces voltage fluctuations across the conductor, which reduce the average current. This phenomenon, called Dynamical Coulomb Blockade (DCB), has the typical consequence that classical laws of impedance composition are violated, leading to the so-called « quantum circuits ». DCB has attracted substantial theoretical and experimental investigations during the last four decades. Nevertheless, those were mainly performed in the limit of weakly transmitting conductors (where electrons jump by Tunnel effect). More recently, in view of its possible experimental investigation, exploring the survival of DCB in good transmitting conductors has become a theoretical challenge. A first analysis, restricted to high energies and very small R, has shown that the DCB is weak, and that is related to the amplitude of current fluctuations (noise) in the isolated conductor. Nevertheless, a more recent study done for arbitrary R and energies has led to the striking conclusion that even for a well-transmitting conductor, the DCB becomes very strong at low energies and is related to the noise of the conductor affected by R (1). This was possible owing to the mapping of this problem to the Tomonaga-Luttinger Liquid (TLL) model, which describes electrons subject to Coulomb interactions in one dimension. This mapping has motivated experimental works which confirm its predictions (both at LPN Marcoussis and Duke University(2)) and has offered the possibility to simulate the control of Coulomb interactions within the TLL model by tuning the resistance R. More recently, a collaboration with F. Pierre’s group at LPN has led to a striking validation of the TLL theory (3). The thesis will deal with many open promising theoretical issues raised by this collaboration as well as the results of FInkelstein’s group. It will also include the extension of the DCB phenomena to the problem of two nanoscale conductors in series, where voltage fluctuations deviate from gaussian distribution. The student will get acquainted with field theory methods and Keldysh technique for out-of-equilibrium transport, and benefit from an exceptional environment. There are potential collaborations with Professor F. Hekking at Grenoble as well as with world-leading experimental groups, such as those of : F. Pierre at LPN, D. Estève (Quantronics group) and C. D. Glattli at CEA, Saclay, H. Bouchiat and R. Deblock at LPS, Orsay, B. Huard at ENS Paris.
(1) I. Safi and H. Saleur, One-Channel Conductor in an Ohmic Environment: Mapping to a Tomonaga-Luttinger Liquid and Full Counting Statistics. Phys. Rev. Lett. 93, 126602 (2004).
(2) C. Altimiras, U. Gennser, A. Cavanna, D. Mailly & F. Pierre, Experimental Test of the Dynamical Coulomb Blockade Theory for Short Coherent Conductors. Phys. Rev. Lett. 99, 256805 (2007); F. D. Parmentier and al. Strong back-action of a linear circuit on a single electronic quantum channel. Nature Phys. 7, 935 (2011); H. T. Mebrahtu, et al, Quantum phase transition in a resonant level coupled to interacting leads. Nature 488, 61-64 (2012); H. T. Mebrahtu and al, Observation of Majorana Quantum Critical Behavior in a Resonant Level Coupled to a Dissipative Environment. ArXiv:1212.3857, submitted to Nature Phys.
(3) S. Jezouin, M. Albert, F. D. Parmentier, A. Anthore, U. Gennser, A. Cavanna, I. Safi and F. Pierre, Tomonaga-Luttinger physics in electronic quantum circuits, Nature Communications
4,1802 (2013).