# Browsing by Author "Liu, DE"

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Item Open Access Detecting a Majorana-fermion zero mode using a quantum dot(Physical Review B - Condensed Matter and Materials Physics, 2011-11-16) Liu, DE; Baranger, HUWe propose an experimental setup for detecting a Majorana zero mode consisting of a spinless quantum dot coupled to the end of a p-wave superconducting nanowire. The Majorana bound state at the end of the wire strongly influences the conductance through the quantum dot: Driving the wire through the topological phase transition causes a sharp jump in the conductance by a factor of 1/2. In the topological phase, the zero-temperature peak value of the dot conductance (i.e., when the dot is on resonance and symmetrically coupled to the leads) is e2/2h. In contrast, if the wire is in its trivial phase, the conductance peak value is e2/h, or if a regular fermionic zero mode occurs on the end of the wire, the conductance is 0. The system can also be used to tune Flensberg's qubit system to the required degeneracy point. © 2011 American Physical Society.Item Open Access From weak- to strong-coupling mesoscopic Fermi liquids(EPL, 2012-01-01) Liu, DE; Burdin, S; Baranger, HU; Ullmo, DWe study mesoscopic fluctuations in a system in which there is a continuous connection between two distinct Fermi liquids, asking whether the mesoscopic variation in the two limits is correlated. The particular system studied is an Anderson impurity coupled to a finite mesoscopic reservoir described by the random matrix theory, a structure which can be realized using quantum dots. We use the slave boson mean-field approach to connect the levels of the uncoupled system to those of the strong-coupling Nozières' Fermi liquid. We find strong but not complete correlation between the mesoscopic properties in the two limits and several universal features. © 2012 Europhysics Letters Association.Item Open Access Kondo effect and mesoscopic fluctuations(Pramana - Journal of Physics, 2011-11-01) Ullmo, D; Burdin, S; Liu, DE; Baranger, HUTwo 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.Item Open Access Mesoscopic Anderson box: Connecting weak to strong coupling(Physical Review B - Condensed Matter and Materials Physics, 2012-04-27) Liu, DE; Burdin, S; Baranger, HU; Ullmo, DWe study the Anderson impurity problem in a mesoscopic setting, namely the "Anderson box," in which the impurity is coupled to finite reservoir having a discrete spectrum and large sample-to-sample mesoscopic fluctuations. Note that both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. We study how the statistical fluctuations in these two problems are connected, using random matrix theory and the slave boson mean-field approximation (SBMFA). First, for a resonant level model such as results from the SBMFA, we find the joint distribution of energy levels with and without the resonant level present. Second, if only energy levels within the Kondo resonance are considered, the distributions of perturbed levels collapse to universal forms for both orthogonal and unitary ensembles for all values of the coupling. These universal curves are described well by a simple Wigner-surmise-type toy model. Third, we study the fluctuations of the mean-field parameters in the SBMFA, finding that they are small. Finally, the change in the intensity of an eigenfunction at an arbitrary point is studied, such as is relevant in conductance measurements. We find that the introduction of the strongly coupled impurity considerably changes the wave function but that a substantial correlation remains. © 2012 American Physical Society.Item Open Access Mesoscopic fluctuations in the Fermi-liquid regime of the Kondo problem(European Physical Journal B, 2013-08-01) Ullmo, D; Liu, DE; Burdin, S; Baranger, HUWe consider the low temperature regime of the mesoscopic Kondo problem, and in particular the relevance of a Fermi-liquid description of this regime. Mesoscopic fluctuations of both the quasiparticle energy levels and the corresponding wavefunctions are large in this case. These mesoscopic fluctuations make the traditional approach to Fermi-liquids impracticable, as it assumes the existence of a limited number of relevant parameters. We show here how this difficulty can be overcome and discuss the relationship between the resulting Fermi-liquid description "à la Nozières" and the mean field slave fermion approximation. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.Item Open Access Tunable quantum phase transitions in a resonant level coupled to two dissipative baths(Physical Review B - Condensed Matter and Materials Physics, 2014-02-18) Liu, DE; Zheng, H; Finkelstein, G; Baranger, HUWe study tunneling through a resonant level connected to two dissipative bosonic baths: one is the resistive environment of the source and drain leads, while the second comes from coupling to potential fluctuations on a resistive gate. We show that several quantum phase transitions (QPT) occur in such a model, transitions which emulate those found in interacting systems such as Luttinger liquids or Kondo systems. We first use bosonization to map this dissipative resonant level model to a resonant level in a Luttinger liquid, one with, curiously, two interaction parameters. Drawing on methods for analyzing Luttinger liquids at both weak and strong coupling, we obtain the phase diagram. For strong dissipation, a Berezinsky-Kosterlitz-Thouless QPT separates strong-coupling and weak-coupling (charge localized) phases. In the source-drain symmetric case, all relevant backscattering processes disappear at strong coupling, leading to perfect transmission at zero temperature. In fact, a QPT occurs as a function of the coupling asymmetry or energy of the resonant level: the two phases are (i) the system is cut into two disconnected pieces (zero transmission), or (ii) the system is a single connected piece with perfect transmission, except for a disconnected fractional degree of freedom. The latter arises from the competition between the two fermionic leads (source and drain), as in the two-channel Kondo effect. © 2014 American Physical Society.