arXiv subjects

Dong E. Liu

Publications and source records attributed to Dong E. Liu.

86 records · Page 5Linked to original sources

arXiv2015

Majorana zero modes choose Euler numbers - revealed by full counting statistics

We study transport properties of a quantum dot coupled to a Majorana zero mode and two normal leads. We investigate the full counting statistics of charge tunneling events which allows one to extract complete information about current fluctuations. Using a Keldysh path-integral approach, we compute the cumulant generating function. We first consider a noninteracting spinless regime, and find that for the symmetric dot-lead couplings, the zero-frequency cumulants exhibit a universal pattern of Euler numbers, independent of the microscopic parameters. For a spinful case, the Coulomb interaction effects are discussed for both strong interaction (single-electron occupancy regime) and weak interactions (perturbative regime). Compared to the case without Majorana coupling, we show that, while the tunneling conductance might exhibit zero-bias anomaly, the full counting statistics is qualitatively different in the presence of the Majorana coupling.

cond-mat.mes-hall↗

arXiv2014

Thermalization mechanism for time-periodic finite isolated interacting quantum systems

We present a theory to describe thermalization mechanism for time-periodic finite isolated interacting quantum systems. The long time asymptote of natural observables in Floquet states is directly related to averages of these observables governed by a time-independent effective Hamiltonian. We prove that if the effective system is nonintegrable and satisfies eigenstate thermalization hypothesis, quantum states of such time-periodic isolated systems will thermalize. After a long time evolution, system will relax to a stationary state, which only depends on an initial energy of the effective Hamiltonian and follows a generalized eigenstate thermalization hypothesis. A numerical test for the periodically modulated Bose-Hubbard model, with the extra nearest neighbor interaction on the bosonic lattice, agrees with the theoretical predictions.

cond-mat.stat-mech↗

arXiv2014

Tunable Quantum Phase Transitions in a Resonant Level Coupled to Two Dissipative Baths

We 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.

cond-mat.mes-hall↗

arXiv2013

Thermal transport and quench relaxation in nonlinear Luttinger liquids

One-dimensional electrons with a linearized dispersion relation are equivalent to a collection of harmonic plasmon modes, which represent long wavelength density oscillations. An immediate consequence of this Luttinger model of one-dimensional electron systems is the absence of inelastic scattering processes responsible for the relaxation of nonequilibrium states. In a generic nonlinear Luttinger liquid plasmons may decay and thus acquire a finite lifetime. We show that equilibration of plasmons is hierarchical and has profound implications for the dynamics after a thermal quench. We also develop a thermal transport theory and compute thermal conductance of the nonlinear Luttinger liquid by treating the collision integral of plasmons in a manifestly nonperturbative way.

cond-mat.str-el↗

arXiv2013

Tunneling Spectroscopy of a Spiral Luttinger Liquid in Contact with Superconductors

One-dimensional wires with Rashba spin-orbit coupling, magnetic field, and strong electron-electron interactions are described by a spiral Luttinger liquid model. We develop a theory to investigate the tunneling density of states into a spiral Luttinger liquid under the proximity effect with superconductors. This approach provides a way to disentangle the delicate interplay between superconducting correlations and strong electron interactions. If the wire-superconductor boundary is dominated by Andreev reflection, we find that in the vicinity of the interface the zero-bias tunneling anomaly reveals a power law enhancement with the unusual exponent. Far away from the interface strong correlations inherent to the Luttinger liquid prevail and restore conventional suppression of the tunneling density of states at the Fermi level, which acquire, however, a Friedel-like oscillatory envelope with the period renormalized by the strength of the interaction.

cond-mat.mes-hall↗

arXiv2013

Proposed Method for Distinguishing Majorana Peak from Other Peaks: Tunneling Spectroscopy with Ohmic Dissipation using Resistive Electrodes

We propose a scheme to distinguish zero-energy peaks due to Majorana from those due to other effects at finite temperature by simply replacing the normal metallic lead with a resistive lead (large R kΩ) in the tunneling spectroscopy. The dissipation effects due to the large resistance change the tunneling conductance significantly in different ways. The Majorana peak remains increase as temperature decreases G T^(2r-1) for r=e^2 R/h<1/2. The zero-energy peak due to other effects splits into two peaks at finite temperature and the conductance at zero voltage bias varies with temperature by a power law. The dissipative tunneling with a Majorana mode belongs to a same universal class as the unstable critical point of the case with a non-Majorana mode.

cond-mat.mes-hall↗

arXiv2012

Floquet Majorana Fermions for Topological Qubits

We introduce and develop an approach to realizing a topological phase transition and non-Abelian statistics with dynamically induced Floquet Majorana Fermions (FMFs). When the periodic driving potential does not break fermion parity conservation, FMFs can encode quantum information. Quasi-energy analysis shows that a stable FMF zero mode and two other satellite modes exist in a wide parameter space with large quasi-energy gaps, which prevents transitions to other Floquet states under adiabatic driving. We also show that in the asymptotic limit FMFs preserve non-Abelian statistics and, thus, behave like their equilibrium counterparts.

cond-mat.mes-hall↗

arXiv2012

Fermi-liquid regime of the mesoscopic Kondo problem

We consider the low temperature regime of the mesoscopic Kondo problem, and in particular the relevance of a Fermi-liquid description of this regime. Using two complementary approaches -- a mean field slave fermion approximation on the one hand and a Fermi-liquid description "à la Nozières" supplemented by an argument of separation of scale on the other hand -- we show that they both lead to (essentially) the same quasi-particle spectra, providing in this way a strong indication that they both give the correct physics of this regime.

cond-mat.mes-hall↗

arXiv2012

Quantum Phase Transition in a Resonant Level Coupled to Interacting Leads

An interacting one-dimensional electron system, the Luttinger liquid, is distinct from the "conventional" Fermi liquids formed by interacting electrons in two and three dimensions. Some of its most spectacular properties are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Here, we create a system which emulates tunneling in a Luttinger liquid, by controlling the interaction of the tunneling electron with its environment. We further replace a single tunneling barrier with a double-barrier resonant level structure and investigate resonant tunneling between Luttinger liquids. For the first time, we observe perfect transparency of the resonant level embedded in the interacting environment, while the width of the resonance tends to zero. We argue that this unique behavior results from many-body physics of interacting electrons and signals the presence of a quantum phase transition (QPT). In our samples many parameters, including the interaction strength, can be precisely controlled; thus, we have created an attractive model system for studying quantum critical phenomena in general. Our work therefore has broadly reaching implications for understanding QPTs in more complex systems, such as cold atoms and strongly correlated bulk materials.

cond-mat.mes-hall↗

arXiv2012

Mesoscopic Anderson Box: Connecting Weak to Strong Coupling

Both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. In an Anderson box, mesoscopic fluctuations of the effective single particle properties will be large. We study how the statistical fluctuations at low temperature 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.

cond-mat.mes-hall↗

arXiv2012

From Weak- to Strong-Coupling Mesoscopic Fermi Liquids

We 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 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.

cond-mat.mes-hall↗

arXiv2011

Detecting a Majorana-Fermion Zero Mode Using a Quantum Dot

We 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 e^2/2h. In contrast, if the wire is in its trivial phase, the conductance peak value is e^2/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 [PRL 106, 090503 (2011)] to the required degeneracy point.

cond-mat.mes-hall↗

arXiv2010

Quantum Phase Transition and Dynamically Enhanced Symmetry in Quadruple Quantum Dot System

We propose a system of four quantum dots designed to study the competition between three types of interactions: Heisenberg, Kondo and Ising. We find a rich phase diagram containing two sharp features: a quantum phase transition (QPT) between charge-ordered and charge-liquid phases, and a dramatic resonance in the charge liquid visible in the conductance. The QPT is of the Kosterlitz-Thouless type with a discontinuous jump in the conductance at the transition. We connect the resonance phenomenon with the degeneracy of three levels in the isolated quadruple dot and argue that this leads to a Kondo-like dynamical enhancement of symmetry from U(1) x Z_2 to U(1) x U(1).

cond-mat.mes-hall↗

arXiv2010

Conductance of Quantum Impurity Models from Quantum Monte Carlo

The conductance of two Anderson impurity models, one with two-fold and another with four-fold degeneracy, representing two types of quantum dots, is calculated using a world-line quantum Monte Carlo (QMC) method. Extrapolation of the imaginary time QMC data to zero frequency yields the linear conductance, which is then compared to numerical renormalization group results in order to assess its accuracy. We find that the method gives excellent results at low temperature (T<Tk) throughout the mixed valence and Kondo regimes, but it is unreliable for higher temperature.

cond-mat.mes-hall↗