Large Hubbard U limit of the Kane-Mele model on a zigzag ribbon of honeycomb lattice near half-filling is studied via a renormalized mean-field theory. The ground state exhibits time-reversal symmetry (TRS) breaking d + i d-wave superconductivity. At
large spin-orbit coupling, the Z2 phase with non-trivial spin Chern number in the pure Kane-Mele model is persistent into the TRS broken state (called spin-Chern phase), and has two pairs of counter-propagating helical Majorana modes at the edges. As the spin-orbit coupling is reduced, the system undergoes a topological quantum phase transition from the spin-Chern to chiral superconducting states. Possible relevance of our results to adatom-doped graphene and irridate compounds is discussed.
The quantum criticality of the two-lead two-channel pseudogap Anderson model is studied. Based on the non-crossing approximation, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a pow
er-law vanishing conduction electron density of states, $propto |omega-mu_F|^r$ ($0<r<1$) near the Fermi energy. Equilibrium and non-equilibrium quantum critical properties at the two-channel Kondo (2CK) to local moment (LM) phase transition are addressed by extracting universal scaling functions in both linear and non-linear conductances, respectively. Clear distinctions are found on the critical exponents between linear and non-linear conductance. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.
We study the quantum phases and phase transitions of the Kane-Mele Hubbard (KMH) model on a zigzag ribbon of honeycomb lattice at a finite size via the weak-coupling renormalization group (RG) approach. In the non-interacting limit, the KM model is k
nown to support topological edge states where electrons show helical property with orientations of the spin and momentum being locked. The effective inter-edge hopping terms are generated due to finite-size effect. In the presence of an on-site Coulomb repulsive interaction and the inter-edge hoppings, special focus is put on the stability of the topological edge states (TI phase) in the KMH model against (i) the charge and spin gaped (II) phase, (ii) the charge gaped but spin gapless (IC) phase and (iii) the spin gaped but charge gapless (CI) phase depending on the number (even/odd) of the zigzag ribbons, doping level (electron filling factor) and the ratio of the Coulomb interaction to the inter-edge tunneling. We discuss different phase diagrams for even and odd numbers of zigzag ribbons. We find the TI-CI, II-IC, and II-CI quantum phase transitions are of the Kosterlitz-Thouless (KT) type. By computing various correlation functions, we further analyze the nature and leading instabilities of these phases.
We present a detailed study for the finite-frequency current noise of a Kondo quantum dot in presence of a magnetic field by using a recently developed real time functional renormalization group approach [Phys. Rev. B $mathbf{83}$, 201303(R) (2011)].
The scaling equations are modified in an external magnetic field; the couplings and non-local current vertices become strongly anisotropic, and develop new singularities. Consequently, in addition to the natural emission threshold frequency, $hbaromega = |eV|$, a corresponding singular behavior is found to emerge in the noise spectrum at frequencies $hbar omega approx |eVpm B|$. The predicted singularities are measurable with present-day experimental techniques.
Based on the non-crossing approximation, we calculate both the linear and nonlinear conductance within the two-lead two-channel single-impurity Anderson model where the conduction electron density of states vanishes in a power-law fashion $ propto |o
mega-mu_F|^r$ with $r=1$ near the Fermi energy, appropriate for an hexagonal system. For given gate voltage, we address the universal crossover from a two-channel Kondo phase, argued to occur in doped graphene, to an unscreened local moment phase. We extract universal scaling functions in conductance governing charge transfer through the two-channel pseudogap Kondo impurity and discuss our results in the context of a recent scanning tunneling spectroscopy experiment on Co-doped graphene.
The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phase transition in a spinless dissi
pative resonant-level model, extending earlier work [Phys. Rev. Lett. 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization group approach is applied to compute the non-equilibrium current in the presence of a finite bias voltage V. In the linear response regime V ->0, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the non-equilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the non-equilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for V< T, while it obeys a distinct non-equilibrium profile for V>T. We furthermore provide new signatures of the transition in the finite-frequency current noise and AC conductance via the recently developed Functional Renormalization Group (FRG) approach. The generalization of our analysis to non-equilibrium transport through a resonant level coupled to two chiral Luttinger-liquid leads, generated by the fractional quantum Hall edge states, is discussed. Our work on dissipative resonant level has direct relevance to the experiments in a quantum dot coupled to resistive environment, such as H. Mebrahtu et al., Nature 488, 61, (2012).
We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinge
r parameter $0<K<1$. The model has been studied in Ref. 21, and was mapped onto an anisotropic two-channel Kondo model via bosonization. For K<1, the strong coupling 2CK fixed point was argued to be stable for infinitesimally weak tunnelings between dot and the 2DTI based on a simple scaling dimensional analysis[21]. We re-examine this model beyond the bare scaling dimension analysis via a 1-loop renormalization group (RG) approach combined with bosonization and re-fermionization techniques near weak-coupling and strong-coupling (2CK) fixed points. We find for K -->1 that the 2CK fixed point can be unstable towards the 1CK fixed point and the system may undergo a quantum phase transition between 1CK and 2CK fixed points. The QPT in our model comes as a result of the combined Kondo and the helical Luttinger physics in 2DTI, and it serves as the first example of the 1CK-2CK QPT that is accessible by the controlled RG approach. We extract quantum critical and crossover behaviors from various thermodynamical quantities near the transition. Our results are robust against particle-hole asymmetry for 1/2<K<1.
We theoretically investigate the non-equilibrium quantum phase transition in a generic setup: the pseudogap Kondo model where a quantum dot couples to two-left (L) and right (R)-voltage-biased fermionic leads with power-law density of states (DOS) wi
th respect to their Fermi levels {mu}_L/R, {rho}_c,L(R) ({omega}) propto |{omega} - {mu}_L(R) |r, and 0 < r < 1. In equilibrium (zero bias voltage) and for 0 < r < 1/2, with increasing Kondo correlations, in the presence of particle-hole symmetry this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo phase. Via a controlled frequency-dependent renormalization group (RG) approach, we compute analytically and numerically the non-equilibrium conductance, conduction electron T-matrix and local spin susceptibility at finite bias voltages near criticality. The current-induced decoherence shows distinct nonequilibrium scaling, leading to new universal non-equilibrium quantum critical behaviors in the above observables. Relevance of our results for the experiments is discussed.
