We study the electronic properties of the confined honeycomb lattice in the presence of the intrinsic spin-orbit (ISO) interaction and perpendicular magnetic field, and report on uncommon aspects of the quantum spin Hall conductance corroborated by p
eculiar properties of the edge states. The ISO interaction induces two specific gaps in the Hofstadter spectrum, namely the weak topological gap defined by Beugeling et al [Phys. Rev. B 86, 075118 (2012)], and spin-imbalanced gaps in the relativistic range of the energy spectrum. We analyze the evolution of the helical states with the magnetic field and with increasing Anderson disorder. The edge localization of the spin-dependent states and its dependence on the disorder strength is shown. The quantum transport, treated in the Landauer-B{u}ttiker formalism, reveals interesting new plateaus of the quantum spin Hall effect (QSHE), and also of the integer quantum Hall effect (IQHE), in the energy ranges corresponding to the spin-imbalanced gaps. The properties of the spin-dependent transmittance matrix that determine the symmetries with respect to the spin, energy and magnetic field of the longitudinal and transverse resistance are shown.
The specific topology of the line centered square lattice (known also as the Lieb lattice) induces remarkable spectral properties as the macroscopically degenerated zero energy flat band, the Dirac cone in the low energy spectrum, and the peculiar Ho
fstadter-type spectrum in magnetic field. We study here the properties of the finite Lieb lattice with periodic and vanishing boundary conditions. We find out the behavior of the flat band induced by disorder and external magnetic and electric fields. We show that in the confined Lieb plaquette threaded by a perpendicular magnetic flux there are edge states with nontrivial behavior. The specific class of twisted edge states, which have alternating chirality, are sensitive to disorder and do not support IQHE, but contribute to the longitudinal resistance. The symmetry of the transmittance matrix in the energy range where these states are located is revealed. The diamagnetic moments of the bulk and edge states in the Dirac-Landau domain, and also of the flat states in crossed magnetic and electric fields are shown.
We investigate theoretically the transport properties of the side-coupled double quantum dots in connection with the experimental study of Sasaki {it et al.} Phys.Rev.Lett.{bf 103}, 266806 (2009). The novelty of the set-up consists in connecting the
Kondo dot directly to the leads, while the side dot provides an interference path which affects the Kondo correlations. We analyze the oscillations of the source-drain current due to the periodical Coulomb blockade of the many-level side-dot at the variation of the gate potential applied on it. The Fano profile of these oscillations may be controlled by the temperature, gate potential and interdot coupling. The non-equilibrium conductance of the double dot system exhibits zero bias anomaly which, besides the usual enhancement, may show also a suppression (a dip-like aspect) which occurs around the Fano {it zero}. In the same region, the weak temperature dependence of the conductance indicates the suppression of the Kondo effect. Scaling properties of the non-equilibrium conductance in the Fano-Kondo regime are discussed. Since the SIAM Kondo temperature is no longer the proper scaling parameter, we look for an alternative specific to the double-dot. The extended Anderson model, Keldysh formalism and equation of motion technique are used.
We address the quantum dot phase measurement problem in an open Aharonov-Bohm interferometer, assuming multiple transport channels. In such a case, the quantum dot is characterized by more than one intrinsic phase for the electrons transmission. It i
s shown that the phase which would be extracted by the usual experimental method (i.e. by monitoring the shift of the Aharonov-Bohm oscillations, as in Schuster {it et al.}, Nature {bf 385}, 417 (1997)) does not coincide with any of the dot intrinsic phases, but is a combination of them. The formula of the measured phase is given. The particular case of a quantum dot containing a $S=1/2$ spin is discussed and variations of the measured phase with less than $pi$ are found, as a consequence of the multichannel transport.
We study the differential conductance in the Kondo regime of a quantum dot coupled to multiple leads. When the bias is applied symmetrically on two of the leads ($V$ and $-V$, as usual in experiments), while the others are grounded, the conductance t
hrough the biased leads always shows the expected enhancement at {it zero} bias. However, under asymmetrically applied bias ($V$ and $lambda V$, with $lambda>0$), a suppression - dip - appears in the differential conductance if the asymmetry coefficient $lambda$ is beyond a given threshold $lambda_0= sqrt[3]{1+r}$ determined by the ratio $r$ of the dot-leads couplings. This is a recipe to determine experimentally this ratio which is important for the quantum-dot devices. This finding is a direct result of the Keldysh transport formalism. For the illustration we use a many-lead Anderson Hamiltonian, the Green functions being calculated in the Lacroix approximation, which is generalized to the case of nonequilibrium.
We analyze the electronic transport through a quantum dot that contains a magnetic impurity. The coherent transport of electrons is governed by the quantum confinement inside the dot, but is also influenced by the exchange interaction with the impuri
ty. The interplay between the two gives raise to the singlet-triplet splitting of the energy levels available for the tunneling electron. In this paper, we focus on the charge fluctuations and, more precisely, the height of the conductance peaks. We show that the conductance peaks corresponding to the triplet levels are three times higher than those corresponding to singlet levels, if electronic correlations are neglected (for non-interacting dots, when an exact solution can be obtained). Next, we consider the Coulomb repulsion and the many-body correlations. In this case, the singlet/triplet peak height ratio has a complex behavior. Usually the highest peak corresponds to the state that is lowest in energy (ground state), regardless if it is singlet or triplet. In the end, we get an insight on the Kondo regime for such a system, and show the formation of three Kondo peaks. We use the equation of motion method with appropriate decoupling.
We apply the Keldysh formalism in order to derive a current formula easy to use for a system with many sites, one of which is interacting. The main technical challenge is to deal with the lesser Green function. It turns out that, in the case of the l
eft-right symmetry, the knowledge of the lesser Green function is not necessary and an exact current formula can be expressed in terms of retarded Green functions only. The application is done for a triangular interferometer which gives a good account of the Fano-Kondo effect. It is found that the interference effects, in the context of Kondo correlations, give rise to a point in the parameters space where the conductance is temperature-independent. We include a comparison with the results from the Ngs ansatz, which are less accurate, but can be used also in the absence of the above mentioned symmetry.
