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.
We study resonant all-electric adiabatic spin pumping through a quantum dot with two nearby levels by using a Fermi liquid approach in the strongly interacting regime, combined with a projective numerical renormalization group (NRG) theory. Due to sp
in-orbit coupling, a strong spin pumping resonance emerges at every charging transition, which allows for the transfer of a spin $~ hbar/2$ through the device in a single pumping cycle. Depending on the precise geometry of the device, controlled pure spin pumping is also possible.
We show how the density-matrix numerical renormalization group (DM-NRG) method can be used in combination with non-Abelian symmetries such as SU(N), where the decomposition of the direct product of two irreducible representations requires the use of
a so-called outer multiplicity label. We apply this scheme to the SU(3) symmetrical Anderson model, for which we analyze the finite size spectrum, determine local fermionic, spin, superconducting, and trion spectral functions, and also compute the temperature dependence of the conductance. Our calculations reveal a rich Fermi liquid structure.
We analyze the equilibrium frequency-dependent spin current noise and spin conductance through a quantum dot in the local moment regime. Spin current correlations behave markedly differently from charge correlations. Equilibrium spin correlations are
characterized by two universal scaling functions in the absence of an external field: one of them is related to charge correlations, while the other one describes cross-spin correlations. We characterize these functions using a combination of perturbative and non-perturbative methods. We find that at low temperatures spin cross-correlations are suppressed at frequencies below the Kondo scale, $T_K$, and a dynamical spin accumulation resonance is found at the Kondo energy, $omega sim T_K$. At higher temperatures, $T>T_K$, surprising low-frequency anomalies related to overall spin conservation appear in the spin noise and spin conductance, and the Korringa rate is shown to play a distinguished role. The transient spin current response also displays universal and singular properties.
We construct a real time current-conserving functional renormalization group (RG) scheme on the Keldysh contour to study frequency-dependent transport and noise through a quantum dot in the local moment regime. We find that the current vertex develop
s a non-trivial non-local structure in time, governed by a new set of RG equations. Solving these RG equations, we compute the complete frequency and temperature-dependence of the noise spectrum. For voltages large compared to the Kondo temperature, $eV gg k_BT_K$, two sharp anti-resonances are found in the noise spectrum at frequencies $hbar omega = pm e V$, and correspondingly, two peaks in the ac conductance through the dot.
We construct a semi-microscopic theory, to describe the optical conductivity of GaMnAs in the dilute limit, x = 1%. We construct an effective Hamiltonian that captures inside-impurity band optical transitions as well as transitions between the valenc
e band and the impurity band. All parameters of the Hamiltonian are computed from microscopic variational calculations. We find a metal-insulator transition within the impurity band in the concentration range, x = 0.2 -0.3 for uncompensated and x = 1-3% for compensated samples, in good agreement with the experiments. We find an optical mass m_opt = m_e, which is almost independent of the impurity concentration excepting in the vicinity of the metal-insulator transition, where it reaches values as large as m_opt = 10 m_e. We also reproduce a mid-infrared peak at hbar omega = 200 meV, which redshifts upon doping, in quantitative agreement with the experiments.
Quantum impurity models describe interactions between some local degrees of freedom and a continuum of non-interacting fermionic or bosonic states. The investigation of quantum impurity models is a starting point towards the understanding of more com
plex strongly correlated systems, but quantum impurity models also provide the description of various correlated mesoscopic structures, biological and chemical processes, atomic physics and describe phenomena such as dissipation or dephasing. Prototypes of these models are the Anderson impurity model, or the single- and multi-channel Kondo models. The numerical renormalization group method (NRG) proposed by Wilson in mid 70s has been used in its original form for a longtime as one of the most accurate and powerful methods to deal with quatum impurity problems. Recently, a number of new developments took place: First, a spectral sum-conserving density matrix NRG approach (DM-NRG) has been developed, which has also been generalized for non-Abelian symmetries. In this manual we introduce some of the basic concepts of the NRG method and present recently developed Flexible DM-NRG code. This code uses user-defined non-Abelian symmetries dynamically, computes spectral functions, expectation values of local operators for user-defined impurity models. The code can also use a uniform density of states as well as a user-defined density of states. The current version of the code assumes fermionic baths and it uses any number of U(1), SU(2) charge SU(2) or Z(2) symmetries. The Flexible DM-NRG code can be downloaded from http://www.phy.bme.hu/~dmnrg
We compare experimental resistivity data on Ga_{1-x}Mn_xAs films with theoretical calculations using a scaling theory for strongly disordered ferromagnets. All characteristic features of the temperature dependence of the resistivity can be quantitati
vely understood through this approach as originating from the close vicinity of the metal-insulator transition. In particular, we find that the magnetic field induced changes in resistance cannot be explained within a mean-field treatment of the magnetic state, and that accounting for thermal fluctuations is crucial for a quantitative analysis. Similarly, while the non-interacting scaling theory is in reasonable agreement with the data, we find clear evidence in favor of interaction effects at low temperatures.
