Kondo effect in coupled quantum dots with RKKY interaction: Finite temperature and magnetic field effects

We study transport through two quantum dots coupled by an RKKY interaction as a function of temperature and magnetic field. By applying the Numerical Renormalization Group (NRG) method we obtain the transmission and the linear conductance. At zero temperature and magnetic field, we observe a quantum phase transition between the Kondo screened state and a local spin singlet as the RKKY interaction is tuned. Above the critical RKKY coupling the Kondo peak is split. However, we find that both finite temperature and magnetic field restore the Kondo resonance. Our results agree well with recent transport experiments on gold grain quantum dots in the presence of magnetic impurities.Comment: 4 pages, 5 figure

Angular Normal Modes of a Circular Coulomb Cluster

We investigate the angular normal modes for small oscillations about an equilibrium of a single-component coulomb cluster confined by a radially symmetric external potential to a circle. The dynamical matrix for this system is a Laplacian symmetrically circulant matrix and this result leads to an analytic solution for the eigenfrequencies of the angular normal modes. We also show the limiting dependence of the largest eigenfrequency for large numbers of particles

Base reaction optimization of redundant manipulators for space applications

One of the problems associated with redundant manipulators which were proposed for space applications is that the reactions transmitted to the base of the manipulator as a result of the motion of the manipulator will cause undesirable effects on the dynamic behavior of the supporting space structure. It is therefore necessary to minimize the magnitudes of the forces and moments transmitted to the base. It is shown that kinematic redundancy can be used to solve the dynamic problem of minimizing the magnitude of the base reactions. The methodology described is applied to a four degree-of-freedom spatial manipulator with one redundant degree-of-freedom

Two-stage Kondo effect in side-coupled quantum dots: Renormalized perturbative scaling theory and Numerical Renormalization Group analysis

We study numerically and analytically the dynamical (AC) conductance through a two-dot system, where only one of the dots is coupled to the leads but it is also side-coupled to the other dot through an antiferromagnetic exchange (RKKY) interaction. In this case the RKKY interaction gives rise to a ``two-stage Kondo effect'' where the two spins are screened by two consecutive Kondo effects. We formulate a renormalized scaling theory that captures remarkably well the cross-over from the strongly conductive correlated regime to the low temperature low conductance state. Our analytical formulas agree well with our numerical renormalization group results. The frequency dependent current noise spectrum is also discussed.Comment: 6 pages, 7 figure

Surface segregation and the Al problem in GaAs quantum wells

Low-defect two-dimensional electron systems (2DESs) are essential for studies of fragile many-body interactions that only emerge in nearly-ideal systems. As a result, numerous efforts have been made to improve the quality of modulation-doped Al$_x$Ga$_{1-x}$As/GaAs quantum wells (QWs), with an emphasis on purifying the source material of the QW itself or achieving better vacuum in the deposition chamber. However, this approach overlooks another crucial component that comprises such QWs, the Al$_x$Ga$_{1-x}$As barrier. Here we show that having a clean Al source and hence a clean barrier is instrumental to obtain a high-quality GaAs 2DES in a QW. We observe that the mobility of the 2DES in GaAs QWs declines as the thickness or Al content of the Al$_x$Ga$_{1-x}$As barrier beneath the QW is increased, which we attribute to the surface segregation of Oxygen atoms that originate from the Al source. This conjecture is supported by the improved mobility in the GaAs QWs as the Al cell is cleaned out by baking

Specific volumes of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy in the liquid, glass, and crystalline states

The specific volumes of the Zr41.2Ti13.8CU12.5Ni10.0Be2.25 alloy as a function of temperature, T, are determined by employing an image digitizing technique and numerical calculation methods applied to the electrostatically levitated spherical alloy. The linear fitting of the volumes of the alloy in the liquid, V-l, glass, V-g, and crystalline V-c, states in the temperature ranges shown in parentheses are V-l(T) = 0.1583 + 8.877 x 10(-6)T(cm^(3)/g) (700-1300 K); V-g(T) = 0.1603 + 5.528 x 10^(-6)T (400-550 K); V-c(T) = 0.1583 + 6.211 x 10(-6)T(400-850 K). The average volume thermal expansion coefficients within the temperature ranges are determined to be 5.32, 3.39, and 3.83 x 10^(-5) (1/K) for the liquid, glass, and crystalline states, respectively

Nanoscale, Phonon-Coupled Calorimetry with Sub-Attojoule/Kelvin Resolution

We have developed an ultrasensitive nanoscale calorimeter that enables heat capacity measurements upon minute, externally affixed (phonon-coupled) samples at low temperatures. For a 5 s measurement at 2 K, we demonstrate an unprecedented resolution of ΔC ~ 0.5 aJ/K (~36 000 k_B). This sensitivity is sufficient to enable heat capacity measurements upon zeptomole-scale samples or upon adsorbates with sub-monolayer coverage across the minute cross sections of these devices. We describe the fabrication and operation of these devices and demonstrate their sensitivity by measuring an adsorbed ^4He film with optimum resolution of ~3 × 10^(-5) monolayers upon an active surface area of only ~1.2 × 10^(-9) m^2

Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding

The quantum Hall states at filling factors $\nu=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. For the first time we report experimental evidence for the non-Abelian nature of excitations at $\nu=7/2$ and examine the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles, by measuring resistance oscillations as a function of magnetic field in Fabry-P\'erot interferometers using new high purity heterostructures. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near $\nu=5/2$ and $7/2$, indicating stability of the fermion parity. When phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with fermion parity change. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.Comment: A significantly revised version; 54 double-column pages containing 14 pages of main text + Supplementary Materials. The figures, which include a number of new figures, are now incorporated into the tex

Equivalence of the Falicov-Kimball and Brandt-Mielsch forms for the free energy of the infinite-dimensional Falicov-Kimball model

Falicov and Kimball proposed a real-axis form for the free energy of the Falicov-Kimball model that was modified for the coherent potential approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form for the free energy of the dynamical mean field theory solution of the Falicov-Kimball model. It has long been known that these two formulae are numerically equal to each other; an explicit derivation showing this equivalence is presented here.Comment: 4 pages, 1 figure, typeset with ReVTe