Kondo resonance line-shape of magnetic adatoms on decoupling layers

The zero-bias resonance in the dI/dV tunneling spectrum recorded using a scanning tunneling microscope above a spin-1/2 magnetic adatom (such as Ti) adsorbed on a decoupling layer on metal surface can be accurately fitted using the universal spectral function of the Kondo impurity model both at zero field and at finite external magnetic field. Excellent agreement is found both for the asymptotic low-energy part and for the high-energy logarithmic tails of the Kondo resonance. For finite magnetic field, the nonlinear fitting procedure consists in repeatedly solving the impurity model for different Zeeman energies in order to obtain accurate spectral functions which are compared with the experimental dI/dV curves. The experimental results at zero field are sufficiently restraining to enable an unprecedented reliability in the determination of the Kondo temperature, while at finite fields the results are more ambiguous and two different interpretations are proposed

Magnetic anisotropy effects on quantum impurities in superconducting host

We study the magnetic anisotropy effects on the localized sub-gap excitations induced by quantum impurities coupled to a superconducting host. We establish the ground-state phase diagrams for single-channel and two-channel high-spin Kondo impurities; they unveil surprising complexity that results from the (multi-stage) Kondo screening in competition with the superconducting correlations and the magnetic anisotropy splitting of the spin multiplets. We discuss the possibility of detecting the Zeeman splitting of the sub-gap states, which would provide an interesting spectroscopic tool for studying the magnetism on the single-atom level. We also study the problem of two impurities coupled by the Heisenberg exchange interaction, and we follow the evolution of the sub-gap states for both antiferromagnetic and ferromagnetic coupling. For sufficiently strong antiferromagnetic coupling, the impurities bind into a singlet state that is non-magnetic, thus the sub-gap states move to the edge of the gap and can no longer be discerned. For ferromagnetic coupling, some excited states remain present inside the gap.Comment: 14 pages, 16 figures (significantly extended version, includes a section on the two-impurity effects

Fano-Kondo effect in side-coupled double quantum dots at finite temperatures and the importance of the two-stage Kondo screening

We study the zero-bias conductance through the system of two quantum dots, one of which is embedded directly between the source and drain electrodes, while the second dot is side-coupled to the first one through a tunneling junction. Modeling the system using the two-impurity Anderson model, we compute the temperature-dependence of the conductance in various parameter regimes using the numerical renormalization group. We consider the non-interacting case, where we study the extent of the departure from the conventional Fano resonance line shape at finite temperatures, and the case where the embedded and/or the side-coupled quantum dot is interacting, where we study the consequences of the coexistence of the Kondo and Fano effects. If the side-coupled dot is very weakly interacting, the occupancy changes by two when the on-site energy crosses the Fermi level and a Fano-resonance-like shape is observed. If the interaction on the side-coupled dot is sizeable, the occupancy changes only by one and a very different line-shape results, which is strongly and characteristically temperature dependent. These results suggest an intriguing alternative interpretation of the recent experimental results study of the transport properties of the side-coupled double quantum dot [Sasaki et al., Phys. Rev. Lett. 103, 266806 (2009)]: the observed Fano-like conductance anti-resonance may, in fact, result from the two-stage Kondo effect in the regime where the experimental temperature is between the higher and the lower Kondo temperature.Comment: 9 pages, 11 figures. In V2: updated references, 3 new figures, additional discussio

Convergence acceleration and stabilization for dynamical-mean-field-theory calculations

The convergence to the self-consistency in the dynamical-mean-field-theory (DMFT) calculations for models of correlated electron systems can be significantly accelerated by using an appropriate mixing of hybridization functions which are used as the input to the impurity solver. It is shown that the techniques and the past experience with the mixing of input charge densities in the density-functional-theory (DFT) calculations are also effective in DMFT. As an example, the increase of the computational requirements near the Mott metal-insulator transition in the Hubbard model due to critical slowing down can be strongly reduced by using the modified Broyden's method to numerically solve the non-linear self-consistency equation. Speed-up factors as high as 3 were observed in practical calculations even for this relatively well behaved problem. Furthermore, the convergence can be achieved in difficult cases where simple linear mixing is either not effective or even leads to divergence. Unstable and metastable solutions can also be obtained. We also determine the linear response of the system with respect to the variations of the hybridization function, which is related to the propagation of the information between the different energy scales during the iteration.Comment: 9 pages, 8 figure

Spin-charge separation and simultaneous spin and charge Kondo effect

We study the spin-charge separation in a Kondo-like model for an impurity with a spin and a charge (isospin) degree of freedom coupled to a single conduction channel (the ``spin-charge'' Kondo model). We show that the spin and charge Kondo effects can occur simultaneously at any coupling strength. In the continuum (wide-band or weak coupling) limit, the Kondo screening in each sector is independent, while at finite bandwidth and strong coupling the lattice effects lead to a renormalization of the effective Kondo exchange constants; nevertheless, universal spin and charge Kondo effects still occur. We find similar behavior in the two-impurity Anderson model with positive and negative electron-electron interaction and in the two-impurity Anderson-Holstein model with a single phonon mode. We comment on the applicability of such models to describe the conductance of deformable molecules with a local magnetic moment.Comment: 13 pages, 11 figure

Integrability of a globally coupled complex Riccati array: quadratic integrate-and-fire neurons, phase oscillators and all in between

We present an exact dimensionality reduction for dynamics of an arbitrary array of globally coupled complex-valued Riccati equations. It generalizes the Watanabe-Strogatz theory [Phys. Rev. Lett. 70, 2391 (1993)] for sinusoidally coupled phase oscillators and seamlessly includes quadratic integrate-and-fire neurons represented by the special case of real-valued Riccati equations. It provides a low dimensional description to a wide new class of complex dynamical systems, warranting their rigorous analysis and thus providing deep insights into their collective dynamics. This result represents a significant advancement in our comprehending of coupled oscillatory systems and opens up many new avenues of research.Comment: 6 pages, 4 figure

Numerical renormalization group study of two-channel three-impurity triangular clusters

We study triangular clusters of three spin-1/2 Kondo or Anderson impurities that are coupled to two conduction leads. In the case of Kondo impurities, the model takes the form of an antiferromagnetic Heisenberg ring with Kondo-like exchange coupling to continuum electrons. We show that this model exhibits many types of the behavior found in various simpler one and two-impurity models, thereby enabling the study of crossovers between a number of Fermi-liquid (FL) and non-Fermi-liquid (NFL) fixed points. In particular, we explore a direct crossover between the two-impurity Kondo-model NFL fixed point and the two-channel Kondo-model NFL fixed point. We show that the concept of the two-stage Kondo effect applies even in the case when the first-stage Kondo state is of NFL type. In the case of Anderson impurities, we consider the transport properties of three coupled quantum dots. This class of models includes as limiting cases the familiar serial double quantum dot and triple quantum dot nanostructures. By extracting the quasiparticle scattering phase shifts, we compute the low-temperature conductance as a function of the inter-impurity tunneling-coupling. We point out that due to the existence of exponentially low temperature scales, there is a parameter range where the stable "zero-temperature" fixed point is essentially never reached (not even in numerical renormalization group calculations). The "zero-temperature" conductance is then of no interest and it may only be meaningful to compute the conductance at finite temperature. This illustrates the perils of studying the conductance in the ground state and considering thermal fluctuations only as a small correction.Comment: 12 pages, 13 figure

Magnetoresistive biosensors with on-chip pulsed excitation and magnetic correlated double sampling.

Giant magnetoresistive (GMR) sensors have been shown to be among the most sensitive biosensors reported. While high-density and scalable sensor arrays are desirable for achieving multiplex detection, scalability remains challenging because of long data acquisition time using conventional readout methods. In this paper, we present a scalable magnetoresistive biosensor array with an on-chip magnetic field generator and a high-speed data acquisition method. The on-chip field generators enable magnetic correlated double sampling (MCDS) and global chopper stabilization to suppress 1/f noise and offset. A measurement with the proposed system takes only 20 ms, approximately 50× faster than conventional frequency domain analysis. A corresponding time domain temperature correction technique is also presented and shown to be able to remove temperature dependence from the measured signal without extra measurements or reference sensors. Measurements demonstrate detection of magnetic nanoparticles (MNPs) at a signal level as low as 6.92 ppm. The small form factor enables the proposed platform to be portable as well as having high sensitivity and rapid readout, desirable features for next generation diagnostic systems, especially in point-of-care (POC) settings

Imprints of radial migration on the Milky Way’s metallicity distribution functions

Recent analysis of the SDSS-III/Apache Point Observatory Galactic Evolution Experiment (APOGEE) Data Release 12 stellar catalog has revealed that the Milky Way’s (MW) metallicity distribution function (MDF) changes shape as a function of radius, transitioning from being negatively skewed at small Galactocentric radii to positively skewed at large Galactocentric radii. Using a high-resolution, N-body+SPH simulation, we show that the changing skewness arises from radial migration—metal-rich stars form in the inner disk and subsequently migrate to the metal-poorer outer disk. These migrated stars represent a large fraction (>50%) of the stars in the outer disk; they populate the high-metallicity tail of the MDFs and are, in general, more metal-rich than the surrounding outer disk gas. The simulation also reproduces another surprising APOGEE result: the spatially invariant high-[α/Fe] MDFs. This arises in the simulation from the migration of a population formed within a narrow range of radii (3.2 ±1.2 kpc) and time (8.8 ± 0.6 Gyr ago), rather than from spatially extended star formation in a homogeneous medium at early times. These results point toward the crucial role radial migration has played in shaping our MW