Kondo effect in three-dimensional Dirac and Weyl systems

Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac point, Dirac semimetals are in fact unlikely candidates for a Kondo effect due to the pseudogapped density of states. However, the influence of a nearby quantum critical point leads to the unconventional evolution of Kondo physics for even tiny deviations in the chemical potential. Separating the degenerate Dirac nodes produces a Weyl phase: time-reversal symmetry-breaking precludes Kondo due to an effective impurity magnetic field, but different Kondo variants are accessible in time-reversal invariant Weyl systems.Comment: 4+ pages, 2 figure

Real-space renormalization group flow in quantum impurity systems: local moment formation and the Kondo screening cloud

The existence of a length-scale $\xi_K\sim 1/T_K$ (with $T_K$ the Kondo temperature) has long been predicted in quantum impurity systems. At low temperatures $T\ll T_K$, the standard interpretation is that a spin-$\tfrac{1}{2}$ impurity is screened by a surrounding `Kondo cloud' of spatial extent $\xi_K$. We argue that renormalization group (RG) flow between any two fixed points (FPs) results in a characteristic length-scale, observed in real-space as a crossover between physical behaviour typical of each FP. In the simplest example of the Anderson impurity model, three FPs arise; and we show that `free orbital', `local moment' and `strong coupling' regions of space can be identified at zero temperature. These regions are separated by two crossover length-scales $\xi_{\text{LM}}$ and $\xi_K$, with the latter diverging as the Kondo effect is destroyed on increasing temperature through $T_K$. One implication is that moment formation occurs inside the `Kondo cloud', while the screening process itself occurs on flowing to the strong coupling FP at distances $\sim \xi_K$. Generic aspects of the real-space physics are exemplified by the two-channel Kondo model, where $\xi_K$ now separates `local moment' and `overscreening' clouds.Comment: 6 pages; 5 figure

The effect of movement variability on putting proficiency during the golf putting stroke

Movement variability has been considered important to execute an effective golf swing yet is comparatively unexplored regarding the golf putt. Movement variability could potentially be important considering the small margins of error between a successful and a missed putt. The aim of this study was to assess whether variability of body segment rotations influence putting performance (ball kinematic measures). Eight golfers (handicap range 0–10) performed a 3.2 m level putt wearing retro-reflective markers which were tracked using a three-dimensional motion analysis system sampling at 120 Hz. Ball roll kinematics were recorded using Quintic Ball Roll launch monitor. Movement (segment) variability was calculated based on a scalene ellipsoid volume concept and correlated with the coefficient of variation of ball kinematics. Statistical analysis showed no significant relationships between segment variability and putting proficiency. One significant relationship was identified between left forearm variability and horizontal launch angle, but this did not result in deficits in putting success. Results show that performance variability in the backswing and downswing is not related to putting proficiency or the majority of ball roll measures. Differing strategies may exist where certain golfers may have more fluid movement patterns thereby effectively utilising variability of movement. Therefore, golf instructors should consider movement variability when coaching the golf putt

The Rain Forests of Home: an Atlas of People and Place

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Two-channel Kondo physics in odd impurity chains

We study odd-membered chains of spin-(1/2) impurities, with each end connected to its own metallic lead. For antiferromagnetic exchange coupling, universal two-channel Kondo (2CK) physics is shown to arise at low energies. Two overscreening mechanisms are found to occur depending on coupling strength, with distinct signatures in physical properties. For strong inter-impurity coupling, a residual chain spin-(1/2) moment experiences a renormalized effective coupling to the leads; while in the weak-coupling regime, Kondo coupling is mediated via incipient single-channel Kondo singlet formation. We also investigate models where the leads are tunnel-coupled to the impurity chain, permitting variable dot filling under applied gate voltages. Effective low-energy models for each regime of filling are derived, and for even-fillings where the chain ground state is a spin singlet, an orbital 2CK effect is found to be operative. Provided mirror symmetry is preserved, 2CK physics is shown to be wholly robust to variable dot filling; in particular the single-particle spectrum at the Fermi level, and hence the low-temperature zero-bias conductance, is always pinned to half-unitarity. We derive a Friedel-Luttinger sum rule and from it show that, in contrast to a Fermi liquid, the Luttinger integral is non-zero and determined solely by the `excess' dot charge as controlled by gate voltage. The relevance of the work to real quantum dot devices, where inter-lead charge-transfer processes fatal to 2CK physics are present, is also discussed. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of these problems.Comment: 21 pages, 19 figure

Kondo effect on the surface of 3D topological insulators: Signatures in scanning tunneling spectroscopy

We investigate the scattering off dilute magnetic impurities placed on the surface of three-dimensional topological insulators. In the low-temperature limit, the impurity moments are Kondo-screened by the surface-state electrons, despite their exotic locking of spin and momentum. We determine signatures of the Kondo effect appearing in quasiparticle interference (QPI) patterns as recorded by scanning tunneling spectroscopy, taking into account the full energy dependence of the T matrix as well as the hexagonal warping of the surface Dirac cones. We identify a universal energy dependence of the QPI signal at low scanning energies as the fingerprint of Kondo physics, markedly different from the signal due to non-magnetic or static magnetic impurities. Finally, we discuss our results in the context of recent experimental data.Comment: 9 pages, 9 figure