Gate-controlled Kondo screening in graphene: Quantum criticality and electron-hole asymmetry

Magnetic impurities in neutral graphene provide a realization of the pseudogap Kondo model, which displays a quantum phase transition between phases with screened and unscreened impurity moment. Here, we present a detailed study of the pseudogap Kondo model with finite chemical potential mu. While carrier doping restores conventional Kondo screening at lowest energies, properties of the quantum critical fixed point turn out to influence the behavior over a large parameter range. Most importantly, the Kondo temperature T_K shows an extreme asymmetry between electron and hole doping. At criticality, depending on the sign of mu, T_K follows either the scaling prediction T_K ~ |mu| with a universal prefactor, or T_K ~ |mu|^x with x = 2.6. This asymmetry between electron and hole doping extends well outside the quantum critical regime and also implies a qualitative difference in the shape of the tunneling spectra for both signs of mu.Comment: 6 pages, 6 figs; (v2) extended discussion of RG flow, final version as publishe

Interaction effects on almost flat surface bands in topological insulators

We consider ferromagnetic instabilities of two-dimensional helical Dirac fermions hosted on the surface of three-dimensional topological insulators. We investigate ways to increase the role of interactions by means of modifying the bulk properties which in turn changes both the surface Dirac theory and the screening of interactions. We discuss both the long-ranged part of the Coulomb interactions controlled by the dimensionless coupling constant $\alpha = e^{2}/(\hbar \epsilon v_{F}^{\mathrm{surf}})$ as well as the effects of local interactions parametrized by the ratio $U_{\mathrm{surf}}/D_{\mathrm{surf}}$ of a local interaction on the surface, $U_{\mathrm{surf}}$, and the surface bandwidth, $D_{\mathrm{surf}}$. If large compared to 1, both mechanisms can induce spontaneously surface ferromagnetism, thereby gapping the surface Dirac metal and inducing an anomalous quantum Hall effect. We investigate two mechanisms which can naturally lead to small Fermi velocities $v_{F}^{\mathrm{surf}}$ and a corresponding small bandwidth $D_{\mathrm{surf}}$ at the surface when the bulk band gap is reduced. The same mechanisms can, however, also lead to an enhanced screening of surface interactions. While in all considered cases the long-ranged part of the Coulomb interaction is screened efficiently, $\alpha \lesssim 1$, we discuss situations, where $U_{\mathrm{surf}}/D_{\mathrm{surf}}$ becomes \emph{parametrically}\ large compared to 1, thus inducing surface magnetism.Comment: 15 pages, 8 figures, published version with minor updat

Landau levels of Majorana fermions in a spin liquid

Majorana fermions were originally proposed as elementary particles acting as their own antiparticles. In recent years, it has become clear that Majorana fermions can instead be realized in condensed-matter systems as emergent quasiparticles, a situation often accompanied by topological order. Here we propose a physical system which realizes Landau levels - highly degenerate single-particle states usually resulting from an orbital magnetic field acting on charged particles - for Majorana fermions. This is achieved in a variant of a quantum spin system due to Kitaev which is distorted by triaxial strain. This strained Kitaev model displays a spin-liquid phase with charge-neutral Majorana-fermion excitations whose spectrum corresponds to that of Landau levels, here arising from a tailored pseudo-magnetic field. We show that measuring the dynamic spin susceptibility reveals the Landau-level structure by a remarkable mechanism of probe-induced bound-state formation.Comment: 4+6 pages, 2+6 figures; v2: final version, Phys. Rev. Lett. (accepted

Fractional impurity moments in two-dimensional non-collinear magnets

We study dilute magnetic impurities and vacancies in two-dimensional frustrated magnets with non-collinear order. Taking the triangular-lattice Heisenberg model as an example, we use quasiclassical methods to determine the impurity contributions to the magnetization and susceptibility. Most importantly, each impurity moment is not quantized, but receives non-universal screening corrections due to local relief of frustration. At finite temperatures, where bulk long-range order is absent, this implies an impurity-induced magnetic response of Curie form, with a prefactor corresponding to a fractional moment per impurity. We also discuss the behavior in an applied magnetic field, where we find a singular linear-response limit for overcompensated impurities, and propose experiments to test our theory.Comment: 4 pages, 4 fig

Kondo lattices with inequivalent local moments: Competitive vs. co-operative Kondo screening

While standard heavy fermion metals feature a single spin-1/2 local moment per unit cell, more complicated systems with multiple distinct local moments have been synthesized as well, with Ce_3Pd_20(Si,Ge)_6 being one example. Here, we discuss the physics of a Kondo lattice model with two local-moment sublattices, coupled with different Kondo couplings to conduction electrons. The phase diagram will be strongly modified from that of the standard Kondo lattice if the characteristic screening temperatures of the distinct moments are well separated. Therefore, we investigate the interplay between the two Kondo effects using a local self-energy approximation via slave bosons. We find that the two Kondo effects can either compete or co-operate depending on the conduction-band filling. In the regime of competition, small differences in the two Kondo couplings can lead to huge differences in the respective Kondo scales, due to non-trivial many-body effects. We also study the low-temperature properties of the collective heavy Fermi-liquid state and propose a connection to depleted Kondo lattice systems.Comment: 14 pages, 15 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

Quantum phase transitions and thermodynamics of the power-law Kondo model

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\rho(\omega) \sim |\omega|^r$, with exponent $-1<r<0$. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents $r$ and $(-r)$, combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases, and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.Comment: 13 pages, 11 figure

The fate of topological-insulator surface states under strong disorder

Three-dimensional topological insulators feature Dirac-like surface states which are topologically protected against the influence of weak quenched disorder. Here we investigate the effect of surface disorder beyond the weak-disorder limit using large-scale numerical simulations. We find two qualitatively distinct regimes: Moderate disorder destroys the Dirac cone and induces diffusive metallic behavior at the surface. Even more remarkably, for strong surface disorder a Dirac cone reappears, as new weakly disordered "surface" states emerge in the sample beneath the disordered surface layer, which can be understood in terms of an interface between a topological and an Anderson insulator. Together, this demonstrates the drastic effect of disorder on topological surface states, which cannot be captured within effective two-dimensional models for the surface states alone.Comment: 4.3 pages, 4 fig

Family reunification for migrants under subsidiary protection in Germany: An instrument for strategic political positioning Matthias Busse and Lars Ludolph. CEPS Commentary, 21 November 2017

The debate over migration policy played a major role in the recent collapse of German coalition talks, a first indication of how the AfD changed the country’s political discourse