Modification of the Lifshitz-Kosevich formula for anomalous quantum oscillations in inverted insulators

It is generally believed that quantum oscillations are a hallmark of a Fermi surface and the oscillations constitute the ringing of it. Recently, it was understood that in order to have well defined quantum oscillations you do not only not need well defined quasiparticles, but also the presence of a Fermi surface is unnecessary. In this paper we investigate such a situation for an inverted insulator from a analytical point of view. Even in the insulating phase clear signatures of quantum oscillations are observable and we give a fully analytical formula for the strongly modified Lifshitz-Kosevich amplitude which applies in the clean as well as the disordered case at finite temperatures.Comment: 8 figure

The antiferromagnetic Ising model on the swedenborgite lattice

Geometrical frustration in spin systems often results in a large number of degenerate ground states. In this work we study the antiferromagnetic Ising model on the three dimensional swedenborgite lattice which is a specific stacking of Kagom\'e and triangular layers. The model contains two exchange couplings, one within the Kagom\'e layer, another one in between Kagom\'e and triangular layers. We determine the phase diagram with and without easy axis magnetic field and calculate the ground state degeneracy explicitly in terms of the residual entropy. At zero field we find two different ground state manifolds separated by a first order transition at T = 0 and equal exchange couplings. We also determine the T = 0 phase diagram in a magnetic field and find a rich phase diagram with both degenerate and non-degenerate phases depending on the field strength and out-of-plane coupling.Comment: 7 pages, 8 figure

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

Interplay of disorder and interactions in subcritically tilted and anisotropic three-dimensional Weyl fermions

We study the effects of disorder and Coulomb interactions on the physics of three-dimensional type-I Weyl fermions with tilted and anisotropic dispersions in a renormalization group approach. To lowest non-trivial loop order we show that the tendency of the Coulomb interactions to restore the symmetry of the dispersion in the semimetallic region of the phase diagram dominates the stabilization of the tilt and anisotropy favored by weak disorder. We argue that the topology of the renormalization flow of the disorder and Coulomb couplings is essentially determined by gauge invariance, so that these findings continue to hold qualitatively at any order in perturbation theory.Comment: 9+5 page

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