Lars Fritz

The physics of Kondo impurities in graphene

This article summarizes our understanding of the Kondo effect in graphene, primarily from a theoretical perspective. We shall describe different ways to create magnetic moments in graphene, either by adatom deposition or via defects. For dilute moments, the theoretical description is in terms of effective Anderson or Kondo impurity models coupled to graphenes Dirac electrons. We shall discuss in detail the physics of these models, including their quantum phase transitions and the effect of carrier doping, and confront this with existing experimental data. Finally, we will point out connections to other quantum impurity problems, e.g., in unconventional superconductors, topological insulators, and quantum spin liquids.

Skyrmion lattice phase in three-dimensional chiral magnets from Monte Carlo simulations

Chiral magnets, such as MnSi, display a rich finite temperature phase diagram in an applied magnetic field. The most unusual of the phases encountered is the so called A-phase characterized by a triangular lattice of skyrmion tubes. Its existence cannot be captured within a mean-field treatment of a Landau-Ginzburg functional but thermal fluctuations to Gaussian order are required to stabilize it. In this note we go beyond Gaussian order in a fully non-perturbative study of a three dimensional lattice spin model using classical Monte Carlo simulations. We demonstrate that the A-phase is indeed stabilized by thermal fluctuations and furthermore we reproduce the full phase diagram found in experiment. The thermodynamic signatures of the helimagnetic transition upon cooling from the paramagnet are qualitatively consistent with experimental findings and lend further support to the Brazovskii scenario which describes a fluctuation driven first order transition due to the abundance of soft modes.

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 μ. 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 TK shows an extreme asymmetry between electron and hole doping. At criticality, depending on the sign of μ, TK follows either the scaling prediction TK∝|μ| with a universal prefactor, or TK∝|μ|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 μ.

Topological insulators in magnetic fields: quantum Hall effect and edge channels with a nonquantized θ term.

We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains quantized even in situations where the θ term in the bulk and the associated surface Hall conductivities, σ(xy)(S), are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the θ term changes by ±2πn along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels.

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 physics due to an effective impurity magnetic field, but different Kondo variants are accessible in time-reversal invariant Weyl systems.

Theory of inelastic scattering from quantum impurities

We use the framework setup recently to compute nonperturbatively inelastic scattering from quantum impurities G. Zarand et al., Phys. Rev. Lett. 93, 107204 2004 to study the energy dependence of the singleparticle S matrix and the inelastic scattering cross section for a number of quantum impurity models. We study the case of the spin S =1/2 two-channel Kondo model, the Anderson model, and the usual S =1/2 singlechannel Kondo model. We discuss the difference between non-Fermi-liquid and Fermi-liquid models and study how a crossover between the non-Fermi-liquid and Fermi-liquid regimes appears in the case of channel anisotropy for the S =1/2 two-channel Kondo model. We show that for the most elementary non-Fermi-liquid system, the two-channel Kondo model, half of the scattering remains inelastic even at the Fermi energy. Details of the derivation of the reduction formulas and a simple path integral approach to connect the T matrix to local correlation functions are also presented.

Kondo effect on the surface of three-dimensional 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.

Exact crossover Green function in the two-channel and two-impurity Kondo models.

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.

Quantum criticality of the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions

We investigate the zero-temperature phase diagram of the nearest-neighbor kagome antiferromagnet in the presence of Dzyaloshinksii-Moriya interaction. We develop a theory for the transition between Z2 spin liquids with bosonic spinons and a phase with antiferromagnetic long-range order. Connections to recent numerical studies and experiments are discussed.

Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions

We study the combined effect of interactions and disorder on topological order in one dimension. Toward that end, we consider a generalized Kitaev chain including fermion-fermion interactions and disorder in the chemical potential. We determine the phase diagram by performing density-matrix renormalization-group calculations on the corresponding spin-1/2 chain. We find that moderate disorder or repulsive interactions individually stabilize the topological order, which remains valid for their combined effect. However, both repulsive and attractive interactions lead to a suppression of the topological phase at strong disorder.