Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)$times$U(1) symmetry. Using large-scale auxiliary- field quantum Monte
Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly-interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition towards an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data is consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.
We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the textit{decoupled} fixed-point, leading to the existence of a Kondo-breakdown phase and a Kondo-break
down critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-N calculations as well as extensive auxiliary-field quantum Monte Carlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.
Cotunneling into Kondo systems, where an electron enters a $f$-electron material via a cotunneling process through the local-moment orbital, has been proposed to explain the characteristic lineshapes observed in scanning-tunneling-spectroscopy (STS)
experiments. Here we extend the theory of electron cotunneling to Kondo-lattice systems where the bulk hybridization between conduction and $f$ electrons is odd under inversion, being particularly relevant to Kondo insulators. Compared to the case of even hybridization, we show that the interference between normal tunneling and cotunneling processes is fundamentally altered: it is entirely absent for layered, i.e., quasi-two-dimensional materials, while its energy dependence is strongly modified for three-dimensional materials. We discuss implications for STS experiments.
Employing the $mathbf{k}cdotmathbf{p}$ expansion for a family of tight-binding models for SmB$_6$, we analytically compute topological surface states on a generic $(lmn)$ surface. We show how the Dirac-cone spin structure depends on model ingredients
and on the angle $theta$ between the surface normal and the main crystal axes. We apply the general theory to $(001)$, $(110)$, $(111)$, and $(210)$ surfaces, for which we provide concrete predictions for the spin pattern of surface states which we also compare with tight-binding results. As shown in previous work, the spin pattern on a $(001)$ surface can be related to the value of mirror Chern numbers, and we explore the possibility of topological phase transitions between states with different mirror Chern numbers and the associated change of the spin structure of surface states. Such transitions may be accessed by varying either the hybridization term in the Hamiltonian or the crystal-field splitting of the low-energy $f$ multiplets, and we compute corresponding phase diagrams.
For the strongly correlated topological insulator SmB6 we discuss the influence of a 2x1 reconstruction of the (001) surface on the topological surface states. Depending on microscopic details, the reconstruction can be a weak or a strong perturbatio
n to the electronic states. While the former leads to a weak backfolding of surface bands only, the latter can modify the surface-state dispersion and lead to a Lifshitz transition. We analyze the quasiparticle interference signal: while this tends to be weak in models for SmB6 in the absence of surface reconstruction, we find that the 2x1 reconstruction can induce novel peaks. We discuss experimental implications.
A fascinating type of symmetry-protected topological states of matter are topological Kondo insulators, where insulating behavior arises from Kondo screening of localized moments via conduction electrons, and non-trivial topology emerges from the str
ucture of the hybridization between the local-moment and conduction bands. Here we study the physics of Kondo holes, i.e., missing local moments, in three-dimensional topological Kondo insulators, using a self-consistent real-space mean-field theory. Such Kondo holes quite generically induce in-gap states which, for Kondo holes at or near the surface, hybridize with the topological surface state. In particular, we study the surface-state quasiparticle interference (QPI) induced by a dilute concentration of surface Kondo holes and compare this to QPI from conventional potential scatterers. We treat both strong and weak topological-insulator phases and, for the latter, specifically discuss the contributions to QPI from inter-Dirac-cone scattering.
