Phase diagram of a pseudogap Anderson model with application to graphene

Abstract

The Anderson model of an s-wave single-orbital correlated impurity placed on a noninteracting honeycomb lattice, a simplified model for studying an impurity on graphene, is used to investigate pseudogap Kondo problem. In this model, there are two quantum phases: the phase of free impurity local moment and the Kondo phase where this local moment is fully screened. The transition between these two phases is under investigation. The work focuses mostly on the case where the impurity is placed on top of a lattice site. In this case, the full phase diagram is constructed using three parameters: the Hubbard interaction U , the hybridization strength v0 and the impurity energy level d . The phase diagram exhibits linear (U c , c d ) phase boundary, the slope of which, as well as the critical value c d , depends strongly on v 2 0 . Further analysis shows that the real part of the self energy at zero frequency and the impurity occupancy can help to understand the behaviors of the phase boundaries. The dependence of the phase transition on the impurity position is briefly discussed, revealing difficulties that one needs to solve in order to realize the pseudogap Kondo model in the realistic graphene lattice.In the experimental aspect, the pseudogap Kondo model has been used to interpret reasonably a new type of QCPs that occurs in heavy fermion systems [8,22,27] or to study impurity local moment in unconventional superconductors [28]. However, the difficulty in realizing the model in experiments is the main issue that hinders the progress of research in this topic. Indeed there

Critical Behavior of a Correlated Impurity on Graphene

“…First, it allows for direct testing the possibility to realize the pseudogap Kondo physics on graphene. Second, our previous work [26] showed that for impurity on top of a carbon of the graphene lattice, the results are rather similar to those of the conventional pseudogap impurity model [16] at , thus the results presented in this work can be also applied to case. Following the above description, the Hamiltonian of this model is composed of three parts [26] which can be constructed in real space.…”

“…Second, our previous work [26] showed that for impurity on top of a carbon of the graphene lattice, the results are rather similar to those of the conventional pseudogap impurity model [16] at , thus the results presented in this work can be also applied to case. Following the above description, the Hamiltonian of this model is composed of three parts [26] which can be constructed in real space. The kinetic Hamiltonian of the host is written in the tight-binding form with only the nearest neighbor hopping :…”

“…1(a)]. At this position, the hybridization function [29,3], which describes the dynamics of electrons hopping between the impurity and the host material, is only different from the DOS of graphene by a prefactor [26]. As the DOS of graphene is linear in frequency around the Fermi level [24] [see Fig.…”

“…In general, the position of the impurity plays an important role in this hybridization, thus affecting the local physics of the impurity. However, in this work, we assume that the impurity position is on top of a site in the honeycomb lattice, which results in the hybridization function only different from the DOS of the graphene lattice by a prefactor [26]. The use of graphene as the host material is two-fold.…”

“…Throughout this work, we employ the hybridization expansion continuous-time Quantum Monte Carlo method (CT-HYB) [27][28][29] to treat the model, which is implemented in the TRIQS package [30,31]. CT-HYB is a nonzero-temperature method which can solve the model numerically exactly and has been proved to work rather well with pseudogap Anderson impurity models [11,12,26]. Compared with the numerical renormalization group (NRG) method [32], the disadvantages of the CT-HYB is that it is unable to go to low-temperature regime and is computationally demanding.…”