In the presence of a perpendicular magnetic field, ABC-stacked trilayer graphene's chiral band structure supports a 12-fold degenerate N = 0 Landau level (LL). Along with the valley and spin degrees of freedom, the zeroth LL contains additional quantum numbers associated with the LL orbital index n = 0, 1, 2. Remote inter-layer hopping terms and external potential difference ∆B between the layers lead to LL splitting by introducing a gap ∆LL between the degenerate zeroenergy triplet LL orbitals. Assuming that the spin and valley degrees of freedom are frozen, we study the phase diagram of this system resulting from competition of the single particle LL splitting and Coulomb interactions within the Hartree-Fock approximation at integer filling factors. Above a critical value ∆ c LL of the external potential difference i,e, for |∆LL| > ∆ c LL , the ground state is a uniform quantum Hall state where the electrons occupy the lowest unoccupied LL orbital index. For |∆LL| < ∆ c LL (which corresponds to large positive or negative values of ∆B) the uniform QH state is unstable to the formation of a crystal state at integer filling factors. This phase transition should be characterized by a Hall plateau transition as a function of ∆LL at a fixed filling factor. We also study the properties of this crystal state and discuss its experimental detection.

Defect-induced magnetic moments are at the center of the research effort on spintronic applications of graphene. Here we study the problem of a nonmagnetic impurity in graphene with a new theoretical method, inhomogeneous cluster dynamical mean field theory (I-CDMFT), which takes into account interaction-induced short-range correlations while allowing long-range inhomogeneities. The system is described by a Hubbard model on the honeycomb lattice. The impurity is modeled by a local potential. For a large enough potential, interactions induce local antiferromagnetic correlations around the impurity and a net total spin 1 2 appears, in agreement with Lieb's theorem. Bound states caused by the impurity are visible in the local density of states (LDOS) and have their energies shifted by interactions in a spin-dependent way, leading to the antiferromagnetic correlations. Our results take into account dynamical correlations; nevertheless they qualitatively agree with previous mean-field and density functional theory (DFT) studies. Moreover, they provide a relation between impurity potential and on-site repulsion U that could in principle be used to determine experimentally the value of U .

The computation of transport coefficients, even in linear response, is a major challenge for theoretical methods that rely on analytic continuation of correlations functions obtained numerically in Matsubara space. While maximum entropy methods can be used for certain correlation functions, this is not possible in general, important examples being the Seebeck, Hall, Nernst and Reggi-Leduc coefficients. Indeed, positivity of the spectral weight on the positive real-frequency axis is not guaranteed in these cases. The spectral weight can even be complex in the presence of broken time-reversal symmetry. Various workarounds, such as the neglect of vertex corrections or the study of the infinite frequency or Kelvin limits have been proposed. Here, we show that one can define auxiliary response functions that allow to extract the desired real-frequency susceptibilities from maximum entropy methods in the most general multiorbital cases with no particular symmetry. As a benchmark case, we study the longitudinal thermoelectric response and corresponding Onsager coefficient in the single-band two-dimensional Hubbard model treated with dynamical mean-field theory (DMFT) and continuous-time quantum Monte Carlo (CTQMC). We thereby extend to transport coefficients the maximum entropy analytic continuation with auxiliary functions (MaxEntAux method), developed for the study of the superconducting pairing dynamics of correlated materials. PACS numbers: 71.27.+a, 72.10.-d, 72.10.Bg, 72.15.Jf, 72.20.Pa a. Introduction. Transport properties are of interest for both fundamental and applied purposes. For example, while thermoelectric power tells us about the nature of charge carriers, materials with large thermoelectric power could lead to various applications, including efficient conversion of heat loss into useful electricity [1 -7]. Unfortunately, computing transport coefficients from numerical results is no simple task. Usually, one starts by computing the corresponding response functions in Matsubara frequency using the Kubo formula. For quantum Monte-Carlo data in particular, the most direct way to extract the real-frequency dependent response functions is then to perform maximum entropy analytic continuations (MEACs) [8,9]. However, as we explain in more details below, MEAC is not always trivial since it requires that the spectral weight of response functions is real and positive, which is not necessarily the case in general.Many approaches have been investigated to circumvent this major problem for the Seebeck coefficient [10][11][12][13][14][15][16][17][18][19], the Hall coefficient [20-24] and the Nernst coefficient [25] for instance, but all of them are either approximations or analytic methods that are exact only in a certain frequency limit [26]. The most common approach consists in neglecting vertex corrections, in which case it is possible to compute transport coefficients directly from the single-particle spectral weight. This is not possible when vertex corrections are included, which seems to be a necessary step in...

Introduction Inhibition capabilities have been shown to be a strong predictor of social and educational life outcomes (Mischel & Ebbesen, 1970; Shoda et al., 1990). Inhibition capabilities have an enormous impact on attention and impulsivity (Bari & Robbins, 2013). These two executive functions are associated with numerous psychiatric disorders but are not well understood in terms of white matter (WM) connectivity (Puiu et al., 2018). Novel techniques and statistical approaches in neuroimaging bring us closer to a biologically sustained model. Objectives This research aims to: 1) identify WM connections associated with attention/impulsivity performance and 2) characterize the differences in WM microstructure associated with the variation of the performance. Methods 157 children (GESTE cohort, 8-12 years, 27 Dx ADHD, 2 Dx ASD) with b=1500mm2/s, 2mm isotropic dMRI acquisitions were included. Tractography was performed with TractoFlow pipeline (Theaud et al., 2020). Dimensionality reduction of diffusion metrics yielded two components : microstructural complexity (DTI Metrics, AFD & NuFo) and axonal density (AFD_fixel) (Chamberland et al., 2019). Attention/impulsivity were evaluated with the CPT3. Multivariate linear regression was performed in python. Results Lower microstructural complexity was associated with poorer attentional performance on regions of the parietal lobe to the occipital gyrus (P-O, p=0.044, R2=0.14, Figure 1.) and the Broadman’s area 8 to area 6 (SF8-SF6, p=0.002, R2=0.12, Figure 1.). Lower axonal density was associated with a less impulsive pattern on SF8-SF6 (p=0.001, R2=0.13, Figure 1.). Results remained significant when removing children with an ADHD or ASD diagnosis. Conclusions We identified underlying difference in WM microstructure that may be associated with the variation in attention/impulsivity performance in school-aged children. Disclosure No significant relationships.