Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach
Elizaveta Safonova
Nanocenter CENN, Slovenia
Using an extension of Efetov’s supersymmetric formalism, we analytically investigate spectral properties of Lévy and Lévy–Rosenzweig–Porter random matrix ensembles with strongly non-Gaussian, power-law distributed off-diagonal elements. Employing a functional Hubbard–Stratonovich transformation, we compute the mean spectral density ρ(E) in the large-matrix limit and show that it depends sensitively on the control parameter governing the transition between ergodic and fractal (non-ergodic extended) phases, thus serving as an order parameter. We also derive the global density-of-states correlation function R(ω) in the non-ergodic extended phase across all relevant frequency ranges. At low frequencies it exhibits GUE-type oscillations damped at the Thouless scale ETh=ΔΓ/2π, while at high frequencies it matches cavity-approach results.
Related publications:
https://scipost.org/SciPostPhys.18.1.010
https://scipost.org/SciPostPhys.20.1.003
Anomalous Hall effect in rhombohedral graphene
Vera Mikheeva
Nanocenter CENN, Slovenia
Motivated by recent experiments on rhombohedral multilayer graphene and the discovery of the anomalous Hall effect in its spontaneous spin-valley polarized state, we theoretically investigate the Hall conductivity of this system. We consider two distinct regimes of disorder: weak dense impurities and sparse strong scatterers. Our analysis accounts for all key physical mechanisms contributing to the Hall effect. We include effects arising from the internal geometry of the energy bands as well as various types of asymmetric scattering processes, including complex interference effects between impurities. To describe the influence of strong impurities, we further incorporate non-Gaussian scattering mechanisms. Finally, we supplement our analytical results for the isotropic model with numerical calculations that account for the specific shape of the energy bands (trigonal warping), which is essential for understanding the low-energy properties of rhombohedral graphene.
Related publication:
arXiv:2510.20804