We construct a heavy fermion representation for twisted bilayer graphene (TBG) systems. Two local orbitals (per spin/valley) are analytically found, which exactly the maximally localized zero modes of continuum Hamiltonian near AA-stacking center. They have similar properties to Wannier functions found in recent study, but also clear interpretation as zeroth pseudo Landau levels (ZLL) Dirac fer...

In this paper we introduce strongly $left[  V_{2},lambda_{2},M,pright]-$summable double vsequence spaces via Orlicz function and examine someproperties of the resulting these spaces. Also we give natural relationshipbetween these spaces and $S_{lambda_{2}}-$statistical convergence.

We discuss relations between several known (some false, some open) conjectures on 3-edgeconnected, cubic graphs and how they all fit into the same framework related to cuts in matchings. We then provide a construction of 3-edge-connected digraphs satisfying the property that for every even subgraph E, the graph obtained by contracting the edges of E is not strongly connected. This disproves a r...

Enforcing a straight-line condition of the total energy upon removal/addition of fractional electrons on eigen states has been successfully applied to atoms and molecules for calculating ionization potentials and electron affinities, but fails for solids due to the extended nature of the eigen orbitals. Here we have extended the straight-line condition to the removal/addition of fractional elec...

An exciton is a quasiparticle in a solid-state system comprising an electron and a hole — the absence of an electron. It has an energy spectrum akin to that of the hydrogen atom, so it may be considered as an artificial hydrogen atom in a solid-state environment, with the hole playing the part of the proton. The concept of excitons has first been formulated in the early 1930s by Yakov Frenkel, ...

This thesis presents an efficient approach to calculate dynamical properties of solids with strong electron correlations. The fast cluster method, a socalled finite temperature Lanczos method is combined with the Dynamical mean-field theory (DMFT) in order to study orbital degenerate systems as function of temperature. The full local Coulomb interaction was taken into account in all calculation...