Hubbard Model in Materials Science: Electrical Conductivity and Reflectivity of Models of Some 2D Materials

The Hubbard Model: Basic Ideas and Some Results

“…This section contains various examples of results obtained by using the HM, taken from previous work of the present author (such as refs and ).…”

“…The final expression for the electrical conductivity of a 1D system is within the memory function method given by ref : σ R ( ω 0 ) = ( 1 / 2 χ 0 ) ( ω P 2 / π ) false[ ω 0 2 − false( b t false) 2 false] − 1 ( U t / N 2 ) 2 × S and the symbol S denotes the following function: .25ex2ex S = 42.49916 × false( 1 + exp ( β false( prefix− μ − 2 t false) ) false) − 2 + 78.2557 × false( 1 + exp ( β false( prefix− μ + 2 t cos ( 1 + π ) false) ) false) − 2 + ( b t / false( ω 0 + b t false) …”

“…The chemical potential of the electron gas on a 1D lattice is given by μ = false( β t false) 6 ( n s − 1 ) | t | 1.1029 + .1694 false( β t false) 2 + .0654 false( β t false) 4 where n is the filling factor of the lattice, N the number of sites in the lattice, and b a numerical constant.…”

“…The final expression for the electrical conductivity of a 1D system is within the memory function method given by ref ( 8 ): and the symbol S denotes the following function: where b = −4 × [1 + cos(1 – π)], μ denotes the chemical potential of the electron gas on a 1D lattice, s is the lattice constant, and L = N × s is the length of the specimen. The imaginary part of the conductivity is given by and …”

“…The chemical potential of the electron gas on a 1D lattice is given by 8 where n is the filling factor of the lattice, N the number of sites in the lattice, and b a numerical constant.…”