Self-Consistent Average Green's Function in Random Lattices: A Generalized Coherent-Potential Approximation (n) and Its Diagrammatic Equivalents

1971 ◽  
Vol 4 (12) ◽  
pp. 4354-4363 ◽  
Author(s):  
B. G. Nickel ◽  
J. A. Krumhansl
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Coherent Potential Approximation ◽  
Potential Approximation ◽  
Random Lattices ◽  
Self Consistent

scholarly journals Many-impurity scattering on the surface of a topological insulator

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
José Luis Hernando ◽  
Yuriko Baba ◽  
Elena Díaz ◽  
Francisco Domínguez-Adame
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Topological Insulator ◽  
Disordered Systems ◽  
Spectral Properties ◽  
Random Distribution ◽  
Surface States ◽  
Impurity Scattering ◽  
Self Consistent ◽  
The Impact

AbstractWe theoretically address the impact of a random distribution of non-magnetic impurities on the electron states formed at the surface of a topological insulator. The interaction of electrons with the impurities is accounted for by a separable pseudo-potential method that allows us to obtain closed expressions for the density of states. Spectral properties of surface states are assessed by means of the Green’s function averaged over disorder realisations. For comparison purposes, the configurationally averaged Green’s function is calculated by means of two different self-consistent methods, namely the self-consistent Born approximation (SCBA) and the coherent potential approximation (CPA). The latter is often regarded as the best single-site theory for the study of the spectral properties of disordered systems. However, although a large number of works employ the SCBA for the analysis of many-impurity scattering on the surface of a topological insulator, CPA studies of the same problem are scarce in the literature. In this work, we find that the SCBA overestimates the impact of the random distribution of impurities on the spectral properties of surface states compared to the CPA predictions. The difference is more pronounced when increasing the magnitude of the disorder.

THE SELF CONSISTENT COHERENT POTENTIAL APPROXIMATION TO THE HUBBARD MODEL

1990 ◽  
Vol 04 (08) ◽  
pp. 549-560 ◽  
Author(s):  
MASSIMO CORRIAS
Keyword(s):  
Hubbard Model ◽  
Interaction Strength ◽  
Exact Formula ◽  
Coherent Potential Approximation ◽  
The Self ◽  
Potential Approximation ◽  
Double Occupancy ◽  
Occupancy Probability ◽  
Self Consistent

We introduce, by an exact formula for the double occupancy probability δ in the Hubbard model, a self consistent version of the CPA which is aimed at taking into better account correlations of the electrons motion. We show that CPA breaks down at large values of the interaction strength, and we suggest a way of overcoming this limitation along the lines of the model proposed here.

Sign in / Sign up

Export Citation Format

Share Document