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Analytic structure of Bloch functions for linear molecular chains

Domenii publicaţii > Fizica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: E. Prodan

Editorial: Phys. Rev. B, 73, p.035128, 2006.


This paper deals with Hamiltonians of the form H=p^2/2m+v(r), with v(r) periodic along the z direction, v(x,y,z+b)=v(x,y,z), and x, y confined in a finite domain. The wave functions of H are the well-known Bloch functions phi_{n,lambda}(r), with the fundamental property phi_{n,lambda}(x,y,z+b)=lambda phi_{n,lambda}(x,y,z) and similar for the derivative. We give the generic analytic structure (i.e., the Riemann surface) of phi_{n,lambda}(r) and their corresponding energy E_n(lambda) as functions of lambda. We show that they are different branches of two multivalued analytic functions, with an essential singularity at lambda=0 and additional branch points, which are generically of order 1 and 3, respectively. We show where these branch points come from, how they move when we change the potential, and how to estimate their location. Based on these results, we give two applications: a compact expression of the Green’s function and a discussion of the asymptotic behavior of the density matrix for insulating molecular chains.

Cuvinte cheie: Bloch functions, periodic potentials, Wannier functions