Singular integrals over the Brillouin zone: the analytic-quadratic method for the density of states
- 30 September 1986
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 19 (27) , 5337-5364
- https://doi.org/10.1088/0022-3719/19/27/010
Abstract
A new and simple scheme for evaluating analytically singular integrals over the Brillouin zone which uses a local quadratic expansion is described. It is shown that the commonly used linear schemes of Jepsen and Andersen (1971) and of Lehmann and Taut (1972) converge only slowly in the vicinity of Van Hove singularities. Several examples are discussed. It is concluded that the new, quadratic, analytic scheme is at least an order of magnitude more efficient and is as simple to apply in practice as the linear scheme. The special case of the density of states is given in detail in this paper, the extension of general singular integrals is treated in a separate article.Keywords
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