By Jian-Xin Zhu
The objective of this ebook is to supply an ordinary but systematic description of the Bogoliubov-de Gennes (BdG) equations, their certain symmetry homes and their relation to Green’s functionality thought. particularly, it introduces readers to the supercell strategy for the suggestions of the BdG equations, in addition to different similar recommendations for extra swiftly fixing the equations in functional applications.
The BdG equations are derived from a microscopic version Hamiltonian with an efficient pairing interplay and entirely trap the neighborhood digital constitution via self-consistent options through designated diagonalization. This technique has been effectively generalized to check many elements of traditional and unconventional superconductors with inhomogeneities – together with defects, ailment or the presence of a magnetic box – and turns into a fair extra beautiful selection whilst the first-principles details of a regular superconductor is included through the development of a low-energy tight-binding version. additional, the lattice BdG process is key whilst theoretical effects for neighborhood digital states round such defects are in comparison with the scanning tunneling microscopy measurements.
Altogether, those lectures supply a well timed primer for graduate scholars and non-specialist researchers, whereas additionally delivering an invaluable reference advisor for specialists within the field.
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Additional resources for Bogoliubov-de Gennes Method and Its Applications
R/ Á ! 67) and EnQ2 Á EnQ1 . This property has a significant consequence. , Eq. 60), instead of both Eqs. 61), and obtain all information essential for the measurable. It saves the computational time significantly, which is desirable for the real-space inhomogeneous or disordered problems, even in a collinear spin-polarization. Note again here that this simplification exists in the absence of the spin-orbit coupling and other spin-flip scattering terms in the Hamiltonian. However, a more general symmetry property, as will be shown in the next chapter, can be derived even in the presence of these terms.
Ri ; t/ e2 D e ! ri ; t/; JxP . ri /i : ! / D N! q; t/; JxP . q; t0 /i ie2 hKx i : ! 82) 50 2 BdG Equations in Tight-Binding Model Since the correlation function in Eq. q; t/; JxP . q; 0/i N! 0 ! q; t/; JxP . q; 0/i C hKx i i! / C hKx i ; i! q; t/; JxP . 85) The frequency-dependent, uniform electrical conductivity is given by taking the limit q ! / C hKx i : i! 86) The dc conductivity is obtained by taking first the limit q ! 0 and then the limit ! 0. 0 i! 87) Be reminded that the order of these limits cannot be reversed.
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Bogoliubov-de Gennes Method and Its Applications by Jian-Xin Zhu