Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential

Abstract

For a reliable fully-relativistic Korringa-Kohn-Rostoker Green function method, an accurate solution of the underlying single-site scattering problem is necessary. We present an extensive discussion on numerical solutions of the related differential equations by means of standard methods for a direct solution and by means of integral equations. Our implementation is tested and exemplarily demonstrated for a spherically symmetric treatment of a Coulomb potential and for a Mathieu potential to cover the full-potential implementation. For the Coulomb potential we include an analytic discussion of the asymptotic behaviour of irregular scattering solutions close to the origin ($r\ll 1$).

16 pages, 6 figures, preprint

References in corpus (1)

• Onset of Magnetic Order in Strongly-Correlated Systems from ab initio Electronic Structure Calculations: Application to Transition Metal Oxides

Cited by in corpus (22)

• Prediction and observation of the first antiferromagnetic topological insulator
• Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects
• Topological magnetic materials of the (MnSb${}_2$Te${}_4$)$\cdot$(Sb${}_2$Te${}_3$)${}_n$ van der Waals compounds family
• Spectroscopic perspective on the interplay between electronic and magnetic properties of magnetically doped topological insulators
• Fully relativistic multiple scattering calculations for general potentials
• Impurity states in the magnetic topological insulator V:(Bi,Sb)${}_2$Te${}_3$
• When superconductivity does not fear magnetism: Insight into electronic structure of RbEuFe${}_4$As${}_4$
• Dynamic electron-phonon and spin-phonon interactions due to inertia
• Thickness-dependent electronic and magnetic properties of ${\gamma }^{\prime }$-Fe${}_4$N atomic layers on Cu(001)
• Exchange scaling of ultrafast angular momentum transfer in 4$f$ antiferromagnets
• Impact of oxygen doping and oxidation state of iron on the electronic and magnetic properties of BaFeO$_{3-δ}
• The effect of hydrostatic pressure and uniaxial strain on the electronic structure of Pb${}_{\text{1-x}}$Sn${}_{\text{x}}$Te
• Ab initio design of quaternary Heusler compounds for reconfigurable magnetic tunnel diodes and transistors
• Deterministic control of an antiferromagnetic spin arrangement using ultrafast optical excitation
• Instability of the topological surface state in Bi${}_2$Se${}_3$ upon deposition of gold
• First-principles investigations of the magnetic phase diagram of Gd${}_{1-x}$Ca${}_x$MnO${}_3$
• Large Tunneling Anisotropic Magnetoresistance mediated by Surface States
• Spin waves in alloys at finite temperatures: application for FeCo magnonic crystal
• Quantum Magnetic Properties in Perovskite with Anderson Localized Artificial Spin-1/2
• Topological insulator in a helicoidal magnetization field
• A full-potential approach to the relativistic single-site Green's function
• Eigenmodes of a disordered FeCo magnonic crystal at finite temperatures