coherent potential approximation

In the context of calculations of the electronic structure of materials, the coherent potential approximation is frequently combined with the Korringa–Kohn–Rostoker (KKR) formulation of density functional theory (DFT) to describe the electronic structure of systems with lattice-based disorder, such as substitutional alloys and magnetic materials at finite temperature.{{Cite journal |last=Ebert |first=H |last2=Ködderitzsch |first2=D |last3=Minár |first3=J |date=2011-09-01 |title=Calculating condensed matter properties using the KKR-Green's function method—recent developments and applications |url=https://iopscience.iop.org/article/10.1088/0034-4885/74/9/096501 |journal=Reports on Progress in Physics |volume=74 |issue=9 |pages=096501 |doi=10.1088/0034-4885/74/9/096501 |issn=0034-4885}}{{Cite book |last=Faulkner, Stocks, Wang |first= |title=Multiple Scattering Theory: Electronic structure of solids |date=December 2018 |publisher=IoP Publishing |isbn=978-0-7503-1490-9 |location=Bristol, UK |doi=10.1088/2053-2563/aae7d8}} The KKR formulation of DFT is also sometimes referred to as multiple scattering theory (MST). When the KKR formulation of DFT is combined with the CPA, it is sometimes referred to as the KKR-CPA.

The KKR formulation of DFT rephrases the usual eigenvalue-eigenvector problem (i.e. solving some effective Schrödinger equation) into an electronic scattering problem.{{Cite book |last=Faulkner |first=J S |url=https://doi.org/10.1088/2053-2563/aae7d8 |title=Multiple Scattering Theory |last2=Stocks |first2=G Malcolm |last3=Wang |first3=Yang |date=2018-12-01 |publisher=IOP Publishing |isbn=978-0-7503-1490-9 |doi=10.1088/2053-2563/aae7d8}} It does so by partitioning the one-electron potential of DFT into a collection of spatially-localised potentials around each ionic site, before considering an electron propagating through the system and scattering from these localised potentials. In this manner, the Green's function of the system is obtained. In a system where there is lattice-based disorder (for example, in a substitutional alloy) the CPA provides a means by which to average multiple potentials associated with a single lattice site and obtain an average Green's function (and consequent electron density) in a physically meaningful way. Although the approach was originally formulated for potentials described within either the muffin tin or atomic sphere approximations (where the spatially localised potential is assumed spherically symmetric) it is now commonplace to use so-called full-potential calculations,{{Cite journal |last=Asato |first=M. |last2=Settels |first2=A. |last3=Hoshino |first3=T. |last4=Asada |first4=T. |last5=Blügel |first5=S. |last6=Zeller |first6=R. |last7=Dederichs |first7=P. H. |date=1999-08-15 |title=Full-potential KKR calculations for metals and semiconductors |url=https://link.aps.org/doi/10.1103/PhysRevB.60.5202 |journal=Physical Review B |volume=60 |issue=8 |pages=5202–5210 |doi=10.1103/PhysRevB.60.5202}} where the one-electron potential can have arbitrary spatial dependence.

The KKR-CPA has been used with success to study the physics of a variety of alloy systems,{{Cite journal |last=Gonis |first=Antonios |last2=Butler |first2=W. H. |last3=Stocks |first3=G. M. |date=1983-05-09 |title=First-Principles Calculations of Cluster Densities of States and Short-Range Order in ${\mathrm{Ag}}_{c}{\mathrm{Pd}}_{1\ensuremath{-}c}$ Alloys |url=https://link.aps.org/doi/10.1103/PhysRevLett.50.1482 |journal=Physical Review Letters |volume=50 |issue=19 |pages=1482–1485 |doi=10.1103/PhysRevLett.50.1482}}{{Cite journal |last=Johnson |first=D. D. |last2=Nicholson |first2=D. M. |last3=Pinski |first3=F. J. |last4=Gyorffy |first4=B. L. |last5=Stocks |first5=G. M. |date=1986-05-12 |title=Density-Functional Theory for Random Alloys: Total Energy within the Coherent-Potential Approximation |url=https://link.aps.org/doi/10.1103/PhysRevLett.56.2088 |journal=Physical Review Letters |volume=56 |issue=19 |pages=2088–2091 |doi=10.1103/PhysRevLett.56.2088}}{{Cite journal |last=Stocks |first=G. M. |last2=Butler |first2=W. H. |date=1982-01-04 |title=Mass and Lifetime Enhancement due to Disorder on ${\mathrm{Ag}}_{c}{\mathrm{Pd}}_{1\ensuremath{-}c}$ Alloys |url=https://link.aps.org/doi/10.1103/PhysRevLett.48.55 |journal=Physical Review Letters |volume=48 |issue=1 |pages=55–58 |doi=10.1103/PhysRevLett.48.55}}{{Cite journal |last=Gyorffy |first=B. L. |last2=Stocks |first2=G. M. |date=1983-01-31 |title=Concentration Waves and Fermi Surfaces in Random Metallic Alloys |url=https://link.aps.org/doi/10.1103/PhysRevLett.50.374 |journal=Physical Review Letters |volume=50 |issue=5 |pages=374–377 |doi=10.1103/PhysRevLett.50.374}} including those where disorder is only present on one sub-lattice{{Cite journal |last=Pindor |first=A J |last2=Temmerman |first2=W M |last3=Gyorffy |first3=B L |date=March 1983 |title=KKR CPA for two atoms per unit cell: application to Pd and PdAg hydrides |url=https://iopscience.iop.org/article/10.1088/0305-4608/13/8/009 |journal=Journal of Physics F: Metal Physics |volume=13 |issue=8 |pages=1627–1644 |doi=10.1088/0305-4608/13/8/009 |issn=0305-4608}}{{Cite journal |last=Long |first=N H |last2=Ogura |first2=M |last3=Akai |first3=H |date=2009-02-11 |title=New type of half-metallic antiferromagnet: transition metal pnictides |url=https://iopscience.iop.org/article/10.1088/0953-8984/21/6/064241 |journal=Journal of Physics: Condensed Matter |volume=21 |issue=6 |pages=064241 |doi=10.1088/0953-8984/21/6/064241 |issn=0953-8984}} (the 'inhomogeneous' CPA). In addition, it has been shown that the CPA can very effectively describe magnetism at finite temperature, by considering (weighted) averages taken over all possible spin orientations. This is referred to as the 'disordered local moment' (DLM) picture{{Cite journal |last=Pindor |first=A J |last2=Staunton |first2=J |last3=Stocks |first3=G M |last4=Winter |first4=H |date=May 1983 |title=Disordered local moment state of magnetic transition metals: a self-consistent KKR CPA calculation |url=https://iopscience.iop.org/article/10.1088/0305-4608/13/5/012 |journal=Journal of Physics F: Metal Physics |volume=13 |issue=5 |pages=979–989 |doi=10.1088/0305-4608/13/5/012 |issn=0305-4608}}{{Cite journal |last=Staunton |first=J. |last2=Gyorffy |first2=B.L. |last3=Pindor |first3=A.J. |last4=Stocks |first4=G.M. |last5=Winter |first5=H. |date=November 1984 |title=The “disordered local moment” picture of itinerant magnetism at finite temperatures |url=https://doi.org/10.1016/0304-8853(84)90367-6 |journal=Journal of Magnetism and Magnetic Materials |volume=45 |issue=1 |pages=15–22 |doi=10.1016/0304-8853(84)90367-6 |issn=0304-8853}} and can be used to describe the ferromagnetic phase transition in metals.{{Cite journal |last=Gyorffy |first=B L |last2=Pindor |first2=A J |last3=Staunton |first3=J |last4=Stocks |first4=G M |last5=Winter |first5=H |date=June 1985 |title=A first-principles theory of ferromagnetic phase transitions in metals |url=https://iopscience.iop.org/article/10.1088/0305-4608/15/6/018 |journal=Journal of Physics F: Metal Physics |volume=15 |issue=6 |pages=1337–1386 |doi=10.1088/0305-4608/15/6/018 |issn=0305-4608}}

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Category:Wave mechanics

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