Charge-density-wave (CDW) and spin-density-wave (SDW) instabilities are direct manifestations of collective electron behaviour in metals. Determining whether an instability is driven by Fermi-surface geometry, orbital-selective scattering, or momentum-dependent electron-phonon coupling remains material dependent. The standard diagnostic, the static electronic susceptibility χ(q), is commonly evaluated as a Lindhard sum over Kohn-Sham eigenvalues, which neglects orbital structure and can be sensitive to smearing and interpolation. This project develops, validates, and applies a first-principles framework for bare and interacting longitudinal susceptibility using Green's functions within the full-potential linear muffin-tin orbital (FP-LMTO) code RSPt, following Katsnelson and Lichtenstein [1] and the magnetic-response formalism of Sandratskii and Kübler [2].
The workflow has three stages. First, self-consistent FP-LMTO calculations (RSPt, PBE96) are performed on dense Brillouin-zone meshes for non-spin-polarised and collinear spin-polarised reference states. Because the response calculation samples the full Brillouin zone without symmetry reduction, the potential and mesh require higher convergence than conventional total-energy calculations. Second, site- and orbital-resolved Matsubara Green's functions are multiplied in real space and summed over 1024–1200 Matsubara frequencies to obtain the spin-resolved bare susceptibility χ⁰σ(R) for neighbour clusters extending to several lattice parameters. This is the dominant computational stage, scaling with k-points, Matsubara frequencies, and neighbour pairs. Third, χ⁰σ(R) is Fourier transformed to reciprocal space, and interacting longitudinal spin (χzz) and charge (χnn) responses are obtained from the RPA Dyson equation K = (I − XU)⁻¹X at each q.
The scientific objectives are: (1) validate the framework for CDW systems 2H-NbSe₂ [3,4] and LaTe₃, the SDW metal bcc Cr [5,6], FeSe, and bcc Fe as a Stoner control; (2) extend the method to magnetically ordered reference states, including G-type AFM Cr and stripe-(π,0) AFM FeSe, requiring substantially larger supercells; (3) resolve incommensurate response features, where a displacement δ from a high-symmetry point requires real-space bubbles extending approximately R ≈ a/δ and correspondingly dense meshes; and (4) apply the validated framework to challenging materials, including BaFe₂Al₉, whose first-order CDW has been associated with Fermi-surface nesting [7], together with GdTe₃ and CaFe₂As₂.
A key feature is that χ⁰ is retained in its orbital indices. This enables direct identification of orbital-selective response: bcc Cr and FeSe show predominantly diagonal contributions, whereas 2H-NbSe₂ is dominated by off-diagonal orbital-mixing terms, information not accessible from the projected density of states or Fermi surface alone.