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Seminar: Analyzing ARPES data on a Fermi surface crossing pass

Prof. Konrad Matho
Institut Néel, Grenoble, France

Time: 4 pm, Sep 21th, 2023

Place: East 4 teaching building, Room 242

Bio:  Prof. Konrad Matho studied in Göttingen, Berlin and Grenoble, participated in the French-German cooperation on large instruments in Grenoble and became a French civil servant in the CNRS, until retirement in 2007. He is a theorist working on strong electron correlation and has done many works in the field of strong electron correlation. He is one of the main initial organizers of the now-popular conference CORPES (international conference for electron correlation and angle-resolved photoemission spectroscopy). 

Many-body correlations are commonly extracted from ARPES data via the sudden approximation. This framework involves a square matrix G(k,w) of Green functions in thermal equilibrium and a column vector M of dipolar matrix elements, defining a scalar, complex function G(k,w)=M+G M. The intrinsic, k-resolved spectral function is derived from Im(G), taking the limit Im(w) -> 0. The exact matrix G being unknown for any quantum model of interest for material science, an ansatz for the scalar G has to be made. The principle of causality requires G to be holomorphic as function of w in the two open half plains where Im(w) is finite and has a definite sign. A causal ansatz obeys the criterion sgn(Im(G(w)))=-sgn(Im(w)), called the Herglotz property. The real w-axis does not belong to either domain of analyticity but forms the boundary between them. By analytical continuation onto the boundary and beyond, one encounters singularities that influence the physical spectrum more or less, depending on their distance from the boundary. 

A point k=kF on the Fermi surface (FS) is characterized by a singularity in the analytic continuation of G(kF,w), positioned exactly at w=0. Since thermal broadening already pushes the singularity beyond the boundary, a FS is only sharply defined at temperature T=0. The analytical structure of G(k,w) is constrained by the hermiticity of the self energy, combined with the Herglotz property. In particular, the spectral intensity at the Fermi edge diverges for k=kF but drops to zero for other points k in the Brillouin zone.

Assuming T=0, the singular behavior expected on a FS crossing path is still masked in the ARPES data by extrinsic broadening. Two sources of broadening can be modeled analytically: (i) The convolution with a Lorentzian noise spectrum of half width dL is obtained by evaluating the holomorphic G(k,w) at a distance dL from the real w-axis. A well known example is the Voigt profile, derived from the same holomorphic function as the unconvoluted Gaussian, in this case the complex error function. (ii) The finite angular resolution of ARPES is modeled by convoluting G(k,w) with a smooth distribution k+Dk, centered on the nominal momentum k. Mechanisms (i) and (ii) cap the divergence in different ways. By systematically increasing their strength, either independently or in combination, a surprising variety of line shapes is generated. This allows to assess, whether the experimental resolution is sufficient to have confidence in the many-body parameters extracted from the data, particularly near a fixed point of strong correlations.

To generate various line shapes, an ansatz for the intrinsic G(k,w) at T=0 is made, using the two band periodic Anderson model [1]. An isolated pole is assumed as singularity, causing a Fermi liquid scenario. Other singularities, causing non-FL scenarios, are briefly reviewed [2-4].

[1] A. Generalov et al., Phys. Rev. B 95, 184433 (2017)
[2] K. Matho and A. Mueller, Physica C 317–318, 585 (1999)
[3] K. Matho, J. of Phys. & Chem. of Solids, 56, No. 12, 1735 (1995)
[4] J. W. Allen et al., , J. of Phys. & Chem. of Solids, 56, No. 12, 1849 (1995)