# 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).

**Abstract**

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].

**References**

[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)