Matthias Geilhufe


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Works at Nordic Institute for Theoretical Physics
Visiting address Roslagstullsbacken 23, hus 13
Postal address Nordiska institutet för teoretisk fysik 106 91 Stockholm

About me

Group Theory Book

A course on group theory in solid state physics and photonics together with a detailed description about the application of  our Mathematica group theory package GTPack can be found in our book Group Theory in Solid State Physics and Photonics: Problem Solving with Mathematica. The book contains hands-on examples covering basic group theory to advanced applications.

W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics: Problem Solving with Mathematica, Wiley-VCH, ISBN: 978-3-527-41133-7, 2018

More information about the book and the Mathematica group theory package GTPack can be found at

Research Interests

Materials informatics and Organic Materials Database

We have developed the Organic Materials Database - OMDB, transfering methodology from data science into functional materials research. The OMDB hosts, electronic, crystal, and magnetic structure information of more than 32,000 previously synthesized organic molecular crystals and metal organic frameworks which were obtained by means of high throughput calculations. The OMDB is free to use and contains advanced pattern matching functionality and machine learning based property prediction tools.

The OMDB can be accessed via

Selected publications:

Symmetry Principles of Quantum Matter

Quantum matter describes a class of phenomena where quantum effects remain dominant over a wide range of energy and length scales. The realization of quantum matter is typically strongly bound to symmetry, symmetry breaking, and topology. I apply and develop group theory based methodology to investigate quantum matter in the static and time domain, with particular focus on Dirac materials and superconductors.

Selected publications:

  • R. M. Geilhufe and  W.  Hergert, GTPack:   A  Mathematica  Group  Theory  Package  for Application  in  Solid-State  Physics  and  Photonics,  Frontiers  in  Physics, 6,  86  (2018)
  • R. M. Geilhufe and A. V. Balatsky, Symmetry analysis of odd- and even-frequency superconducting gap symmetries for time-reversal symmetric interactions, Physical Review B, 97, 024507 (2018)

Full list of publications

Full list of publications can be found at google scholar.


A selection from Stockholm University publication database
  • 2019. Anna Pertsova (et al.). Physical Review B 99 (20)

    We present the result of an ab initio search for new Dirac materials among inverse perovskites. Our investigation is focused on the less studied class of lanthanide antiperovskites containing heavy f-electron elements in the cation position. Some of the studied compounds have not yet been synthesized experimentally. Our computational approach is based on density functional theory calculations which account for spin-orbit interaction and strong correlations of the f-electron atoms. We find several promising candidates among lanthanide antiperovskites which host bulk Dirac states close to the Fermi level. Specifically, our calculations reveal massive three-dimensional Dirac states in materials of the class A(3)BO, where A=Sm, Eu, Gd, Yb, and B=Sn, Pb. In materials with finite magnetic moment, such as Eu3BO (B=Sn, Pb), the degeneracy of the Dirac nodes is lifted, leading to appearance of Weyl nodes.

  • 2019. R. Matthias Geilhufe, Francisco Guinea, Vladimir Juričić. Physical Review B 99 (2)

    We propose a class of topological metals, which we dub Hund nodal line semimetals, arising from the strong Coulomb interaction encoded in the Hund's coupling between itinerant electrons and localized spins. We here consider a particular twisted spin configuration, which is realized in the double-exchange model which describes the manganite oxides. The resulting effective tetragonal lattice of electrons with hoppings tied to the local spin features an antiunitary nonsymmorphic symmetry that, in turn, together with another nonsymmorphic but unitary glide-mirror symmetry, protects crossings of a double pair of bands along a high-symmetry line on the Brillouin zone boundary. We also discuss the stability of Hund nodal line semimetals with respect to symmetry breaking arising from various perturbations of the twisted phase. Our results motivate further studies of other realizations of this state of matter, for instance, in different spin backgrounds, properties of its drumhead surface states, as well as its stability to disorder and interactions among the itinerant electrons.

Show all publications by Matthias Geilhufe at Stockholm University

Last updated: January 8, 2020

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