Observation of triple-point Fermions

Credit: Hugo Dil (EPFL)

Credit: Hugo Dil (EPFL)

An international study, led by EPFL, has discovered a material that gives rise to rare, “triple-point” Fermions. The researchers have been able, for the first time, to identify the spins associated with them.

Fermions can either exist as individual particles, like electrons, protons, and neutrons, or as so-called quasiparticles. The latter are composed of many components, but behave like a single fermion particle. What characterises fermions is that their spin, or intrinsic magnetic moment, has a value of ½ and that they obey the Pauli exclusion principle; i.e. two particles with the same spin can’t occupy the same state and place.

As a result, fermionic states can be single (one spin) or degenerate (both spins). If fermion states cross they can thus either form four fermions (Dirac equation) or two fermions (Weyl equation), and these are the only options for free particles. But in crystals, and only under special circumstances, the possibility of three fermions crossing was recently predicted.

This intermediate state can then change into either a Dirac- or Weyl-type system depending on external influences. But how can the fermions’ spins wind around such a special triple point?

Now, a collaboration of scientists from the Paul Scherrer Institute, EPFL’s School of Basic Sciences, and others, has studied a material, Germanium telluride (GeTe), in which this “triple point” phenomenon could be experimentally verified. Although this is the second ever material where such triple fermions were found, the group have been able, for the first time, to identify the spin winding around it. The study is published in Physical Review Letters.

“Our study confirms that the special symmetries available in crystals leads to the existence of fermions that are not permitted as free particles,” says Professor Hugo Dil at EPFL. “On top of this, it allows us to study their novel, special properties. These triple, and related, Fermions are expected to play an important role in future topologically protected quantum computations.”

Transition between Dirac, triple, and Weyl Fermions. The colours indicate the spin of the state. Credit: Hugo Dil (EPFL).

Other contributors

  • University of West Bohemia
  • P. J. Šafárik University in Košice (Slovakia)
  • Tsinghua University (Beijing)
  • CY Cergy Paris Université (France)
  • Polish Academy of Sciences
  • National Technical University “KhPI” (Ukraine)
  • Masaryk University (Czech Republic)
  • Johannes Kepler Universität (Austria)

Swiss National Science Foundation (SNSF)

Austrian Science Fund (FWF)

Ministry of Education, Youth and Sports of Czech Republic

Czech Science Foundation (GACR)

Internal Research Grant System

Foundation for Polish Science (IRA Program of EU)

European Regional Development Fund (CEITEC Nano+)


Juraj Krempaský, Laurent Nicolaï, Martin Gmitra, Houke Chen, Mauro Fanciulli, Eduardo B. Guedes, Marco Caputo, Milan Radović, Valentine V. Volobuev, Ondřej Caha, Gunther Springholz, Jan Minár, J. Hugo Dil. Phys. Rev. Lett. 126, 206403, 17 May 2021. DOI: 10.1103/PhysRevLett.126.206403