Topological Materials: New Fermions, Realization of Single Crystals and their Physical Properties

Project Information

TOPMAT

Grant agreement ID: 742068

DOI

10.3030/742068

Project closed

EC signature date 23 June 2017

Start date 1 July 2017

End date 30 June 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 070 000,00

EU contribution

€ 2 070 000,00

Coordinated by

MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Germany

Periodic Reporting for period 4 - TOPMAT (Topological Materials: New Fermions, Realization of Single Crystals and their Physical Properties)

Reporting period: 2022-01-01 to 2022-06-30

Summary of the context and overall objectives of the project

Topology, a mathematical concept, recently became a hot and truly transdisciplinary topic in condensed matter physics, solid state chemistry and materials science. Since there is a direct connection between real space: atoms, valence electrons, bonds and orbitals, and reciprocal space: bands, Fermi surfaces and Berry curvature, a simple classification of topological materials in a single particle picture is possible. Moreover, the properties of single crystals with particular topological electronic structures can mimic phenomena found in high energy physics and cosmology. New classes of quantum materials are found in insulators and semimetals that exhibit non-trivial topologies: they display a plethora of novel phenomena including: topological surface states; new Fermions such as Weyl, Dirac or Majorana; and non-collinear spin textures such as Skyrmions. A hallmark of many of these new quantum properties that are derived from fundamental symmetries of the bulk, is that they are topologically protected. A general scheme to identify all inorganic topological materials including novel Fermions, without high energy counterparts, was proposed that is based on the symmetries and the Wyckhoff positions of relevant space groups. The quantum chemistry approach was also applied to magnetic space groups, obstructed atomic insulators and to structures hosting flat bands, which allows to identify compounds with strong correlations. The translation of these theoretical concepts into realizable materials was one focus of this project. More than 150 different topological materials were synthesized as high-quality single crystals, and their properties were characterized with external stimuli such as temperature, and temperature gradients, light, high magnetic and electric fields, and high pressure, to tune topological phase transitions, electrical transport properties and surface states. There is a high potential to use topological materials for redox catalysis and for high-efficient thermoelectric energy conversion, while relativistic topological materials can serve as model systems for high energy physics and astrophysics via quasiparticles as models for axions, gravitational anomaly etc..

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

•All existing inorganic compounds (based on the symmetries and the Wyckhoff positions of relevant space groups) are theoretically classified into topological or trivial – prediction of new topological compounds including novel Fermions, Nature 2019,Science 2022.
•All centrosymmetric ferromagnets with crossing bands around the Fermi energy are Weyl semimetals or Weyl metals with potential for Hall sensors and large Nernst effect, all ferro- and ferrimagnetic cubic Heusler compounds and Kagome lattice were investigated, npj Comput Mater 2020.
•A giant anomalous Hall effect and a giant Nernst effect was identified in Co3Sn2S2 (Nature Physics 2018) and Co2MnGa ,NPG Materials Asia 2019, Phys. Rev. B 2019.
•Magnetic Weyl materials for high temperature quantum anomalous Hall effect (QAH) were identified including Co3Sn2S2, Fe3GeTe2 and MnAlGe, Advanced Materials 2021. Our scanning-tunneling-microscopy (STM) investigations have revealed that the Co3Sn terraces of Co3Sn2S2 show topological states confined to the edges, which display linear dispersion, Nature Communications 2021.
•All compounds with a known antiferromagnetic structure were theoretically classified into topological or trivial, Nature 2020 – new materials for thermoelectric applications with high power factor were identified in YbMnSb2 and YbMnBi2 , Advanced Materials 2021, Nature Materials 2022.
•Recently a 3D quantum Hall effect was realized by others in ZrTe5, we reproduced the results in ultraclean HfTe5 and have observed even a fractional QHE. In the Heusler compound YPtBi, we have strongly reduced the defect density to realize a zero Landau level already at low magnetic fields, Nature Communications 2020, Nature Communications 2021.
•Chiral new Fermions CoSi, PdGa and PtAl were synthesized and the predicted large chiral Fermi arcs were observed in ARPES and STM, Nature, Nature Physics 2019. Both enantiomers of PdGa were grown for the investigation of the maximal Chern number, Science 2021, and enantiomorphic recognition.
•Compounds with new Fermions were synthesized and characterized with giant chiral Fermi arcs and tested for catalysis ,Nature Physics 2019, Science 2020, npj Computational Materials 2021, Advanced Materials 2020.
•Axion as a quasiparticle was identified for the first time in Ta2Se8I – Nature 2019, Nature Physics 2021.
•New Skyrmion materials were identified in Mn2RhSn with a much lower moment than the anti-Skyrmion Mn2PtSn and in MnPtGa with a different crystal structure and composition.
•A high-pressure Hall measurement set up has been developed. Hall measurements under pressure were used to measure the phase diagram of the axion material Ta2Se8I, Physical Review Materials 2021.
•A single crystal platform with more than 150 compounds has been established within the project, see TOPMAT webpage, and more than 100 samples were sent to collaborators.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

We have characterized so-called 'new fermions' that have no corresponding analogues in high-energy physics. Compared to high- energy physics, symmetries can be broken in the solid. One of these symmetries is inversion symmetry, which is broken in chiral crystals. In a chiral material, the atoms follow a spiral, step-like pattern as in biological systems such as DNA. Single crystals were grown by either a self-flux method (PtAl, PtGa, PdGa) or a Bridgman technique (RhSi, CoSi), or by a chemical vapor transport method (CoSi): both enantiomers are available for PdGa. All crystals grow in the same space group (the P213 space group, no. 198), as MnSi and FeGe, which exhibit the B20 structure type and in which skyrmions were originally found.
While Dirac fermions are four-fold degenerate and Weyl fermions are two-fold degenerate, the new fermions can even show six and eight-fold degeneracies. The so-called Rarita–Schwinger fermion, which obeys the relativistic field equation for spin-3/2 fermions, and other multi-fold fermions were discovered as new kinds of quasi- particles in the materials RhSi, CoSi [Nature 2019], PtAl [Nature Physics 2019] PtGa [Nature Communication 2020] and PdGa [Science 2020] via ARPES. The band structures of the two enantiomers are identical while the phase of the wave function and the chirality of the Weyl points are mirror images of each other in the two enantiomers. The two Weyl crossing points lie at different energies in these systems. This leads to remarkable properties, including a giant circular photogalvanic current [Science Advances 2020], a chiral magnetic effect, and other transport and optical effects that are forbidden in Weyl semimetals. In addition, the electrons on the surfaces of these crystals exhibit a highly unusual helicoid structure that spirals around two high-symmetry momenta, and the complex band topology results in exceptionally long and robust Fermi arcs. The complex band topology of the two enantiomers leads to Fermi arcs, which are mirror images of each other. These materials will have a wider impact beyond physics, we are investigating them as materials for enantiomorphic recognition and catalysis (npj Computational Materials 2021, Advanced Materials 2020)

Two crystals grown by the Laser Otical Floating Zone method within the TOPMAT project