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Most electronic properties of metals are determined solely by the low-energystates around the Fermi level, and for topological metals/semimetals, theselow-energy states become distinct because of their unusual energy dispersionand emergent pseudospin degree of freedom. Here, we propose a class ofmaterials which are termed as quadratic contact point (QCP) semimetals. Inthese materials, the conduction and valence bands contact at isolated points inthe Brillouin zone, around which the band dispersions are quadratic along allthree directions. We show that in the absence/presence of spin-orbit coupling,there may exist triply/quadruply-degenerate QCPs that are protected by thecrystalline symmetry. We construct effective models to characterize thelow-energy fermions near these QCPs. Under strong magnetic field, unlike theusual 3D electron gas, there appear unconventional features in the Landauspectrum. The QCP semimetal phase is adjacent to a variety of topologicalphases. For example, by breaking symmetries via Zeeman field or lattice strain,it can be transformed into a Weyl semimetal with Weyl and double Weyl points, aZ2 topological insulator/metal, or a Dirac semimetal. Via first-principlescalculations, we identify realistic materials Cu2Se and RhAs3 as candidates forQCP semimetals.

Quadratic contact point semimetal: Theory and material realization