The standard model of particle physics describes all the known elementary particles, like electrons and quarks. Many of these particles have analogs in condensed matter, where they arise as collective states, or quasiparticles. One example is an electronic state in graphene that behaves like a massless Dirac fermion—a spin-1/2 particle that is not its own antiparticle. But condensed-matter physics may offer a longer list of “elementary particles” than found in the standard model. This is due to the fact that—unlike fundamental particles—quasiparticles in solids are not constrained by so-called Lorentz invariance. A Lorentz-violating quasiparticle is one whose momentum-energy relation depends on the direction it travels. Three separate teams [1–3] have collected the first experimental evidence of quasiparticles called type-II Dirac fermions, which break Lorentz invariance. These electronic states, which have no counterpart in the standard model, could be associated with a new type of superconductivity, which has potential applications in thermoelectric devices and quantum computing.
Relativistic quantum field theories provide the framework for our understanding of elementary particles. For many years now, physicists have turned to low-energy condensed-matter systems as a way to investigate quantum field theories without paying the steep price of a high-energy particle collider [4]. These studies have revealed a number of elementary excitations that—like the type-II Dirac fermions—appear in materials but are not present in the standard model. Recent examples include several topological phases [5–9], one of which is the so-called type-II Weyl fermion [9]. A Weyl fermion is a massless spin-1/2 particle whose antiparticle has the opposite chirality, or “handedness.” Weyl fermions have a close relationship to Dirac fermions: a Dirac fermion can be viewed as two superimposed Weyl fermions of opposite chirality that do not mix, because there are crystalline symmetry constraints. Weyl fermions have not been seen in particle physics, but in condensed matter, two different Weyl-like quasiparticles have been observed in the last couple of years. The first quasiparticle is an analog to the typical, or “type-I,” Weyl fermion of quantum field theory [9]. The other quasiparticle, called a type-II Weyl fermion [10], breaks Lorentz invariance in the same way as the type-II Dirac fermion.
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