Abstract
In the absence of Lorentz symmetry, the pseudospin-1 counterpart of the Weyl fermion (feroton) with linear dispersions and an exact flat band can emerge in condensed matter systems. The flat band branch of the feroton is equivalent to the longitudinal photon in Maxwell theory, which is a redundant degree of freedom due to the emergent (fermionic) gauge symmetry. Upon coupling to an external magnetic field, the fermionic gauge symmetry is broken and the flat band ferotons become gapless excitations characterized by Landau level indices (n > 1). In the long wavelength limit, these gapless modes are of the opposite chirality to the chiral anomaly related zero Landau level, which leads to much more plentiful magnetic transport properties. To further explore the novel properties of these gapless modes, we investigate the quantum oscillation through a generalized Lieb lattice model. We find an extra oscillating behavior which indicates the existence of these exotic gapless modes. We collect known ab initio calculation data from the literature and discuss the possibility of realizing the semi-metallic feroton gas in real materials.
Highlights
Spin-statistics connection for elementary particles which constitute our universe is a general relation based on the Lorentz symmetry of space-time [1, 2], while this relation is not necessary for elementary excitations in condensed matter because of the absence of Lorentz symmetry
In the absence of Lorentz symmetry, the pseudospin-1 counterpart of Weyl fermion with linear dispersions and an exact flat band can emerge in condensed matter systems
The flat band branch of feroton is equivalent to the longitudinal photon in Maxwell theory, which is a redundant degree of freedom due to the emergent gauge symmetry
Summary
Spin-statistics connection for elementary particles which constitute our universe is a general relation based on the Lorentz symmetry of space-time [1, 2], while this relation is not necessary for elementary excitations in condensed matter because of the absence of Lorentz symmetry. All gapless modes are below the chemical potential except for the chiral anomaly induced zero Landau level band, which gives a large negative magnetoresistance similar to that in the WSMs. At a finite Fermi energy, the transverse ferotons of the feroton semimetal in an external field exhibit a quantum oscillation of the DOS as that in WSMs [50]. To explore more exotic effects from the gapless modes, we study the ferotons on a cubic lattice where the perturbed quadratic term near a triply degenerate nodal point is two dimensional. In this case, there is no Landau gap between the n > 1 low energy Landau bands.
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