Figure 3: Emergent fermions in Pentagon Carbon.
From: Three-dimensional Pentagon Carbon with a genesis of emergent fermions
Schematic of the band-crossing evolution in reciprocal space, from (a) a single isospin-1 triplet fermion point at the Brillouin zone centre, to (b) two triply degenerate fermion points along kz-axis (one on each side of Γ point), further to (c) two inter-connected (Hopf link) Weyl loops (with one Weyl loop being centered at Γ point, while the other loop crossing the first Brillouin zone boundary). In a,b, the red line along the kz-axis marks the (twofold) band degeneracy line protected by the fourfold screw-rotational symmetry. Note that the dispersion transverse to this line (that is, in kx–ky plane) is of quadratic type (which can be observed from Fig. 2). (d) The DFT band structure of 3D Pentagon Carbon under broken fourfold screw-rotational symmetry (with uniaxial strain of −1% along z-axis followed by 1% tensile strain along x-axis). The red (blue) dot indicates the crossing point of red (blue) circle in c with the kz-axis.
