Electronic Structure of a Single-Component Molecular Conductor [Pd(dddt)$_2$] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) under High Pressure

We examined high-pressure electronic structure of a single-component molecular conductor [Pd(dddt)$_2$] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) at room temperature, based on the crystal structure determined by single crystal synchrotron X-ray diffraction measurements at 5.9 GPa. The monoclinic unit cell contains four molecules that form two crystallographically independent molecular layers. A tight-binding model of 8 $times$ 8 matrix Hamiltonian gives an electronic structure as a Dirac electron system. The Dirac point describes a loop within the first Brillouin zone, and a nodal line semimetal is obtained. The noticeable property of the Dirac cone with a linear dispersion is shown by calculating density of states (DOS). The Dirac cone in this system is associated with the crossing of HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) bands, which originates from the direct interaction between different molecular layers. This is a newly found mechanism in addition to the indirect one [J. Phys. Soc. Jpn., {bf 86}, 064705 (2017)]. The Dirac points emerge as a line, when the HOMO and LUMO bands meet on the surface and the HOMO-LUMO couplings are absent. Such a mechanism is verified using a reduced model of 4 $times$ 4 matrix Hamiltonian. The deviation of the band energy ($delta E$) at the Dirac point from the Fermi level is very small ($delta E < $ 0.4meV). The nodal line is examined by calculating the parity of the occupied band eigen states at TRIM (Time Reversal Invariant Momentum) showing that the topological number is 1.