Effect of Long-Range Coulomb Interaction on NMR Shift in Massless Dirac Electrons of Organic Conductor

The nuclear magnetic resonance (NMR) with the site-dependent shift, at low temperatures is examined for a massless Dirac electrons in the organic conductor, alpha-(BEDT-TTF)_2I_3, where the sites of the four molecules in the unit cell are given by A (= A'), B, and C. The Dirac cone exists within an energy of 0.01 eV between the conduction and valence bands. The magnetic response function is calculated by taking account of the long-range Coulomb interaction and electron doping. Calculating the interaction within the first order in the perturbation, the chemical potential is determined self-consistently, and the self-energy and vertex corrections are taken to satisfy the Ward identity. The site-dependent shift is calculated at low temperatures of 0.0002 < T < 0.002 (T is temperature in the unit of eV) by correctly treating the wave function of the Dirac cone. At lower (higher) temperatures the self-energy (vertex) correction of the shift at all sites except for B is dominant and the sign is negative (positive), while the sign of the correction at the B site is always negative. For moderate doping, the shift as a function of T takes a minimum. The relevance of the shift to the experiment is discussed.