ENHANCEMENT OF SUPERCONDUCTIVE CRITICAL TEMPERATURES IN ALMOST EMPTY OR FULL BANDS IN TWO DIMENSIONS: POSSIBLE RELEVANCE TO β-HfNCl, C60 AND MgB2

Abstract

We examine the possibility of enhancement of superconductive critical temperature in two-dimensions using the BCS theory. When the Fermi level is near an edge of a band the density of states (DOS) is not particularly high but k-dependent contribution to DOS (electron density on the Fermi surface) has a divergent peak at the bottom or top of the band (van Hove singularity). The attractive phonon-mediated interaction depends on q (momentum transfer) due to finite screening (non-local interaction). Enhancement of the critical temperatures is shown for the first time in this case. The results are qualitatively consistent with the superconductive behaviors of HfNCl (T c ≤ 25 K ) and ZrNCl (T c ≤ 15 K ), C 60 with a field-effect transistor configuration (T c = 52 K ), and MgB 2 (T c ≈ 40 K ) which have unexpectedly high critical temperatures.