Unusual Length Dependence of Conductance of Some Oligomers

Recent experiment found a quantum length dependence of oligothiophene molecule conductance at low bias [Xu et al., nano Lett. \textbf{5}, 1491 (2005)], the long molecule has large conductance. By means of a first-principles method we obtain both the quantum length dependence of conductance at low bias and the classical length dependence of conductance at high bias region for oligothiophene. In between there is an oscillated conductance behavior. The transport behaviors are determined by the distinct electronic structures of the molecular compounds. The various conductance length dependence may appear for the organic compounds. Our further investigation finds that the classical conductance length dependence in polyphenanthrene dithiolates and another unusual conductance length dependence in polyacene ditholates: the quantum length dependence of conductance is at the high bias and the classical length dependence of conductance is at the low bias.