Electric conductivity of the line-centered honeycomb lattice

Abstract

The line-centered honeycomb (LCH) lattice has a single-valley Dirac band intersected by a dispersionless flat band at the band center. We investigate in this work the low-energy conductivity of the LCH lattice by considering the short-range impurities and focus on the role of the flat band when it is broken by disorders. Based on the self-consistent Born approximation and real space Kernel Polynomial methods, we showed that the system has a zero-energy conductivity like Graphene but it varies with the disorder strength. The broken flat band due to the disorder effect will contribute to the electron transport and this delocalization effect can lead to the exotic behaviors of conductivity in the low-energy regime as it slightly increases with the disorder strength and decreases with the chemical potential energy of the system. • This work is a careful theoretical analysis on the optical conductivity of a line-centered honeycomb lattice. • We demonstrate that the flat band can lead to several unconventional behaviors of the system conductivity when it is broken by the disorder. • We find that the low-energy conductivity might increase with the disorder strength and decrease with the chemical potential energy, these two features are very contrary to the physics intuition.