Chiral zero energy modes in two-dimensional disordered Dirac semimetals

摘要

The vacancy-induced chiral zero energy modes (CZEMs) of chiral-unitary-class (AIII) and chiral-symplectic-class (CII) two-dimensional (2D) disordered Dirac semimetals realized on a square bipartite lattice are investigated numerically by using the Kubo-Greenwood formula with the kernel polynomial method. The results show that, for both systems, the CZEMs exhibit the critical delocalization. The CZEM conductivity remains a robust constant (i.e., sigma(CZEM) approximate to 1.05e(2)/h), which is insensitive to the sample sizes, the vacancy concentrations, and the numbers of moments of Chebyshev polynomials, i.e., the dephasing strength. For both kinds of chiral systems, the CZEM conductivities are almost identical. However, they are not equal to that of graphene (i.e., 4e(2)/pi h), which belongs to the chiral orthogonal class (BDI) semimetal on a 2D hexagonal bipartite lattice. In addition, for the case that the vacancy concentrations are different in the two sublattices, the CZEM conductivity vanishes, and thus both systems exhibit localization at the Dirac point. Moreover, a band gap and a mobility gap open around zero energy. The widths of the energy gaps and mobility gaps are increasing with larger vacancy concentration difference. The width of the mobility gap is greater than that of the band gap, and a delta-function-like peak of density of states emerges at the Dirac point within the band gap, implying the existence of numerous localized states.