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Graphene superlattices: Effect of finite size on the density of states and conductance
Author(s) -
HernándezBertrán M. A.,
Duque C. A.,
de DiosLeyva M.
Publication year - 2017
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201600313
Subject(s) - superlattice , conductance , condensed matter physics , graphene , inverse , density of states , transmission coefficient , crystal (programming language) , local density of states , physics , quantum mechanics , transmission (telecommunications) , mathematics , geometry , engineering , computer science , electrical engineering , programming language
We have derived a formula for the density of states ρ N ( E ) of a N ‐period graphene superlattice (SL), which is given as an integral over the inverse of the absolute value of the group delay velocity v x along the SL‐axis. Using that formula, it was shown that ρ N ( E ) exhibits essentially the same structure for all values of N ≥ 5 . It was found that for E < 0 , the effects of finite crystal size modify dramatically the density of states of the corresponding infinite SL, whereas for E > 0 and N ≥ 5 , it is only slightly modified. According to our results, 1 / v x is proportional to the transmission coefficient, which allows us to establish a certain correlation between the properties of ρ N ( E ) and those of the Landauer conductance G N ( E ) of the N ‐period SL. Certainly, G N ( E ) exhibits a peak structure as a function of E , with local dips located at the same energies as those of ρ N ( E ) . The same behavior was observed for the V ‐dependence of G N ( E ) with E = 0 , which is very similar to that of ρ N ( 0 ) . When N increases, the peak positions of both G N ( 0 ) and ρ N ( 0 ) tend to be located at those values of V where new Dirac points appear.