Fano Resonances in Mismatched C$_3$N Nanoribbon Junctions

Abstract

Mismatched junctions formed by two C$_3$N zigzag nanoribbons of different widths provide a useful setting for studying quantum interference effects involving edge state transport. A crucial ingredient for this interference to appear is, besides the presence of edge states, the formation of localized interface states at the mismatched interface of the junction. At the level of a tight-binding model it is shown that, by means of an external gate potential, one of the edge state energy bands can selectively be shifted into the energy range of the localized interface states. The resulting coupling between the edge and localized interface states gives rise to pronounced Fano resonances in both the density of states and the transmission spectrum with line shapes well described by the canonical Fano formula. Furthermore, it is found that the geometrical mismatch of the junction not only determines the number of resonances but also the energetic orientation of their asymmetric line shapes. These results identify mismatched C$_3$N nanojunctions as a tunable and robust platform for engineering interference-driven transport.

Figures (9)

• Figure 1: Unit cell (highlighted) of the ideal C$_3$N zigzag nanoribbon (ZNR) for $N_T=4$ atomic chains and two different edge terminations. For any even $N_T$, these are the only possible edge terminations of the ideal ZNR. For the termination a) (upper panel), all the edge atoms are carbons while for termination b) (lower panel) both carbon and nitrogen atoms form the edge.
• Figure 2: Band structure for different $N_T$. a) $N_T=4$ and C-C edge termination, b) $N_T=4$ and C-N edge, c) $N_T=50$ for C-C edge and d) $N_T=50$ for C-N edge.
• Figure 3: a) LDOS of the shifted band at $E=0.0258$ eV and b) band structure of the periodic $N_T = 50$ ZNR with C-C edge termination, the dashed red line indicates $E=0.0258$ eV. A constant electrostatic potential $v_G=0.8$ eV is added to all sites of the first two chains.
• Figure 4: Density of states of central region $D_C(E)$ (for definition, see main text) for the $N_T=50$ ZNR with C-C edge termination for different configurations. a) ideal periodic ZNR with no extra electrostatic potential. b) Semi-infinite ZNR without additional potential. The sharp peaks correspond to localized surface states formed at the armchair termination of the semi-infinite ZNR. c) ideal periodic ZNR with additional gate potential $v_G=0.8$ eV for all atoms of chains $N=1$ and $N=2$. d) Semi-infinite ZNR with gate potential as in c). Many of the localized states found in b) now hybridize with the energy band of the upper edge state of the ZNR. The remaining sharp peaks correspond to localized corner states. The LDOS corresponding to the two highlighted energies in panels c) and d) are shown in Fig. \ref{['fig:interface_corner_state']}.
• Figure 5: Left panel: LDOS of a semi-infinite ZNR of width $N = 50$ without gate potential at $E = 0.258$ eV (the peak marked by an arrow in Fig. \ref{['fig:DOScomparison']} b)) corresponding to a surface state. Right panel: LDOS of the semi-infinite $N=50$ ZNR with applied gate potential for energy $E=0.068$ eV (the peak marked by an arrow in Fig. \ref{['fig:DOScomparison']} d)) corresponding to a corner state. For both panels, the visualized region consists of $m=16$ unit cells and the hard wall boundary of the semi-infinite ZNRs is indicated by the black region at the left side of the figures.