Antiresonance induced by symmetry-broken contacts in quasi-one-dimensional lattices

We report the effect of symmetry-broken contacts on quantum transport in quasi-one-dimensional lattices. In contrast to one-dimensional (1D) chains, transport in quasi-one-dimensional lattices, which are made up of a finite number of 1D chain layers, is strongly influenced by contacts. Contact symmetry depends on whether the contacts maintain or break the parity symmetry between the layers. With balanced on-site potential, a flatband can be detected by asymmetric contacts, but not by symmetric contacts. In the case of asymmetric contacts with imbalanced on-site potential, transmission is suppressed at certain energies. We elucidate these energies of transmission suppression related to antiresonance using reduced lattice models and Feynman paths. These results provide a nondestructive measurement of flatband energy, which is difficult to detect.

Figure 1

(a) Cross-stitch lattice with two leads. Blue rectangular boxes represent unit cells. The unit cell has two sites, $a$ and $b$, with hopping strengths $d$ (solid lines) and $t$ (dashed line) between the sites. The coupling between sites and leads is ${\gamma }_{a(b,c)}^{i\left(o\right)}$ (long-dashed line). (b) Tunable diamond lattice with two leads. The unit cell has three sites, $a, b$, and $c$, with hopping strengths $d$ (solid lines) and $t$ (dashed line) between sites.

Figure 2

(a) Energy bands for a cross-stitch lattice with a flatband (red line). (b) Transmission probabilities for a cross-stitch lattice of which both $a$ and $b$ sites of the end unit cells are connected to the input and output leads. (c) Transmission probabilities for a cross-stitch lattice of which only the $a$ sites of the end unit cells are connected to the input and output leads. (d) Upper and lower panels show detangled Fano lattices from a cross-stitch lattice with symmetric and asymmetric contacts, respectively, corresponding to (b) and (c). The hopping strength (dashed lines) between Fano states $f_n$ and dispersive chain $p_n$ equals zero. (e) Energy bands for a tunable diamond lattice with a flatband (red line). (f) Transmission probabilities for a tunable diamond lattice of which both $a$ and $b$ sites of the end unit cells are connected to the input and output leads. (g) Transmission probabilities for a tunable diamond lattice of which only the $a$ sites of the end unit cells are connected to the input and output leads. (h) Upper and lower panels show detangled Fano lattices from a tunable diamond lattice with symmetric and asymmetric contacts, respectively, corresponding to (f) and (g).

Figure 3

(a) Energy bands for a cross-stitch lattice with ${\delta }_a=-2$. (b) Transmission probability for a cross-stitch lattice of which both $a$ and $b$ sites of the end unit cells are connected to the input and output leads. (c) Transmission probability for a cross-stitch lattice of which only the $a$ sites of the end unit cells are connected to the input and output leads. (d) Transmission probability for a cross-stitch lattice of which $a$ and $b$ sites of the end unit cells are connected to the input and the output leads, respectively.

Figure 4

(a) Energy bands for a tunable diamond lattice with ${\delta }_a=1$. (b) Transmission probability for a tunable diamond lattice of which both $a$ and $b$ sites of the end unit cells are connected to the input and output leads. (c) Transmission probability for a tunable diamond lattice of which only the $a$ sites of the end unit cells are connected to the input and output leads. (d) Transmission probability for a tunable diamond lattice of which $a$ and $b$ sites of the end unit cells are connected to the input and the output leads, respectively.

Figure 5

(a) Schematic diagram of the end unit cells of a cross-stitch lattice connected to the leads. Both $a$ and $b$ sites are connected to the right lead, but only the $a$ site is connected to the left lead. (b) Schematic diagram of the end unit cells of a tunable diamond lattice connected to the leads. All sites are connected to the right lead, but only the $a$ site is connected to the left lead.