Robust moiré flatbands within a broad band-offset range

Peilong Hong; Yi Liang; Zhigang Chen; Guoquan Zhang

doi:10.1117/1.APN.2.6.066001

Advanced Photonics Nexus, Volume. 2, Issue 6, 066001(2023)

Robust moiré flatbands within a broad band-offset range

Peilong Hong^1,2,3、*, Yi Liang^4、*, Zhigang Chen³, and Guoquan Zhang³

¹University of Electronic Science and Technology of China, School of Optoelectronic Science and Engineering, Chengdu, China

²Anqing Normal University, School of Mathematics and Physics, Anqing, China

³Nankai University, TEDA Applied Physics Institute, School of Physics, The MOE Key Laboratory of Weak-Light Nonlinear Photonics, Tianjin, China

⁴Guangxi University, School of Physical Science and Technology, Center on Nanoenergy Research, Guangxi Key Lab for Relativistic Astrophysics, Nanning, China

show less

Figures & Tables(5)

Fig. 1. (a) Schematic diagram of a silicon moiré superlattice. (b) Band offset adjusted by the thickness ( $h_{2}$ ) of slab-2. Here, the bands are calculated only for a single slab in the absence of the other slab. $k_{a}^{i} = 2 π / a_{i} (i = 1,2)$ . Note that more than two bands for slab-2 emerge within the region of interest by adjusting $h_{2}$ , but only two main bands $L_{i}$ and $U_{i}$ are marked.

Download full size

View in Article

Fig. 2. (a) Moiré bands at different band offsets. The flatbands are marked by different symbols, where $C$ labels the conventional flatbands that emerge and disappear by band-offset tuning, $R$ labels the robust flatbands that preserve. The subscript $A$ (or $B$ ) such as in $R_{A}^{1}$ denotes the center of field pattern at the A (or B) site, and the superscript $i = 1,2, \dots$ denotes different flatbands. Here, $k_{M} = 2 π / a_{M}$ , and the same symbol at different $h_{2}$ indicates that the eigenmodes have similar field patterns. (b) The field patterns $| E_{eigen} (k_{x} = 0) |$ of the four robust flatbands $R_{A}^{1}, R_{A}^{2}, R_{B}^{1}$ , and $R_{B}^{2}$ in a single cell of a periodic superlattice at $h_{2} = 0.7 a_{0}$ . The field magnitude is represented by a reversed hot color map with the maximum in black and the minimum in white.

Download full size

View in Article

Fig. 3. Tunable spectral positions of (a) the $R_{A}^{1}$ and $R_{A}^{2}$ modes and that of (c) the $R_{B}^{1}$ and $R_{B}^{2}$ modes. The quality factors ( $Q$ ) of (b) the $R_{A}^{1}$ and $R_{A}^{2}$ modes and that of (d) the $R_{B}^{1}$ and $R_{B}^{2}$ modes have high values.

Download full size

View in Article

Fig. 4. Two-site coupled-band diagram. (a) The band map represents the lowest two bands $L_{i}$ and $U_{i}$ ( $i = 1,2$ ) of individual slabs of the moiré superlattice. (b) The band structure for an A-site-like fictitious lattice. The interlayer coupling between $L_{1}$ and $L_{2}$ ( $U_{1}$ and $U_{2}$ ) is maximized (as indicated by the arrows). (c) The band map of a B-site-like fictitious lattice. The interlayer coupling between $L_{1}$ and $U_{2}$ is maximized.

Download full size

View in Article

Fig. 5. Coupled bands for the A-site-like and B-site-like fictitious lattices at (a) $h_{2} = 0.4 a_{0}$ , (b) $0.7 a_{0}$ , and (c) $a_{0}$ . (d) The field patterns for the four different band-edge modes as indicated by $A_{1}$ , $A_{2}$ , $B_{1}$ , and $B_{2}$ in (b). Again, the field magnitude is represented by a reversed hot color map.