Effects of asymmetrical rotated rectangular basis on the acoustic band gap in two-dimensional acoustic crystals: the bands are twisted

The band structure and the change in band extrema's position during the rotation of bases are analysed in two-dimensional rectangular-basis acoustic crystals (ACs) with a square lattice. We find that the bands of ACs are twisted and some of the extrema of the bands move anticlockwise or clockwise in the whole area of the first Brillouin zone (BZ) when the bases are rotated clockwise. These make the irreducible BZ expand into the whole first BZ. Therefore, for the ACs with a rectangular basis or similar kind of basis, it is important to study the whole first BZ to obtain the accurate band structure.