Anharmonic Bloch oscillations in a helicoidal lattice

We present a theoretical study on Bloch oscillations in a helicoidal lattice with the first neighbor hopping and a selected N-th neighbor hopping. By the use of a simple variational approach, we analytically predict the occurrence of the anharmonic Bloch oscillation, which includes a specific high-order harmonic caused by the selected N-th neighbor hopping. In numerical simulations, we also observe such anharmonic Bloch oscillations. The variational predictions are indicated to be in excellent agreement with numerical results. In addition, our numerical results show that the wave packet width will perform anharmonic oscillations, whose periods and Bloch oscillations are equal.