Fig. 1: Dynamics of intervalley scatterings and wavefront dislocations.

a A schematic diagram of intervalley interference between the incident wave from position B in \({{{{{\bf{K}}}}}}\) valley and the reflected wave back to position B in \({{{{{\bf{K}}}}}}{^{{\prime} }}\) valley due to the defect potential A. The orbital angular momentum m is zero for these wavefronts. The color scale represents the intensity distributions for both wavefronts and the potential. b A wave scattered by a defect potential accompanied by a spread rotationally asymmetric potential, leading to reflection as a spiral wavefront with a finite orbital angular momentum. c A intervalley scattering process for panel a between two nearest \({{{{{\bf{K}}}}}}\) and \({{{{{\bf{K}}}}}}{^{{\prime} }}\) valleys, involving the pseudospin rotation. Here \({\theta }_{{{{{{\bf{r}}}}}}}\) is the polar angle of the position vector \({{{{{\bf{r}}}}}}\). Black and red arrows denote the vector of momentum q and pseudospin, respectively. \({\theta }_{{{{{{\bf{q}}}}}}}\) is rotation angle of momentum. The color gradient from black to red represents the variation of the phase. d A schematic diagram to show wavefront dislocations in total local density of states(LDOS) with the contribution of pseudospin rotation. Panels a and c are the partial processes of panel d. The q in all the directions scatters with the potential in the middle point and contributes to the accumulation of the phase for the closed loop. Two scattering directions \({{{{{{\bf{q}}}}}}}_{{{{{{\bf{1}}}}}}}\) and \({{{{{{\bf{q}}}}}}}_{{{{{{\bf{2}}}}}}}\) are shown in the figure. The phases from \(2\pi\) to \(4\pi\) are marked in one of the wavefront dislocations and the value of the wave is donated by different colors. e A intervalley scattering process between two nearest \({{{{{\bf{K}}}}}}\) and \({{{{{\bf{K}}}}}}{^{{\prime} }}\) valleys for panel b, involving both pseudospin and orbital angular momentum. The orbital angular momentum effect on valley manifests as the colored distribution with a varied phase. f The wavefront dislocation in LDOS modulation \(\Delta {\rho }_{B}\left({{{{\Delta}}}}{{{{{\bf{K}}}}}},{{{{{\bf{r}}}}}}\right)\propto \cos \left({{{{\Delta }}}}{{{{{\bf{K}}}}}}\cdot {{{{{\bf{r}}}}}}+{\theta }_{{{{{{\bf{r}}}}}}}\right)\) with the contribution from both pseudospin rotation and orbital angular momentum coupling. The white dots in d and f schematically denote the defect position.