Supplemental Materials for "Strain-induced valley polarization, topological states, and piezomagnetism in two-dimensional altermagnetic V$_2$Te$_2$O, V$_2$STeO, V$_2$SSeO, and V$_2$S$_2$O"

See the supplementary material for band structures of V$_2$Te$_2$O with different hubbard U correction values, band structure with the hybrid functional approach, band structures of V$_2$Te$_2$O and V$_2$STeO with SOC included, the magnetic ground state and stable of the monolayer V$_2$Te$_2$O and V$_2$STeO under the strain, band structures with hole doping for monolayer V$_2$Te$_2$O and V$_2$STeO, and results for V$_2$SSeO and V$_2$S$_2$O.