Devil's staircase of odd-number charge order modulations in divalent β-vanadium bronzes under pressure

A novel phase transition with a stepwise evolution of odd-number charge modulation is discovered in $\ensuremath{\beta}$-vanadium bronzes under pressures of about 1 GPa. All the charge modulation vectors of the many kinds of charge-ordered phases can be represented as a primitive lattice translation vector along the $b$ axis multiplied by several odd numbers. This discovery demonstrates interplay between the charge degree of freedom and the crystallographic symmetry. This phenomenon is rationally explained by self-charge transfer (carrier redistribution) between two kinds of subsystems in the structure and sequential symmetry reduction as outlined in Landau theory of phase transitions.