Quantum interference in superposed lattices

Charge transport in solids at low temperature reveals a material's mesoscopic properties and structure. Under a magnetic field, Shubnikov-de Haas (SdH) oscillations inform complex quantum transport phenomena that are not limited by the ground state characteristics and have facilitated extensive explorations of quantum and topological interest in two- and three-dimensional materials. Here, in elemental metal Cr with two incommensurately superposed lattices of ions and a spin-density-wave ground state, we reveal that the phases of several low-frequency SdH oscillations in [Formula: see text] and [Formula: see text] are no longer identical but opposite. These relationships contrast with the SdH oscillations from normal cyclotron orbits that maintain identical phases between [Formula: see text] and [Formula: see text] . We trace the origin of the low-frequency SdH oscillations to quantum interference effects arising from the incommensurate orbits of Cr's superposed reciprocal lattices and explain the observed [Formula: see text]-phase shift by the reconnection of anisotropic joint open and closed orbits.