  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. 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
sigma_xx (rho_xx) and sigma_yy (rho_yy) are opposite, contrast with
oscillations from normal cyclotron orbits that maintain identical phases. 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 pi-phase shift by the reconnection of
anisotropic joint open and closed orbits.
