Quantum interference in superposed lattices

Significance Understanding the Fermi surface is of fundamental importance to metals. Here, we explore a situation where two sets of incommensurate lattices are superposed together in the elemental metal Cr. These two reciprocal lattices are connected through many-body electron correlations that have distinct experimental signatures. They combine to build a Fermi surface with many small de Haas–van Alphen orbits and quantum interference paths that are not detectable by standard photoemission techniques. In the spin- and charge-density-wave state of Cr, this construction leads to Shubnikov–de Haas oscillations with opposite phases between two orthogonal channels of transverse magnetoresistance. This phenomenon represents a natural three-dimensional analogue to topological and Moiré systems.