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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 ${\sigma }_{\mathit{xx}} \left({\rho }_{\mathit{xx}}\right)$and ${\sigma }_{\mathit{yy}} \left({\rho }_{\mathit{yy}}\right)$are no longer identical but opposite. These relationships contrast with the SdH oscillations from normal cyclotron orbits that maintain identical phases between ${\sigma }_{\mathit{xx}} \left({\rho }_{\mathit{xx}}\right)$and ${\sigma }_{\mathit{yy}} \left({\rho }_{\mathit{yy}}\right)$ . 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. 

A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies.