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Exotic topological density waves in cold atomic Rydberg fermions

Versatile controllability of interactions in ultracold atomic and molecular gases has now reached an unprecedented era where quantum correlations and unconventional many-body phases can be studied with no corresponding analogs in solid state systems. Recent experiments in Rydberg atomic gases have achieved exquisite control over non-local interactions, allowing novel quantum phases unreachable with the usual local interactions in atomic systems. Here, we study Rydberg dressed atomic fermions in a three dimensional optical lattice predicting the existence of hitherto unheard-of exotic mixed topological density wave phases. We show that varying spatial range of the non-local interaction leads to a rich phase diagram containing various bond density waves, with unexpected spontaneous time-reversal symmetry breaking. Quasiparticles in these chiral phases experience emergent gauge fields and form three dimensional quantum Hall and Weyl semimetal states. Remarkably, certain density waves even exhibit mixed topologies beyond the existing topological classification. Experimental signatures of density waves and their topological properties are predicted in time-of-flight measurements.