Excitons are Super!

Long-range Coulomb interaction plays a significant role in low dimensional systems. In this talk, we will present a few examples how Coulomb interaction can modify, even induce new phases of matter. First example is spatially indirect exciton condensates(SIEXC) in the case of a two-dimensional semiconductor bilayer formed by two transition metal dichalcogenides (TMD) that are separated and surrounded by an insulator, for example hexagonal boron nitride (hBN). Because of the spin and valley degrees of freedom, there are two distinct condensate phases with different number of condensate flavors as layer separation and exciton density vary. Second example is exciton-polariton condensate in multiple quantum wells system which can be described by a microscopic equilibrium polariton condensate theory. We treat exciton conduction and valence band states explicitly providing a mechanism for electrical manipulation of polariton condensates. Third example is new interaction-induced time-reversal symmetry broken nematic insulator(NTRB) phase near normal insulator/ quantum spin Hall insulator phase transitions. We demonstrate that this NTRB is inevitable because of the large energy difference between s-wave and p-wave excitons. Last example is Weyl semimetal instability against long-range Coulomb interaction. Though strong enough interaction can open the gap by internode interband pairing, finite band Chern number jumps are retained indicating the robustness of the topological non-trivial features.