Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong density wave fluctuations in two dimensions. While the weak-coupling theory finds the fully gapped chiral state to be energetically stable, we show that strong density wave fluctuations result in an additional contribution to the free energy of a superconductor with multicomponent order parameters, which generally favors nematic superconductivity. Our theory sheds light on the recent observation of rotational symmetry breaking in the superconducting state of twisted bilayer graphene.

When a strongly correlated system supports well-defined quasiparticles, it allows for an elegant one-body effective description within the non-Hermitian topological theory. While the microscopic many-body Hamiltonian of a closed system remains Hermitian, the one-body quasiparticle Hamiltonian is non-Hermitian due to the finite quasiparticle lifetime. We use such a non-Hermitian description in the heavy-fermion two-dimensional systems with the momentum-dependent hybridization to reveal a fascinating phenomenon which can be directly probed by the spectroscopic measurements, the bulk "Fermi arcs." Starting from a simple two-band model, we first combine the phenomenological approach with the perturbation theory to show the existence of the Fermi arcs and reveal their connection to the topological exceptional points, special points in the Brillouin zone where the Hamiltonian is nondiagonalizable. The appearance of such points necessarily requires that the electrons belonging to different orbitals have different lifetimes. This requirement is naturally satisfied in the heavy-fermion systems, where the itinerant c electrons experience much weaker interaction than the localized f electrons. We then utilize the dynamical mean field theory to numerically calculate the spectral function and confirm our findings. We show that the concept of the exceptional points in the non-Hermitian quasiparticle Hamiltonians is a powerful tool for predicting new phenomena in strongly correlated electron systems.