Bogolyubov excitons as a microscopic origin of two-level systems

Two-level systems (TLS) are a leading source of decoherence and dielectric loss in Josephson-junction qubits, yet their microscopic origin remains unresolved. We propose an intrinsic, purely electronic TLS candidate: subgap bound states of Bogolyubov quasiparticles. We show that, in a model of a conventional superconductor with electron-electron attraction in the $s$-wave channel and repulsion in higher-angular-momentum channels, the latter produce an effective attraction between Bogolyubov quasiparticles, forming bound states. These Bogolyubov excitons resemble Bardasis--Schrieffer excitons but are driven by repulsive interactions. Bulk Bogolyubov excitons are not easily detectable through single-particle tunneling or other conventional probes, but we show that surface excitons couple to an external electric field and behave as two-level systems. We examine an idealized model of a bulk superconductor proximity-coupled to a two-dimensional repulsive metal, which could represent an external metallic or semiconductor layer or an underscreened region of the superconductor. The two levels correspond to the absence and presence of a single exciton, which carries an electric dipole moment and exhibits an avoided crossing with a resonator, as observed for TLS. Because this mechanism requires no defects and cannot be eliminated by screening or annealing, it suggests that TLS-like excitations may be intrinsic to superconductors.