Evidence for a gap in the density of states of two-level systems in amorphous silicon

We measure the material-based quantum two-level systems (TLSs) within amorphous silicon. They are probed within the dielectric of capacitors in high-Q superconducting LC resonators. In addition to a microwave probe field, the TLS's energy is swept by an applied electric-field to the capacitor plates. The non-equilibrium loss at various resonator microwave fields is thus studied by sweeps of many TLSs through resonance, where they may undergo Landau-Zener transitions. The intrinsic material loss is measured in the single photon limit. However, at high bias rates, excess loss is measured far larger than the intrinsic loss, which contradicts to the general understanding of the well-established standard TLS model. The excess intrinsic loss is bias rate dependent, which leads to the discovery of a gap in the density of states of a second type of TLS. Remarkably, once the bias rate dependent density of states is taken into consideration, the excess loss is found to scale according to Landau-Zener theory, similar to the standard TLS, which in return validates its TLS origin. The second TLS type possesses a large dipole moment (~200 Debye) compared to the standard TLS (~7 Debye).