**Ultimate limit to the accelerating field of Superconducting RF cavities**

A fundamental understanding of the physical processes and material properties that lead to the higher quality factors and higher accelerating fields is being pursued theoretically and experimentally in CAPST. Recent theoretical research provides new insight into the upper limit to the maximum accelerating field (*superheating field*). Impurities infused into the inner surface of SRF cavities form an inhomogeneous impurity diffusion layer that substantially increases in the superheating field of SRF cavities. Accelerating fields as high as 45 MV/m have been achieved with N-doped Niobium. Recent theoretical predictions push the theoretical limit to 60 MV/m. Published in *Physical Review Research 1, 012015(R) *(2019).

**Quantization of Superconducting Circuits with Time-dependent Flux**

In standard circuit quantization theory there exists a gauge freedom when formulating the Hamiltonian for a circuit threaded by external flux. Depending on the choice of gauge, the external flux may be associated with any of the potential energy terms. For example, in a fluxonium qubit, the external flux may be associated with the potential energy of the Josephson junction, or that of the superinductor. However, this freedom leads to inconsistent predictions of qubit relaxation rates induced by time-dependent fluctuations of the external flux. CAPST researchers have extended the theory of circuit quantization to include time-dependent external flux in otder to resolve this and related inconsistencies, and to provide a theoretical formulation capable of handling a wide variety of superconducting quantum circuits. Published in *Physical Review B 99, 174512 *(2019).

**Bosonic Excitations in Topological Superconductors**

One of the key features of spontaneous symmetry breaking in condensed matter and quantum field theory is the emergence of new elementary quanta: phonons in crystalline solids, magnons in ferromagnets, the Higgs and gauge bosons of the standard model. The recent discovery of twofold rotation symmetry in superconducting compounds, M_{x}Bi_{2}Se_{3} ( M=Cu, Sr, Nb) is compatible with odd-parity, time-reversal invariant superconductivity belonging to the two-dimensional E_{u} representation of the D_{3d} symmetry group. The in-plane anisotropy is represented by a *nematic* superconducting order parameter. CAPST researchers recently predicted two characteristic bosonic excitations in nematic SCs: *nematicity* and *chirality* modes. Published in *Physical Review Letters* 123, 237001 (2019).

Selection rules show that microwave photons couple to the chiral Higgs mode, leading to a pronounced absorption peak for photons with energy below the superconducting gap edge at ω=2Δ that provides a distinct signature of odd-parity nematic superconductivity.

**Anomalous Thermal Hall Effect in Topological Superconductors**

Chiral superconductors exhibit novel transport properties that depend on the topology of the order parameter, topology of the Fermi surface and the structure of the impurity potential. In the case of electronic heat transport, impurities induce a zero-field *anomalous **thermal **Hall conductivity*. The effect originates from branch-conversion scattering of Bogoliubov quasiparticles by the chiral order parameter, induced by potential scattering. The former transfers angular momentum between the condensate and the excitations that transport heat. The anomalous thermal Hall conductivity is shown to depend to the structure of the electron-impurity potential, as well as the winding number, ν, of the chiral order parameter, ∆(p) = |∆(p)| e^{iνφp} . The results provide quantitative formulae for interpreting heat transport experiments seeking to identify broken T and P symmetries, as well as the topology of chiral superconductors. Available on arXiv: 1911.06299 (2019).