In the case of Barreto-Naehrig pairing-friendly curves of embedding degree 12 of order r, recent efficient Ate pairings such as R-ate, optimal, and Xate pairings achieve Miller loop lengths of (1/4) log2 r . On the other hand, the twisted Ate pairing requires (3/4) log2 r loop iterations, and thus is usually slower than the recent efficient Ate pairings. This paper proposes an improved twisted ...

We use the shell model Monte Carlo approach to study thermal properties and pair correlations in 54,56,58Fe and in 56Cr. The calculations are performed with the modified Kuo-Brown interaction in the complete 1p0f model space. We find generally that the proton-proton and neutron-neutron J = 0 pairing correlations, which dominate the ground state properties of even-even nuclei, vanish at temperat...

To guide experimental work on the search for Majorana zero-energy modes, we calculate the superconducting pairing symmetry of a three-dimensional topological insulator in combination with an s-wave superconductor. We show how the pairing symmetry changes across different topological regimes. We demonstrate that a dominant p-wave pairing relation is not sufficient to realise a Majorana zero-ener...