Kramers pairs of Majorana corner states in a topological insulator bilayer

We consider a system consisting of two tunnel-coupled two-dimensional topological insulators proximitized by a top and bottom superconductor with a phase difference of $\pi$ between them. We show that this system exhibits a time-reversal invariant second-order topological superconducting phase characterized by the presence of a Kramers pair of Majorana corner states at all four corners of a rectangular sample. We furthermore investigate the effect of a weak time-reversal symmetry breaking perturbation and show that an in-plane Zeeman field leads to an even richer phase diagram exhibiting two nonequivalent phases with two Majorana corner states per corner as well as an intermediate phase with only one Majorana corner state per corner. We derive our results analytically from continuum models describing our system. In addition, we also provide independent numerical confirmation of the resulting phases using discretized lattice representations of the models, which allows us to demonstrate the robustness of the topological phases and the Majorana corner states against parameter variations and potential disorder

Field-tuned quantum tunneling in a supramolecule dimer [Mn4]2[Mn_4]_2

Field-tuned quantum tunneling in two single-molecule magnets coupled antiferromagnetically and formed a supramolecule dimer is studied. We obtain step-like magnetization curves by means of the numerically exact solution of the time-dependent Schr\H{o}dinger equation. The steps in magnetization curves show the phenomenon of quantum resonant tunneling quantitatively. The effects of the sweeping rate of applied field is discussed. These results obtained from quantum dynamical evolution well agree with the recent experiment[W.Wernsdorfer et al. Nature 416(2002)406].Comment: 11 pages, 4 figures, 2 tables. Submited to Phys. Rev.