Isolated pairs of Majorana zero modes in a disordered superconducting lead monolayer.

Majorana zero modes are fractional quantum excitations appearing in pairs, each pair being a building block for quantum computation. Some signatures of Majorana zero modes have been reported at endpoints of one-dimensional systems, which are however required to be extremely clean. An alternative are two-dimensional topological superconductors, such as the Pb/Co/Si(111) system shown recently to be immune to local disorder. Here, we use scanning tunneling spectroscopy to characterize a disordered superconducting monolayer of Pb coupled to underlying Co-Si magnetic islands. We show that pairs of zero modes are stabilized: one zero mode positioned in the middle of the magnetic domain and its partner extended all around the domain. The zero mode pair is remarkably robust, isolated within a hard superconducting gap. Our theoretical scenario supports the protected Majorana nature of this zero mode pair, highlighting the role of magnetic or spin-orbit coupling textures.

Commensurate 4a0-period charge density modulations throughout the Bi2Sr2CaCu2O8+x pseudogap regime.

Theories based upon strong real space (r-space) electron-electron interactions have long predicted that unidirectional charge density modulations (CDMs) with four-unit-cell (4a0) periodicity should occur in the hole-doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector QA of the CDM to evolve continuously as if driven primarily by momentum-space (k-space) effects. Here we introduce phase-resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this technique reveals a virtually doping-independent locking of the local CDM wavevector at [Formula: see text] throughout the underdoped phase diagram of the canonical cuprate Bi2Sr2CaCu2O8 These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi-surface)-based picture of the cuprate CDMs but are consistent with strong-coupling r-space-based theories. Our findings imply that it is the latter that provides the intrinsic organizational principle for the cuprate CDM state.

Universal probes of two-dimensional topological insulators: dislocation and π flux.

We show that the π flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that π flux hosts a Kramers pair of zero modes in the topological Γ (Berry phase Skyrmion at the zero momentum) and M (Berry phase Skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a π flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.