Topological phase transition from nodal to nodeless d-wave superconductivity in electron-doped cuprate superconductors

Unlike the hole-doped cuprates, both nodal and nodeless superconductivity (SC) are observed in the electron-doped cuprates. To understand these two types of SC states, we propose a unified theory by considering the two-dimensional t-J model in proximity to an antiferromagnetic (AF) long-range ordering state. Within the slave-boson mean-field approximation, the d-wave pairing symmetry is still the most energetically favorable even in the presence of the external AF field. In the nodal phase, it is found that the nodes carry vorticity and are protected by the adjoint symmetry of time-reversal and one unit lattice translation. Robust edge modes are obtained, suggesting the nodal d-wave SC being a topological weak-pairing phase. As decreasing the doping concentration or increasing the AF field, the nodes with opposite vorticity annihilate and the nodeless strong-pairing phase emerges. The topological phase transition is characterized by a critical point with anisotropic Bogoliubov quasiparticles, and a universal understanding is thus established for all electron-doped cuprates.Comment: 7 pages, 5 figures; published versio

Flavor Violating Transitions of Charged Leptons from a Seesaw Mechanism of Dimension Seven

A mechanism has been suggested recently to generate the neutrino mass out of a dimension-seven operator. This is expected to relieve the tension between the occurrence of a tiny neutrino mass and the observability of other physics effects beyond it. Such a mechanism would inevitably entail lepton flavor violating effects. We study in this work the radiative and purely leptonic transitions of the light charged leptons. In so doing we make a systematic analysis of the flavor structure by providing a convenient parametrization of the mass matrices in terms of independent physical parameters and diagonalizing them explicitly. We illustrate our numerical results by sampling over two CP phases and one Yukawa coupling which are the essential parameters in addition to the heavy lepton mass. We find that with the stringent constraints coming from the muon decays and the muon-electron conversion in nuclei taken into account the decays of the tau lepton are severely suppressed in the majority of parameter space. There exist, however, small regions in which some tau decays can reach a level that is about 2 orders of magnitude below their current bounds.Comment: v1: 25 pages, 8 figures; v2: proofread version for PRD. Included muon-electron conversion in nuclei at the referee's suggestion and added relevant refs accordingly; main conclusion not changed but bounds on tau lepton decays becoming more stringent; linguistic and editing corrections also mad

Two-dimensional topological superconducting phases emerged from d-wave superconductors in proximity to antiferromagnets

Motivated by the recent observations of nodeless superconductivity in the monolayer CuO$_{2}$ grown on the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ substrates, we study the two-dimensional superconducting (SC) phases described by the two-dimensional $t$-$J$ model in proximity to an antiferromagnetic (AF) insulator. We found that (i) the nodal d-wave SC state can be driven via a continuous transition into a nodeless d-wave pairing state by the proximity induced AF field. (ii) The energetically favorable pairing states in the strong field regime have extended s-wave symmetry and can be nodal or nodeless. (iii) Between the pure d-wave and s-wave paired phases, there emerge two topologically distinct SC phases with ($s+$i$d$) symmetry, i.e., the weak and strong pairing phases, and the weak pairing phase is found to be a $Z_{2}$ topological superconductor protected by valley symmetry, exhibiting robust gapless non-chiral edge modes. These findings strongly suggest that the high-$T_{c}$ superconductors in proximity to antiferromagnets can realize fully gapped symmetry protected topological SC.Comment: 7 pages, 4 figures; revised versio

Qubit fractionalization and emergent Majorana liquid in the honeycomb Floquet code induced by coherent errors and weak measurements

From the perspective of quantum many-body physics, the Floquet code of Hastings and Haah can be thought of as a measurement-only version of the Kitaev honeycomb model where a periodic sequence of two-qubit XX, YY, and ZZ measurements dynamically stabilizes a toric code state with two logical qubits. However, the most striking feature of the Kitaev model is its intrinsic fractionalization of quantum spins into an emergent gauge field and itinerant Majorana fermions that form a Dirac liquid, which is absent in the Floquet code. Here we demonstrate that by varying the measurement strength of the honeycomb Floquet code one can observe features akin to the fractionalization physics of the Kitaev model at finite temperature. Introducing coherent errors to weaken the measurements we observe three consecutive stages that reveal qubit fractionalization (for weak measurements), the formation of a Majorana liquid (for intermediate measurement strength), and Majorana pairing together with gauge ordering (for strong measurements). Our analysis is based on a mapping of the imperfect Floquet code to random Gaussian fermionic circuits (networks) that can be Monte Carlo sampled, exposing two crossover peaks. With an eye on circuit implementations, our analysis demonstrates that the Floquet code, in contrast to the toric code, does not immediately break down to a trivial state under weak measurements, but instead gives way to a long-range entangled Majorana liquid state.Comment: 5 + 6 pages; 3 + 9 figure