Recent experiments by Gutiérrez et al (2016 Nat. Phys. 12 950) on a graphene-copper superlattice have revealed an unusual Kekulé bond texture in the honeycomb lattice-a Y-shaped modulation of weak and strong bonds with a wave vector connecting two Dirac points. We show that this so-called 'Kek-Y' texture produces two species of massless Dirac fermions, with valley isospin locked parallel or antiparallel to the direction of motion. In a magnetic field B, the valley degeneracy of the B-dependent Landau levels is removed by the valley-momentum locking but a B-independent and valley-degenerate zero-mode remains.

Single-particle levels of seven magic nuclei are calculated within the Energy Density Functional (EDF) method by Fayans et al. Three versions of the EDF are used, the initial Fayans functional DF3 and its two variations, DF3-a and DF3-b, with different values of spin-orbit parameters. Comparison is made with predictions of the Skyrme-Hartree-Fock method with the HFB-17 functional. For the DF3-a functional, phonon coupling (PC) corrections to single-particle energies are found self-consistently with an approximate account for the tadpole diagram. Account for the PC corrections improves agreement with the data for heavy nuclei, e.g. for 208 Pb. On the other hand, for lighter nuclei, e.g. 40,48 Ca, PC corrections make the agreement a little worse. As estimations show, the main reason is that the approximation we use for the tadpole term is less accurate for the light nuclei.Comment: 14 pages, 16 figures, 15 table

The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated metal with all-to-all random interactions (average strength J) between N fermions (complex Dirac fermions or real Majorana fermions). In the large-N limit a conformal symmetry emerges that renders the model exactly soluble. Here we study how the non-Fermi liquid behavior of the closed system in equilibrium manifests itself in an open system out of equilibrium. We calculate the current-voltage characteristic of a quantum dot, described by the complex-valued SYK model, coupled to a voltage source via a single-channel metallic lead (coupling strength Γ). A one-parameter scaling law appears in the large-N conformal regime, where the differential conductance G = dI/dV depends on the applied voltage only through the dimensionless combination ξ = eV J/Γ 2 . Low and high voltages are related by the duality G(ξ) = G(π/ξ). This provides for an unambiguous signature of the conformal symmetry in tunneling spectroscopy.

Odd-even double mass differences (DMDs) of magic nuclei are found within an approach starting from the free NN interaction, accounting for particle-phonon coupling (PC) effects. We consider three PC effects: the phonon-induced effective interaction, the renormalization of the "ends" due to the pole PC contribution to the nucleon mass operator, and the change of the single-particle energies. The perturbation theory in g 2 L , where g L is the vertex of the creation of the L-multipole phonon, is used for PC calculations. PC corrections to single-particle energies are found with an approximate accounting for the tadpole diagram. Results for magic 40,48 Ca, 56,78 Ni, 100,132 Sn, and 208 Pb nuclei are presented. For the lighter part of this set of nuclei, from 40 Ca to 56 Ni, the cases divide approximately in half, between those where the PC corrections to DMD values are in good agreement with the data and the ones with the opposite result. In the major part of the cases of worsening description of DMD, a poor applicability of the perturbation theory for the induced interaction is the most probable reason of the phenomenon. For intermediate nuclei, 78 Ni and 100 Sn, there are no sufficiently accurate data on masses of nuclei necessary for finding DMD values. Finally, for heavier nuclei, 132 Sn and 208 Pb, PC corrections always result in better agreement with experiment.