Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

The spectrum of massless Dirac fermions on the surface of a topological insulator in a perpendicular magnetic field $B$ contains a $B$-independent "zeroth Landau level", protected by chiral symmetry. If the Dirac equation is discretized on a lattice by the method of "Wilson fermions", the chiral symmetry is broken and the zeroth Landau level is broadened when $B$ has spatial fluctuations. We show how this lattice artefact can be avoided starting from an alternative nonlocal discretization scheme introduced by Stacey. A key step is to spatially separate the states of opposite chirality in the zeroth Landau level, by adjoining $+B$ and $-B$ regions.Comment: Contribution to a special issue of Annals of Physics in memory of Kostya Efeto

Dynamical simulation of the injection of vortices into a Majorana edge mode

The chiral edge modes of a topological superconductor can transport fermionic quasiparticles, with Abelian exchange statistics, but they can also transport non-Abelian anyons: Majorana zero-modes bound to a {\pi}-phase domain wall that propagates along the boundary. Such an edge vortex is injected by the application of an h/2e flux bias over a Josephson junction. Existing descriptions of the injection process rely on the instantaneous scattering approximation of the adiabatic regime, where the internal dynamics of the Josephson junction is ignored. Here we go beyond that approximation in a time-dependent many-body simulation of the injection process, followed by a braiding of the mobile edge vortex with an immobile Abrikosov vortex in the bulk of the superconductor. Our simulation sheds light on the properties of the Josephson junction needed for a successful implementation of a flying Majorana qubit.Comment: 13 pages 12 figure

Magnetic breakdown spectrum of a Kramers-Weyl semimetal

We calculate the Landau levels of a Kramers-Weyl semimetal thin slab in a perpendicular magnetic field $B$. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band width that oscillates periodically in $1/B$. We interpret the spectrum in terms of a one-dimensional superlattice induced by magnetic breakdown at Weyl points. The band width oscillations may be observed as $1/B$-periodic magnetoconductance oscillations, at weaker fields and higher temperatures than the Shubnikov-de Haas oscillations due to Landau level quantization. No such spectrum appears in a generic Weyl semimetal, the Kramers degeneracy at time-reversally invariant momenta is essential.Comment: 13 pages, 18 figure

Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling

I. Introduction II. Two-dimensional lattice fermions III. Methods to avoid fermion doubling (sine dispersion, sine plus cosine dispersion, staggered lattice dispersion, linear sawtooth dispersion, tangent dispersion) IV. Topologically protected Dirac cone V. Application: Klein tunneling (tangent fermions on a space-time lattice, wave packet propagation) VI. Application: Strong antilocalization (transfer matrix of tangent fermions, topological insulator versus graphene) VII. Application: Anomalous quantum Hall effect (gauge invariant tangent fermions, topologically protected zeroth Landau level) VIII. Application: Majorana metal (Dirac versus Majorana fermions, phase diagram) IX. OutlookComment: review article, 26 pages, 13 figures; V2: added three appendices, and provided code for the various implementation

Localization landscape for Dirac fermions

In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for the scalar wave equation in a random potential, or equivalently for the Schr\"{o}dinger equation of spinless electrons. Here we generalize the concept to the Dirac equation, which includes the effects of spin-orbit coupling and allows to study quantum localization in graphene or in topological insulators and superconductors. The landscape function $u(r)$ is defined on a lattice as a solution of the differential equation $\overline{{H}}u(r)=1$, where $\overline{{H}}$ is the Ostrowsky comparison matrix of the Dirac Hamiltonian. Random Hamiltonians with the same (positive definite) comparison matrix have localized states at the same positions, defining an equivalence class for Anderson localization. This provides for a mapping between the Hermitian and non-Hermitian Anderson model.Comment: 6 pages, 6 figure

Chirality inversion of Majorana edge modes in a Fu-Kane heterostructure

Fu and Kane have discovered that a topological insulator with induced s-wave superconductivity (gap Delta(0), Fermi velocity v (F), Fermi energy mu) supports chiral Majorana modes propagating on the surface along the edge with a magnetic insulator. We show that the direction of motion of the Majorana fermions can be inverted by the counterflow of supercurrent, when the Cooper pair momentum along the boundary exceeds Delta(2)(0)/mu v(F) . The chirality inversion is signaled by a doubling of the thermal conductance of a channel parallel to the supercurrent. Moreover, the inverted edge can transport a nonzero electrical current, carried by a Dirac mode that appears when the Majorana mode switches chirality. The chirality inversion is a unique signature of Majorana fermions in a spinful topological superconductor: it does not exist for spinless chiral p-wave pairing.Theoretical Physic

Revision of the 15N(p,{\gamma})16O reaction rate and oxygen abundance in H-burning zones

The NO cycle takes place in the deepest layer of a H-burning core or shell, when the temperature exceeds T {\simeq} 30 {\cdot} 106 K. The O depletion observed in some globular cluster giant stars, always associated with a Na enhancement, may be due to either a deep mixing during the RGB (red giant branch) phase of the star or to the pollution of the primordial gas by an early population of massive AGB (asymptotic giant branch) stars, whose chemical composition was modified by the hot bottom burning. In both cases, the NO cycle is responsible for the O depletion. The activation of this cycle depends on the rate of the 15N(p,{\gamma})16O reaction. A precise evaluation of this reaction rate at temperatures as low as experienced in H-burning zones in stellar interiors is mandatory to understand the observed O abundances. We present a new measurement of the 15N(p,{\gamma})16O reaction performed at LUNA covering for the first time the center of mass energy range 70-370 keV, which corresponds to stellar temperatures between 65 {\cdot} 106 K and 780 {\cdot}106 K. This range includes the 15N(p,{\gamma})16O Gamow-peak energy of explosive H-burning taking place in the external layer of a nova and the one of the hot bottom burning (HBB) nucleosynthesis occurring in massive AGB stars. With the present data, we are also able to confirm the result of the previous R-matrix extrapolation. In particular, in the temperature range of astrophysical interest, the new rate is about a factor of 2 smaller than reported in the widely adopted compilation of reaction rates (NACRE or CF88) and the uncertainty is now reduced down to the 10% level.Comment: 6 pages, 5 figure

Massless dirac fermions on a space‐time lattice with a topologically protected dirac cone

The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion doubling) or because of singularities at zone boundaries. Here an implementation of Dirac fermions on a space-time lattice that removes both obstructions is introduced. The quasi-energy band structure has a tangent dispersion with a single Dirac cone that cannot be gapped without breaking both time-reversal and chiral symmetries. It is shown that this topological protection is absent in the familiar single-cone discretization with a linear sawtooth dispersion, as a consequence of the fact that there the time-evolution operator is discontinuous at Brillouin zone boundaries.Theoretical Physic

Neutron-induced background by an alpha-beam incident on a deuterium gas target and its implications for the study of the 2H(alpha,gamma)6Li reaction at LUNA

The production of the stable isotope Li-6 in standard Big Bang nucleosynthesis has recently attracted much interest. Recent observations in metal-poor stars suggest that a cosmological Li-6 plateau may exist. If true, this plateau would come in addition to the well-known Spite plateau of Li-7 abundances and would point to a predominantly primordial origin of Li-6, contrary to the results of standard Big Bang nucleosynthesis calculations. Therefore, the nuclear physics underlying Big Bang Li-6 production must be revisited. The main production channel for Li-6 in the Big Bang is the 2H(alpha,gamma)6Li reaction. The present work reports on neutron-induced effects in a high-purity germanium detector that were encountered in a new study of this reaction. In the experiment, an {\alpha}-beam from the underground accelerator LUNA in Gran Sasso, Italy, and a windowless deuterium gas target are used. A low neutron flux is induced by energetic deuterons from elastic scattering and, subsequently, the 2H(d,n)3He reaction. Due to the ultra-low laboratory neutron background at LUNA, the effect of this weak flux of 2-3 MeV neutrons on well-shielded high-purity germanium detectors has been studied in detail. Data have been taken at 280 and 400 keV alpha-beam energy and for comparison also using an americium-beryllium neutron source.Comment: Submitted to EPJA; 13 pages, 8 figure

Impact of a revised 25^{25}Mg(p,γ\gamma)26^{26}Al reaction rate on the operation of the Mg-Al cycle

Proton captures on Mg isotopes play an important role in the Mg-Al cycle active in stellar H-burning regions. In particular, low-energy nuclear resonances in the $^{25}$Mg(p,$\gamma$)$^{26}$Al reaction affect the production of radioactive $^{26}$Al$^{gs}$ as well as the resulting Mg/Al abundance ratio. Reliable estimations of these quantities require precise measurements of the strengths of low-energy resonances. Based on a new experimental study performed at LUNA, we provide revised rates of the $^{25}$Mg(p,$\gamma$)$^{26}$Al$^{gs}$ and the $^{25}$Mg(p,$\gamma$)$^{26}$Al$^{m}$ reactions with corresponding uncertainties. In the temperature range 50 to 150 MK, the new recommended rate of the $^{26}$Al$^{m}$ production is up to 5 times higher than previously assumed. In addition, at T$=100$ MK, the revised total reaction rate is a factor of 2 higher. Note that this is the range of temperature at which the Mg-Al cycle operates in an H-burning zone. The effects of this revision are discussed. Due to the significantly larger $^{25}$Mg(p,$\gamma$)$^{26}$Al$^{m}$ rate, the estimated production of $^{26}$Al$^{gs}$ in H-burning regions is less efficient than previously obtained. As a result, the new rates should imply a smaller contribution from Wolf-Rayet stars to the galactic $^{26}$Al budget. Similarly, we show that the AGB extra-mixing scenario does not appear able to explain the most extreme values of $^{26}$Al/$^{27}$Al, i.e. $>10^{-2}$, found in some O-rich presolar grains. Finally, the substantial increase of the total reaction rate makes the hypothesis of a self-pollution by massive AGBs a more robust explanation for the Mg-Al anticorrelation observed in Globular-Cluster stars