128 research outputs found
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 contains a -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 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 and 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 . The coupling of Fermi arcs on opposite
surfaces broadens the Landau levels with a band width that oscillates
periodically in . 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 -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 is defined on a
lattice as a solution of the differential equation ,
where 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 spaceâtime 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 Mg(p,)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 Mg(p,)Al reaction affect the production
of radioactive Al 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 Mg(p,)Al
and the Mg(p,)Al reactions with corresponding
uncertainties. In the temperature range 50 to 150 MK, the new recommended rate
of the Al production is up to 5 times higher than previously
assumed. In addition, at T 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 Mg(p,)Al
rate, the estimated production of Al 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 Al budget.
Similarly, we show that the AGB extra-mixing scenario does not appear able to
explain the most extreme values of Al/Al, i.e. , 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
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