Resonances for Dirac operators on the half-line

We consider the 1D Dirac operator on the half-line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: (1) asymptotics of counting function, (2) estimates on the resonances and the forbidden domain.     

Real Paley-Wiener theorems for the Clifford Fourier transform

Associated with the Dirac operator and partial derivatives, this paper establishes some real Paley-Wiener type theorems to characterize the Clifford-valued functions whose Clifford Fourier transform (CFT) has compact support. Based on the Riemann-Lebesgue theorem for the CFT, the Boas theorem is provided to describe the CFT of Clifford-valued functions that vanish on a neighborhood of the origin.     

Fabrication of honeycomb AuTe monolayer with Dirac nodal line fermions

Two-dimensional honeycomb lattices show great potential in the realization of Dirac nodal line fermions (DNLFs). Here, we successfully synthesized a gold telluride (AuTe) monolayer by direct tellurizing an Au(111) substrate. Low energy electron diffraction measurements reveal that it is (2×2) AuTe layer stacked onto (3×3) Au(111) substrate. Moreover, scanning tunneling microscopy images show that the AuTe layer has a honeycomb structure. Scanning transmission electron microscopy reveals that it is a single-atom layer. In addition, first-principles calculations demonstrate that the honeycomb AuTe monolayer exhibits Dirac nodal line features protected by mirror symmetry, which is validated by angle-resolved photoemission spectra. Our results establish that monolayer AuTe can be a good candidate to investigate 2D DNLFs and provides opportunities to realize high-speed low-dissipation devices.     

Cosmological imprints of Dirac neutrinos in a keV-vacuum 2HDM

The Dirac neutrino masses could be simply generated by a neutrinophilic scalar doublet with a vacuum being dramatically different from the electroweak one. While the case with an eV-scale vacuum has been widely explored previously, we exploit in this work the desert where the scalar vacuum is of begin{document}$mathcal{O}(mathrm{keV})$end{document} scale. In this regime, there would be rare hope to probe the keV-vacuum neutrinophilic scalar model via the lepton-flavor-violating processes, which makes it distinguishable from the widely considered eV-scale vacuum. Although such a keV-vacuum scenario is inert in the low-energy flavor physics, we show that the baryogenesis realized via the lightest Dirac neutrino can be a natural candidate in explaining the baryon asymmetry of the Universe. Furthermore, the Dirac neutrinos with a keV-vacuum scalar can generate a shift of the effective neutrino number within the range begin{document}$0.097leqslant Delta N_{rm eff}leqslant 0.112$end{document}, which can be probed by the future Simons Observatory experiments. In particular, the model with a minimal value begin{document}$Delta N_{rm eff}=0.097$end{document} can already be falsified by the future CMB Stage-IV and Large Scale Structure surveys, providing consequently striking exploratory avenues in the cosmological regime for such a keV-vacuum scenario.     

Acetylene-Mediated Borophosphene Dirac Materials as Efficient Anode Materials for Lithium-Ion Batteries

Generally, graphynes have been generated by the insertion of acetylenic content (−C≡C−) in the graphene network in different ratios. Also, several aesthetically pleasing architectures of two-dimensional (2D) flatlands have been reported with the incorporation of acetylenic linkers between the heteroatomic constituents. Prompted by the experimental realization of boron phosphide, which has provided new insights on the boron-pnictogen family, we have modelled novel forms of acetylene-mediated borophosphene nanosheets by joining the orthorhombic borophosphene stripes with different widths and with different atomic constituents using acetylenic linkers. Structural stabilities and properties of these novel forms have been assessed using first-principles calculations. Investigation of electronic band structure elucidates that all the novel forms show the linear band crossing closer to the Fermi level at Dirac point with distorted Dirac cones. The linearity in the hole and electronic bands impose the high Fermi velocity to the charge carriers close to that of graphene. Finally, we have also unravelled the propitious features of acetylene-mediated borophosphene nanosheets as anodes in Li-ion batteries.     

Bag Boundaries for Quasispinor Confinement Within Nanolanes on a Graphene Sheet

The problem of bag boundary conditions within a field-theoretic approach is revisited to study confinement of massless Dirac quasispinors in monolayer graphene. While no-flux bag boundaries have previously been used to model lattice termination sites in graphene nanoribbons, a generalized setting is considered in which the confining boundaries are envisaged as arbitrary straight lines drawn across a graphene sheet and the quasispinor currents are allowed to partially permeate (leak) through such boundaries. Specifically focus is on rectangular nanolanes defined as areas confined between a pair of parallel lines at arbitrary separation on an unbounded lattice. It is shown that such nanolanes exhibit a considerable range of bandgap tunability depending on their widths and armchair, zigzag, or intermediate orientation. The case of nanoribbons can be derived as a special limit from the nanolane model. In this case, certain inconsistencies are clarified in previous implementations of no-flux bag boundaries and show that the continuum approach reproduces the tight-binding bandgaps accurately (within just a few percent in relative deviation) even as the nanoribbon width is decreased to just a couple of lattice spacings. This accentuates the proper use of boundary conditions when field-theoretic approaches are applied to graphene systems.     

On the Boltzmann Equation for Fermi–Dirac Particles with Very Soft Potentials: Averaging Compactness of Weak Solutions

The paper considers macroscopic behavior of a Fermi–Dirac particle system. We prove the L ¹-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi–Dirac particles in a periodic box with the collision kernel b(cos θ)|ρ−ρ _*|^γ, which corresponds to very soft potentials: −5 < γ ≤ −3 with a weak angular cutoff: ∫₀ ^π b(cos θ)sin ³θ dθ < ∞. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff–Young inequality, the L ^∞-bounds of the solutions, and a specific property of the value-range of the exponent γ. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy.     

Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.