Quantum Tunneling of Spin Particles in Periodic Potentials with Asymmetric Twin Barriers

The tunneling effect of a periodic potential with an asymmetric twin barrier per period is calculated using the instanton method. The model is derived from the Hamiltonian of a small ferromagnetic particle in an external magnetic field using the spin-coherent-state path integral. The instantons in two neighbouring barriers differ and lead to different level shifts $\triangle\epsilon_1, \triangle\epsilon_2$. We derive with Bloch theory the energy spectrum which has formally the structure of an energy band. The spectrum depends on both level shifts. The removal of Kramer's degeneracy by an external magnetic field is discussed. In addition we find a new kind of quenching of macroscopic quantum coherence which is irrelevant to Kramer's degeneracy.Comment: 18 pages, LaTex, one figur

Calculation of Spin Tunneling Effects in the Presence of an Applied Magnetic Field

The tunneling splitting of the energy levels of a ferromagnetic particle in the presence of an applied magnetic field - previously derived only for the ground state with the path integral method - is obtained in a simple way from Schroedinger theory. The origin of the factors entering the result is clearly understood, in particular the effect of the asymmetry of the barriers of the potential. The method should appeal particularly to experimentalists searching for evidence of macroscopic spin tunneling.Comment: 10 pages, LaTex, 4 figures included using graphic

Arithmetic purity of strong approximation for homogeneous spaces

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a toric variety. We also prove a similar result of strong approximation with Brauer-Manin obstruction for a partial equivariant smooth compactification of a homogeneous space where all invertible functions are constant and the semi-simple part of the linear algebraic group is quasi-split. Some semi-abelian varieties of any given dimension where the complements of a rational point do not satisfy strong approximation with Brauer-Manin obstruction are given

Interacting Dirac fermions under spatially alternating pseudo-magnetic field: Realization of spontaneous quantum Hall effect

Both topological crystalline insulators surfaces and graphene host multi-valley massless Dirac fermions which are not pinned to a high-symmetry point of the Brillouin zone. Strain couples to the low-energy electrons as a time-reversal invariant gauge field, leading to the formation of pseudo-Landau levels (PLL). Here we study periodic pseudo-magnetic fields originating from strain superlattices. We study the low-energy Dirac PLL spectrum induced by the strain superlattice and analyze the effect of various polarized states. Through self-consistent Hartree-Fock calculations we establish that, due to the strain superlattice and PLL electronic structure, a valley-ordered state spontaneously breaking time-reversal and realizing a quantum Hall phase is favored, while others are suppressed.Comment: 13 pages + 2 appendices, 9 figure

Zeeman-Induced Gapless Superconductivity with Partial Fermi Surface

We show that an in-plane magnetic field can drive two-dimensional spin-orbit-coupled systems under superconducting proximity effect into a gapless phase where parts of the normal state Fermi surface are gapped, and the ungapped parts are reconstructed into a small Fermi surface of Bogoliubov quasiparticles at zero energy. Charge distribution, spin texture, and density of states of such "partial Fermi surface" are discussed. Material platforms for its physical realization are proposed.Comment: 5 pages, 2 figure

Macroscopic Quantum Coherence in Small Antiferromagnetic Particle and the Quantum Interference Effects

Starting from the Hamiltonian operator of the noncompensated two-sublattice model of a small antiferromagnetic particle, we derive the effective Lagrangian of a biaxial antiferromagnetic particle in an external magnetic field with the help of spin-coherent-state path integrals. Two unequal level-shifts induced by tunneling through two types of barriers are obtained using the instanton method. The energy spectrum is found from Bloch theory regarding the periodic potential as a superlattice. The external magnetic field indeed removes Kramers' degeneracy, however a new quenching of the energy splitting depending on the applied magnetic field is observed for both integer and half-integer spins due to the quantum interference between transitions through two types of barriers.Comment: 9 pages, Latex, 4 Postscript figure

NeIII/OII as an oxygen abundance indicator in the HII regions and HII galaxies

To calibrate the relationship between Ne3O2 (Ne3O2 = log(\neiii$\lambda3869$/\oii$\lambda3727$)) and oxygen abundances, we present a sample of $\sim$3000 \hii galaxies from the Sloan Digital Sky Survey (SDSS) data release four. They are associated with a sample from the literature intended to enlarge the oxygen abundance region. We calculated the electron temperatures ($T_e$) of 210 galaxies in the SDSS sample with the direct method, and $T_e$ of the other 2960 galaxies in SDSS sample calculated with an empirical method. Then, we use a linear least-square fitting to calibrate the Ne3O2 oxygen abundance indicator. It is found that the Ne3O2 estimator follows a linear relation with \zoh\ that holds for the whole abundance range covered by the sample, from approximately 7.0 to 9.0. The best linear relationship between the Ne3O2 and the oxygen abundance is calibrated. The dispersion between oxygen abundance and Ne3O2 index in the metal rich galaxies may come partly from the moderate depletion of oxygen onto grains. The $Ne3O2$ method has the virtue of being single-valued and not affected by internal reddening. As a result, the $Ne3O2$ method can be a good metallicity indicator in the \hii regions and \hii galaxies, especially in high-redshift galaxies.Comment: 7 pages, 6 figures. A&A accepte

BRST invariant approach to quantum mechanical tunneling

A new approach with BRST invariance is suggested to cure the degeneracy problem of ill defined path integrals in the path-integral calculationof quantum mechanical tunneling effects in which the problem arises due to the occurrence of zero modes. The Faddeev-Popov procedure is avoided and the integral over the zero mode is transformed in a systematic way into a well defined integral over instanton positions. No special procedure has to be adopted as in the Faddeev-Popov method in calculating the Jacobian of the transformation. The quantum mechanical tunneling for the Sine-Gordon potential is used as a test of the method and the width of the lowest energy band is obtained in exact agreement with that of WKB calculations.Comment: 9 pages, LaTe