Relativistic Effects of Mixed Vector-Scalar-Pseudoscalar Potentials for Fermions in 1+1 Dimensions

The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. The cases of mixed vector and scalar P\"{o}schl-Teller-like and pseudoscalar kink-like potentials, already analyzed in previous works, are obtained as particular cases

Unified Treatment of Mixed Vector-Scalar Screened Coulomb Potentials for Fermions

The problem of a fermion subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and quantization conditions are found.Comment: 7 page

On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background

The problem of spin-0 and spin-1 bosons in the background of a general mixing of minimal and nonminimal vector inversely linear potentials is explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. It is shown that spin-0 and spin-1 bosons behave effectively in the same way. An orthogonality criterion is set up and it is used to determine uniquely the set of solutions as well as to show that even-parity solutions do not exist.Comment: 10 page

New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approac

Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein-Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, $V_{v}+V_{s}= \mathrm{constant}$. These intrinsically relativistic and isospectral problems are solved in a case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.Comment: 3 figure

The peremptory influence of a uniform background for trapping neutral fermions with an inversely linear potential

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength

Charge-fluctuation contribution to the Raman response in superconducting cuprates

We calculate the Raman response contribution due to collective modes, finding a strong dependence on the photon polarizations and on the characteristic wavevectors of the modes. We compare our results with recent Raman spectroscopy experiments in underdoped cuprates, $La_{2-x}Sr_xCuO_4$ and $(Y_{1.97}Ca_{0.3})Ba_2CuO_{6.05}$, where anomalous low-energy peaks are observed, which soften upon lowering the temperature. We show that the specific dependence on doping and on photon polarizations of these peaks is only compatible with charge collective excitations at finite wavelength.Comment: 5 pages, 3 figure

Observation of the Kohn anomaly near the K point of bilayer graphene

The dispersion of electrons and phonons near the K point of bilayer graphene was investigated in a resonant Raman study using different laser excitation energies in the near infrared and visible range. The electronic structure was analyzed within the tight-binding approximation, and the Slonczewski-Weiss-McClure (SWM) parameters were obtained from the analysis of the dispersive behavior of the Raman features. A softening of the phonon branches was observed near the K point, and results evidence the Kohn anomaly and the importance of considering electron-phonon and electron-electron interactions to correctly describe the phonon dispersion in graphene systems.Comment: 4 pages, 4 figure

Signatures of nematic quantum critical fluctuations in the Raman spectra of lightly doped cuprates

We consider the lightly doped cuprates Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ and La$_{2-x}$Sr$_x$CuO$_4$ (with $x=0.02$,0.04), where the presence of a fluctuating nematic state has often been proposed as a precursor of the stripe (or, more generically, charge-density wave) phase, which sets in at higher doping. We phenomenologically assume a quantum critical character for the longitudinal and transverse nematic, and for the charge-ordering fluctuations, and investigate the effects of these fluctuations in Raman spectra. We find that the longitudinal nematic fluctuations peaked at zero transferred momentum account well for the anomalous Raman absorption observed in these systems in the $B_{2g}$ channel, while the absence of such effect in the $B_{1g}$ channel may be due to the overall suppression of Raman response at low frequencies, associated with the pseudogap. While in Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ the low-frequency lineshape is fully accounted by longitudinal nematic collective modes alone, in La$_{2-x}$Sr$_x$CuO$_4$ also charge-ordering modes with finite characteristic wavevector are needed to reproduce the shoulders observed in the Raman response. This different involvement of the nearly critical modes in the two materials suggests a different evolution of the nematic state at very low doping into the nearly charge-ordered state at higher doping.Comment: 12 pages with 10 figures, to appear in Phys. Rev. B 201