Variational Approach for the Effects of Periodic Modulations on the Spectrum of Massless Dirac Fermion

In the variational framework, we study the electronic energy spectrum of massless Dirac fermions of graphene subjected to one-dimensional oscillating magnetic and electrostatic fields centered around a constant uniform static magnetic field. We analyze the influence of the lateral periodic modulations in one direction, created by these oscillating electric and magnetic fields, on Dirac like Landau levels depending on amplitudes and periods of the field modulations. We compare our theoretical results with those found within the framework of non-degenerate perturbation theory. We found that the technique presented here yields energies lower than that obtained by the perturbation calculation, and thus gives more stable solutions for the electronic spectrum of massless Dirac fermion subjected to a magnetic field perpendicular to graphene layer under the influence of additional periodic potentials.Comment: 8 pages, 7 figure

Boundaries of Subcritical Coulomb Impurity Region in Gapped Graphene

The electronic energy spectrum of graphene electron subjected to a homogeneous magnetic field in the presence of a charged Coulomb impurity is studied analytically within two-dimensional Dirac-Weyl picture by using variational approach. The variational scheme we used is just based on utilizing the exact eigenstates of two-dimensional Dirac fermion in the presence of a uniform magnetic field as a basis for determining analytical energy eigenvalues in the presence of an attractive/repulsive charged Coulomb impurity. This approach allows us to determine under which conditions bound state solutions can or can not exist in gapped graphene in the presence of magnetic field. In addition, the effects of uniform magnetic field on the boundaries of subcritical Coulomb impurity region in the massless limit are also analyzed. Our analytical results show that the critical impurity strength decreases with increasing gap/mass parameter, and also that it increases with increasing magnetic field strength. In the massless limit, we investigate that the critical Coulomb coupling strength is independent of magnetic field, and its upper value for the ground-state energy is 0.752.Comment: 9 pages,10 figure

Two Electrons in a Quantum Dot: A Unified Approach

Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives closed algebraic solutions for the specific values of magnetic field and spatial confinement length, enables us to see explicitly individual effects of the electron correlation.Comment: 14 page

Experiences of wearing support garments by people living with a urostomy

BACKGROUND:support garments are commonly worn by people with a urostomy but there are no published data about their experiences of doing so. AIMS:to identify the views of people living with a urostomy on the role of support garments. METHODS:a cross-sectional survey of the stoma population's experiences of support garments was conducted in 2018. Recruitment was by social media. The free-text responses provided by a sub-sample of 58 people out of 103 respondents with a urostomy, were analysed. FINDINGS:thematic analysis revealed four themes: physical self-management; psychosocial self-management; lifestyle; and healthcare advice and support. There were mixed feelings about the value of support garments. Many cited a sense of reassurance and confidence and being able to be more sociable and active; others reported discomfort and uncertainty about their value. CONCLUSION:these findings add new understanding of experiences of support garments and provide novel theoretical insights about life with a urostomy

Intrinsic Spin-Orbit Interaction in Graphene

In graphene, we report the first theoretical demonstration of how the intrinsic spin orbit interaction can be deduced from the theory and how it can be controlled by tuning a uniform magnetic field, and/or by changing the strength of a long range Coulomb like impurity (adatom), as well as gap parameter. In the impurity context, we find that intrinsic spin-orbit interaction energy may be enhanced by increasing the strength of magnetic field and/or by decreasing the band gap mass term. Additionally, it may be strongly enhanced by increasing the impurity strength. Furthermore, from the proposal of Kane and Mele [Phys. Rev. Lett. 95, 226801 (2005)], it was discussed that the pristine graphene has a quantized spin Hall effect regime where the Rashba type spin orbit interaction term is smaller than that of intrinsic one. Our analysis suggest the nonexistence of such a regime in the ground state of flat graphene