Polaronic effects in monolayer black phosphorus on polar substrates

We investigate the effect of charge carrier interaction with surface optical phonons on the band properties of monolayer black phosphorus induced by polar substrates. We develop an analytical method based on the Lee-Low-Pines theory to calculate the spectrum of Fr\"ohlich type continuum Hamiltonian in the long-wavelength limit. We examine the modification of a band gap and renormalization of effective masses due to the substrate-related polaronic effect. Our results show that an energy gap in supported monolayer black phosphorus is enlarged depending on a particular substrate and the interlayer distance, $z$. Among the substrate considered, the largest gap broadening at $z=2.5$ \AA{} is observed for the Al$_{2}$O$_{3}$ substrate, which is found to be $\sim 50$ meV. Carrier-phonon coupling also renormalizes the effective masses which is more pronounced along the zigzag direction. Anisotropy of the effective masses becomes stronger by the influence of the polaronic effect corresponding to direction-dependent carrier-phonon coupling. We conclude that substrate phonons have a non-negligible effect on the static band properties of monolayer black phosphorus, which may be further exploited in its experimental and theoretical studies

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

Effect of long-range structural corrugations on magnetotransport properties of phosphorene in tilted magnetic field

Rippling is an inherent quality of two-dimensional materials playing an important role in determining their properties. Here, we study the effect of structural corrugations on the electronic and transport properties of monolayer black phosphorus (phosphorene) in the presence of tilted magnetic field. We follow a perturbative approach to obtain analytical corrections to the spectrum of Landau levels induced by a long-wavelength corrugation potential. We show that surface corrugations have a non-negligible effect on the electronic spectrum of phosphorene in tilted magnetic field. Particularly, the Landau levels are shown to exhibit deviations from the linear field dependence. The observed effect become especially pronounced at large tilt angles and corrugation amplitudes. Magnetotransport properties are further examined in the low temperature regime taking into account impurity scattering. We calculate magnetic field dependence of the longitudinal and Hall resistivities and find that the nonlinear effects reflecting the corrugation might be observed even in moderate fields (\mbox{$B<10$ T})

Učinak trotjednog davanja suplemenata cinka i melatonina na oksidacijski-antioksidacijski sustav u eksperimentalnoj bubrežnoj ishemiji-reperfuziji kod štakora

Renal ischemia-reperfusion directly affects glomerular and tubular epithelium. Oxygen free radicals have a significant part in the pathophysiology of renal ischemia-reperfusion injury. The present study aimed to identify the effects of 3-week zinc, melatonin, and zinc + melatonin supplementation on malondialdehyde (MDA) levels in tissue and plasma and glutathione levels (GSH) in erythrocytes and tissue of rats with experimentally induced renal ischemia-reperfusion injury. The study included Wistar albino rats with a mean weight of 250 g. Study groups were formed as follows: control, sham-control, ischemia + reperfusion, zinc + ischemia-reperfusion, melatonin + ischemia-reperfusion, and zinc + melatonin + ischemia-reperfusion. Animals were supplemented with zinc and melatonin 3 mg/kg/day i.p. for 3 weeks before the induction of ischemia-reperfusion. Renal ischemia-reperfusion was induced in the left kidney under general anesthesia and consisted of ischemia for 45 minutes and reperfusion for 1 hour. After the procedure, animals were sacrificed and blood and kidney samples were collected to analyze MDA and GSH levels. GSH values in kidney tissues and erythrocytes were found to be elevated in the groups supplemented with zinc and melatonin (p<0.005). When MDA values in renal tissue and plasma were examined, it was seen that ischemia significantly elevated this parameter, while zinc and melatonin supplementation significantly inhibited MDA values (p<0.002). The results of the study indicated that oxidative injury of the blood and renal tissues of rats increased in association with ischemia-reperfusion, but zinc and melatonin supplementation before ischemia-reperfusion markedly reduced this oxidative damage.Bubrežna ishemija-reperfuzija izravno djeluje na glomerularni i tubularni epitel. Slobodni radikali kisika imaju značajnu ulogu u patofiziologiji bubrežne ishemijsko-reperfuzijske ozljede. Cilj ovoga ispitivanja bio je utvrditi učinke trotjednog davanja suplemenata cinka, melatonina i cinka + melatonina na tkivne i plazmatske razine malondialdehida (MDA) te na razine razine glutationa (GSH) u eritrocitima i tkivu štakora s eksperimentalno izazvanom bubrežnom ishemijsko-reperfuzijskom ozljedom. Ispitivanje je provedeno na Wistar albino štakorima srednje težine 250 g podijeljenim u sljedeće skupine: kontrolna, lažno kontrolna, ishemija + reperfuzija, cink + ishemija-reperfuzija, melatonin + ishemija-reperfuzija i cink + melatonin + ishemija-reperfuzija. Životinje su dobivale suplemente cinka i melatonina, 3 mg/kg/dan i.p. kroz 3 tjedna prije negoli je izazvana ishemija-reperfuzija. Bubrežna ishemija-reperfuzija izazvana je u lijevom bubregu u općoj anesteziji, a sastojala se od ishemije u trajanju od 45 minuta i reperfuzije u trajanju od 1 sata. Nakon zahvata životinje su žrtvovane, a uzorci krvi i bubrega uzeti su za analizu razina MDA i GSH. Vrijednosti GSH u bubrežnom tkivu i eritrocitima bile su povišene u skupinama koje su dobivale suplemente cinka i melatonina (p<0,005). Ispitivanje vrijednosti MDA u bubrežnom tkivu i plazmi pokazalo je da je ishemija značajno povisila ovaj parametar, dok je davanje suplemenata cinka i melatonina značajno inhibiralo vrijednosti MDA (p<0,002). Rezultati ove studije pokazali su da se oksidativno oštećenje u krvi i bubrežnom tkivu štakora povećalo uz ishemiju-reperfuziju, ali je davanje suplemenata cinka i melatonina prije ishemije-reperfuzije znatno smanjilo oksidativno oštećenje