Abstract: We study the influence of confinement on the atomic collapse due to a Coulomb impurity placed at the center of a graphene quantum dot of radius R. We apply the zigzag or infinite-mass boundary condition and consider both a point-size and a finite-size impurity. As a function of the impurity strength Za, the energy spectra are discrete. In the case of the zigzag boundary condition, the degenerate (with respect to the angular momentum m) zero-energy levels are pulled down in energy as Z alpha increases, and they remain below epsilon = – Z alpha. Our results show that the energy levels exhibit a 1/R dependence in the subcritical regime [Z alpha < |km + 1/2|, k = 1 (-1) for the K (K') valley]. In the supercritical regime (Z alpha > |km + 1/2|) we find a qualitatively very different behavior where the levels decrease as a function of R in a nonmonotonic manner. While the valley symmetry is preserved in the presence of the impurity, we find that the impurity breaks electron-hole symmetry. We further study the energy spectrum of zigzag quantum dots in gapped graphene. Our results show that as the gap increases, the lowest electron states are pushed into the gap by the impurity.

Abstract: The spectrum of a Coulomb impurity in bilayer graphene is investigated as function of the strength of a perpendicular magnetic field for different values of the angular quantum number m and for different values of the gate voltage. We point out fundamental differences between the results from the two-band and four-band model. The supercritical instability and fall-to-center phenomena are investigated in the presence of a magnetic field. We find that in the four-band model the fall-to-center phenomenon occurs as in monolayer graphene, while this is not the case in the two-band model. We find that in a magnetic field the supercritical instability manifests itself as a series of anticrossings in the hole part of the spectrum for states coming from the low-energy band. However, we also find very distinct anticrossings in the electron part of the spectrum that continue into the hole part, which are related to the higher energy band of the four-band model. At these anticrossings, we find a very sharp peak in the probability density close to the impurity, reminiscent for the fall-to-center phenomenon. In this paper, these peculiar and interesting effects are studied for different magnetic field, interlayer coupling, and bias potential strengths.

Abstract: Coupled electron-hole states are realized in a system consisting of a combination of an electrostatic potential barrier and ring-shaped potential well, which resembles a circular dipole. A perpendicular magnetic field induces confined states inside the Landau gaps which are mainly located at the barrier or ring. Hybridizations between the barrier and ring states are seen as anticrossings in the energy spectrum. As a consequence, the energy levels show an oscillating dependence on the electrostatic potential strength in combination with an oscillating migration of the wave functions between the barrier and ring. At the anticrossing points the quantum state consists of a mixture of electron and hole. The present system mimics closely the behavior of a relativistic dipole on gapped graphene.

Abstract: The electronic properties of the two-dimensional material silicene are strongly influenced by the application of a perpendicular electric field E-z and of an exchange field M due to adatoms positioned on the surface or a ferromagnetic substrate. Within the random phase approximation, we investigate how electron-electron interactions are affected by these fields and present analytical and numerical results for the dispersion of plasmons, their lifetime, and their oscillator strength. We find that the combination of the fields E-z and M brings a spin and valley texture to the particle-hole excitation spectrum and allows the formation of spin-and valley-polarized plasmons. When the Fermi level lies in the gap of one spin in one valley, the intraband region of the corresponding spectrum disappears. For zero E-z and finite M the spin symmetry is broken and spin polarization is possible. The lifetime and oscillator strength of the plasmons are shown to depend strongly on the number of spin and valley type electrons that form the electron-hole pairs.

Abstract: The conductance, the transmission, and the reflection probabilities through rectangular potential barriers and p-n junctions are obtained for bilayer graphene taking into account the four bands of the energy spectrum. We have evaluated the importance of the skew hopping parameters gamma(3) and gamma(4) to these properties and show that for energies E > gamma(1)/100 their effect is negligible. For high energies two modes of propagation exist and we investigate scattering between these modes. For perpendicular incidence both propagation modes are decoupled, and scattering between them is forbidden. This extends the concept of pseudospin as defined within the two-band approximation to a four-band model and corresponds to the (anti) symmetry of the wave functions under in-plane mirroring. New transmission resonances are found that appear as sharp peaks in the conductance which are absent in the two-band approximation. The application of an interlayer bias to the system (1) breaks the pseudospin structure, (2) opens a band gap that results in a distinct feature of suppressed transmission in the conductance, and (3) breaks the angular symmetry with respect to normal incidence in the transmission and reflection.

Abstract: The effect of the spatially varying spin current on a skyrmion is numerically investigated. It is shown that an inhomogeneous current density induces an elongation of the skyrmion. This elongation can be controlled using current pulses of different strength and duration. Long current pulses lead to a splitting that forms two replicas of the initial skyrmion while for short pulses the elongated skyrmion relaxes back to its initial circular state through rotation in the MHz-GHz frequency range. The frequency is dependent on the strength of the damping coefficient.

Abstract: The dependence of the excitonic photoluminescence (PL) spectrum of monolayer transition metal dichalcogenides (TMDs) on the tilt angle of an applied magnetic field is studied. Starting from a four-band Hamiltonian we construct a theory which quantitatively reproduces the available experimental PL spectra for perpendicular and in-plane magnetic fields. In the presence of a tilted magnetic field, we demonstrate that the dark exciton PL peaks brighten due to the in-plane component of the magnetic field and split for light with different circular polarizations as a consequence of the perpendicular component of the magnetic field. This splitting is more than twice as large as the splitting of the bright exciton peaks in tungsten-based TMDs. We propose an experimental setup that will allow for accessing the predicted splitting of the dark exciton peaks in the PL spectrum.

Abstract: In the Comment, the authors state that the separation of the relative and center of mass variables in our work is not correct. Here we point out that there is a typographical error, i.e., qi instead of -e, in two of our equations which, when corrected, makes the Comment redundant. Within the ansatzes mentioned in our paper all our results are correct, in contrast to the claims of the Comment.

Abstract: A strong in-plane magnetic field drastically alters the low-energy spectrum of bilayer graphene by separating the parabolic energy dispersion into two linear Dirac cones. The effect of this dramatic change on the transport properties strongly depends on the orientation of the in-plane magnetic field with respect to the propagation direction of the charge carriers and the angle at which they impinge on the electrostatic potentials. For magnetic fields oriented parallel to the potential boundaries an additional propagating mode that results from the splitting into Dirac cones enhances the transmission probability for charge carriers tunneling through the potentials and increases the corresponding conductance. Our results show that the chiral suppression of transmission at normal incidence, reminiscent of bilayer graphene's 2 pi Berry phase, is turned into a chiral enhancement when the magnetic field increases, thus indicating a transition from a bilayer to a monolayer-like system at normal incidence. Further, we find that the typical transmission resonances stemming from confinement in a potential barrier are shifted to higher energy and are eventually transformed into antiresonances with increasing magnetic field. For magnetic fields oriented perpendicular to the potential boundaries we find a very pronounced transition from a bilayer system to two separated monolayer-like systems with Klein tunneling emerging at certain incident angles symmetric around 0, which also leaves a signature in the conductance. For both orientations of the magnetic field, the transmission probability is still correctly described by pseudospin conservation. Finally, to motivate the large in-plane magnetic field, we show that its energy spectrum can be mimicked by specific lattice deformations such as a relative shift of one of the layers. With this equivalence we introduce the notion of an in-plane pseudomagnetic field.

Abstract: Starting from the single-particle Dirac Hamiltonian for charge carriers in monolayer transition metal dichalcogenides (TMDs), we construct a four-band Hamiltonian describing interlayer excitons consisting of an electron in one TMD layer and a hole in the other TMD layer. An expression for the electron-hole interaction potential is derived, taking into account the effect of the dielectric environment above, below, and between the two TMD layers as well as polarization effects in the transition metal layer and in the chalcogen layers of the TMD layers. We calculate the interlayer exciton binding energy and average in-plane interparticle distance for different TMD heterostructures. The effect of different dielectric environments on the exciton binding energy is investigated and a remarkable dependence on the dielectric constant of the barrier between the two layers is found, resulting from competing effects as a function of the in-plane and out-of-plane dielectric constants of the barrier. The polarization effects in the chalcogen layers, which in general reduce the exciton binding energy, can lead to an increase in binding energy in the presence of strong substrate effects by screening the substrate. The excitonic absorbance spectrum is calculated and we show that the interlayer exciton peak depends linearly on a perpendicular electric field, which agrees with recent experimental results.

Abstract: A four-band exciton Hamiltonian is constructed starting from the single-particle Dirac Hamiltonian for charge carriers in monolayer transition metal dichalcogenides (TMDs). The angular part of the exciton wave function can be separated from the radial part, in the case of zero center of mass momentum excitons, by exploiting the eigenstates of the total exciton angular momentum operator with which the Hamiltonian commutes. We explain why this approach fails for excitons with finite center of mass momentum or in the presence of a perpendicular magnetic field and present an approximation to resolve this issue. We calculate the (binding) energy and average interparticle distance of different excited exciton states in different TMDs and compare these with results available in the literature. Remarkably, we find that the intervalley exciton ground state in the -/+ K valley has angular momentum j = +/- 1, which is due to the pseudospin of the separate particles. The exciton mass and the exciton Landau levels are calculated and we find that the degeneracy of exciton states with opposite relative angular momentum is altered by a magnetic field.

Abstract: The magnetization of luminescent Er3+-doped PbF2 nanoparticles (formula Er0.3Pb0.7F2.3) has been studied. Despite the high concentration of the doping Er3+ ions and relatively large size (8 nm) of these nanoparticles we have found no deviation between field-cooled and zero-field-cooled magnetization curves down to T=0.35 K, which points out an ultralow blocking temperature for the reversal of magnetization. We also have found strongly deviating magnetization curves M(H/T) for different temperatures T. These results altogether show that the investigated nanoparticles are not superparamagnetic, but rather each Er3+ ion in these nanoparticles is found in a paramagnetic state down to very low temperatures, which implies the breakdown of the Néel-Brown giant spin model in the case of these nanoparticles. Calculations of magnetization within a paramagnetic model of noninteracting Er3+ ions completely support this conclusion. Due to the ultralow blocking temperature, these nanoparticles have a potential for magnetic field-induced nanoscale refrigeration with an option of their optical localization and temperature control.

Abstract: Based on the Gor'kov formalism for a clean s-wave superconductor, we develop an extended version of the single-band Ginzburg-Landau (GL) theory by means of a systematic expansion in the deviation from the critical temperature T(c), i.e., tau = 1 – T/T(c). We calculate different contributions to the order parameter and the magnetic field: the leading contributions (proportional to tau(1/2) in the order parameter and. t in the magnetic field) are controlled by the standard GL theory, while the next-to-leading terms (proportional to tau(3/2) in the gap and proportional to tau(2) in the magnetic field) constitute the extended GL (EGL) approach. We derive the free-energy functional for the extended formalism and the corresponding expression for the current density. To illustrate the usefulness of our formalism, we calculate, in a semianalytical form, the temperature-dependent correction to the GL parameter at which the surface energy becomes zero, and analytically, the temperature dependence of the thermodynamic critical field. We demonstrate that the EGL formalism is not just a mathematical extension to the theory: variations of both the gap and the thermodynamic critical field with temperature calculated within the EGL theory are found in very good agreement with the full BCS results down to low temperatures, which dramatically improves the applicability of the formalism compared to its standard predecessor.

Abstract: We derive the extended Ginzburg-Landau (GL) formalism for a clean s-wave two-band superconductor by employing a systematic expansion of the free-energy functional and the corresponding matrix gap equation in powers of the small deviation from the critical temperature tau = 1 – T/T-c. The two lowest orders of this expansion produce the equation for T-c and the standard GL theory. It is shown that in agreement with previous studies, this two-band GL theory maps onto the single-band GL model and thus fails to describe the difference in the spatial profiles of the two-band condensates. We prove that this difference appears already in the leading correction to the standard GL theory, which constitutes the extended GL formalism. We derive linear differential equations that determine the leading corrections to the band order parameters and magnetic field, discuss the validity of these equations, and consider examples of an important interplay between the band condensates. Finally, we present numerical results for the thermodynamic critical magnetic field and temperature-dependent band gaps for recent materials of interest, which are in very good agreement with those obtained from the full BCS approach in a wide temperature range. To this end, we emphasize the advantages of our extended GL theory in comparison with the often used two-component GL-like model based on an unreconstructed two-band generalization of the Gor'kov derivation.