Abstract: The energy spectrum and eigenstates of single-layer black phosphorus nanoribbons in the presence of a perpendicular magnetic field and an in-plane transverse electric field are investigated by means of a tight-binding method, and the effect of different types of edges is examined analytically. A description based on a continuum model is proposed using an expansion of the tight-binding model in the long-wavelength limit. Thewave functions corresponding to the flatband part of the spectrum are obtained analytically and are shown to agree well with the numerical results from the tight-binding method for both narrow (10 nm) and wide (100 nm) nanoribbons. Analytical expressions for the critical magnetic field at which Landau levels are formed and the ranges of wave numbers in the dispersionless flatband segments in the energy spectra are derived. We examine the evolution of the Landau levels when an in-plane lateral electric field is applied, and we determine analytically how the edge states shift withmagnetic field. For wider nanoribbons, the conductance is shown to have a characteristic staircase shape in combined magnetic and electric fields. Some of the stairs in zigzag and skewed armchair nanoribbons originate from edge states that are found in the band gap.

Abstract: An effective tight-binding (TB) Hamiltonian for monolayer GeSnH2 is constructed which has an inversion-asymmetric honeycomb structure. The low-energy band structure of our TB model agrees very well with previous ab initio calculations even under biaxial tensile strain. Our model predicts a phase transition at 7.5% biaxial tensile strain in agreement with DFT calculations. Upon 8.5% strain the system exhibits a band gap of 134 meV, suitable for room temperature applications. It is shown that an external applied magnetic field produces a special phase which is a combination of the quantum Hall (QH) and quantum spin Hall (QSH) phases; and at a critical magnetic field strength the QSH phase completely disappears. The topological nature of the phase transition is confirmed from: (1) the calculation of the Z(2) topological invariant, and (2) quantum transport properties of disordered GeSnH2 nanoribbons which allows us to determine the universality class of the conductance fluctuations. The application of an external applied magnetic field reduces the conductance fluctuations by a factor of root 2.

Abstract: It is known that a perpendicular electric field applied to multilayers of graphene modifies the electronic structure near the K point and may induce an energy gap in the electronic spectrum which is tunable by the gate voltage. Here we consider a system of graphene multilayers in the presence of a positively charged top and a negatively charged back gate to control independently the density of electrons on the graphene layers and the Fermi energy of the system. The band structure of three- and four-layer graphene systems in the presence of the top and back gates is obtained using a tight-binding approach. A self-consistent Hartree approximation is used to calculate the induced charges on the different graphene layers. We predict that for opposite and equal charges on the top and bottom layers an energy gap is opened at the Fermi level. For an even number of layers this gap is larger than in the case of an odd number of graphene layers. We find that the circular asymmetry of the spectrum, which is a consequence of the trigonal warping, changes the size of the induced electronic gap, even when the total density of the induced electrons on the graphene layers is low.

Abstract: The effect of different stacking order of graphene multilayers on the electric field induced band gap is investigated. We considered a positively charged top and a negatively charged back gate in order to independently tune the band gap and the Fermi energy of three and four layer graphene systems. A tight-binding approach within a self-consistent Hartree approximation is used to calculate the induced charges on the different graphene layers. We found that the gap for trilayer graphene with the ABC stacking is much larger than the corresponding gap for the ABA trilayer. Also we predict that for four layers of graphene the energy gap strongly depends on the choice of stacking, and we found that the gap for the different types of stacking is much larger as compared to the case of Bernal stacking. Trigonal warping changes the size of the induced electronic gap by approximately 30% for intermediate and large values of the induced electron density.

Abstract: Employing density functional theory-based methods, we investigate monolayer and bilayer structures of hexagonal SnS2, which is a recently synthesized monolayer metal dichalcogenide. Comparison of the 1H and 1T phases of monolayer SnS2 confirms the ground state to be the 1T phase. In its bilayer structure we examine different stacking configurations of the two layers. It is found that the interlayer coupling in bilayer SnS2 is weaker than that of typical transition-metal dichalcogenides so that alternative stacking orders have similar structural parameters and they are separated with low energy barriers. A possible signature of the stacking order in the SnS2 bilayer has been sought in the calculated absorbance and reflectivity spectra. We also study the effects of the external electric field, charging, and loading pressure on the characteristic properties of bilayer SnS2. It is found that (i) the electric field increases the coupling between the layers at its preferred stacking order, so the barrier height increases, (ii) the bang gap value can be tuned by the external E field and under sufficient E field, the bilayer SnS2 can become a semimetal, (iii) the most favorable stacking order can be switched by charging, and (iv) a loading pressure exceeding 3 GPa changes the stacking order. The E-field tunable band gap and easily tunable stacking sequence of SnS2 layers make this 2D crystal structure a good candidate for field effect transistor and nanoscale lubricant applications.

Abstract: Motivated by a recent experiment that reported the successful synthesis of hexagonal (h) AlN [Tsipas et al., Appl. Phys. Lett. 103, 251605 (2013)], we investigate structural, electronic, and vibrational properties of bulk, bilayer, and monolayer structures of h-AlN by using first-principles calculations. We show that the hexagonal phase of the bulk h-AlN is a stable direct-band-gap semiconductor. The calculated phonon spectrum displays a rigid-layer shear mode at 274 cm(-1) and an E-g mode at 703 cm(-1), which are observable by Raman measurements. In addition, single-layer h-AlN is an indirect-band-gap semiconductor with a nonmagnetic ground state. For the bilayer structure, AA'-type stacking is found to be the most favorable one, and interlayer interaction is strong. While N-layered h-AlN is an indirect-band-gap semiconductor for N = 1 – 9, we predict that thicker structures (N >= 10) have a direct band gap at the Gamma point. The number-of-layer-dependent band-gap transitions in h-AlN is interesting in that it is significantly different from the indirect-to-direct crossover obtained in the transition-metal dichalcogenides.

Abstract: The charge density relaxation propagator of a two-dimensional electron system, which is the slope of the imaginary part of the polarization function, exhibits singularities for bosonic momenta having the order of the spin-orbit momentum and depending on the momentum orientation. We have provided an intuitive understanding for this nonanalytic behavior in terms of the interchirality subband electronic transitions, induced by the combined action of Bychkov-Rashba (BR) and Dresselhaus (D) spin-orbit coupling. It is shown that the regular behavior of the relaxation propagator is recovered in the presence of only one BR or D spin-orbit field or for spin-orbit interaction with equal BR and D coupling strengths. This creates a new possibility to influence carrier relaxation properties by means of an applied electric field.

Abstract: The fine structure of the Dirac energy spectrum in graphene induced by electron-optical phonon coupling is investigated in the portion of the spectrum near the phonon emission threshold. The derived new dispersion equation in the immediate neighborhood below the threshold corresponds to an electron-phonon bound state. We find that the singular vertex corrections beyond perturbation theory strongly increase the electron-phonon binding energy scale. The predicted enhancement of the effective electron-phonon coupling can be measured using angle-resolved spectroscopy.

Abstract: The influence of the geometry of a thin superconducting sample on the penetration of the magnetic field lines and the arrangement of vortices are investigated theoretically. We compare the vortex state of superconducting disks, squares, and triangles with the same surface area having nonzero thickness. The coupled nonlinear Ginzburg-Landau equations are solved self-consistently and the important demagnetization effects are taken into account. We calculate and compare quantities such as the free energy, the magnetization, the Cooper-pair density, the magnetic field distribution, and the superconducting current density for the three geometries. For given vorticity the vortex lattice is different for the three geometries, i.e., it tries to adapt to the geometry of the sample. This also influences the stability range of the different vortex states. For certain magnetic field ranges we found a coexistence of a giant vortex placed in the center and single vortices towards the corners of the sample. The H-T phase diagram is obtained for the three investigated geometries and we found that the critical magnetic field is substantially enhanced for the triangle geometry.

Abstract: The superconducting state. of a thin superconducting disk with a hole is studied within the, nonlinear Ginzburg-Landau theory in which the demagnetization effect is accurately taken into account. We find that the flux through the hole is not quantized, the superconducting state is stabilized with increasing size of the hole for fixed radius of the disk, and a transition to a multivortex state is found if the disk is sufficiently large. Breaking the circular symmetry through a non-central-location of the hole in the disk favors the multivortex state.

Abstract: The magnetic coupling between two concentric mesoscopic superconductors with nonzero thickness is studied using the nonlinear Ginzburg-Landau theory. We calculated the free energy, the expelled field, the total field profile, the Cooper-pair density, and the current density distribution. By putting a smaller superconducting disk or ring in the center of a larger ring, the properties change drastically. Extra ground-state transitions are found, where the total vorticity stays the same, but the vorticity of the inner superconductor changes by 1. Due to the magnetic coupling, the current in the external ring exhibits extra jumps at the transition fields where the vorticity of the inner superconductor changes. In this case, for certain temperatures, re-entrant behavior and switching on and off of the superconducting behavior of the rings are found as a function of the magnetic field. A H-T phase diagram is obtained for the situation where the inner ring has a higher critical temperature than the outer ring. An analytic expression for the magnetic coupling is obtained for thin rings and extreme type-II superconductors.

Abstract: Integration of graphene-based two-dimensional materials is essential for nanoelectronics applications. Using density-functional theory, we systematically investigate the electronic properties of vertically stacked graphene-graphitic carbon nitrides (GE/GCN). We also studied the covalently lateral stitched graphene-graphitic carbon nitrides (GE-GCN heterojunctions). The effects of perpendicular electric field on the electronic properties of six different heterostructures, i.e., (i) one layer of GE on top of a layer of CnNm with (n, m) = (3,1), (3,4), and (4,3) and (ii) three heterostructures CnNm/Cn'Nm', where (n, m) not equal (n', m') are elucidated. The most important calculated features are (i) the systems GE/C3N4, C3N/C3N4, GE-C3N, GE-C4N3, and C3N-C3N4 exhibit semiconducting characteristics having small band gaps of Delta(0)=20, 250, 100, 100, 80 meV, respectively while (ii) the systems GE/C4N3, C3N/C4N3, and C3N-C4N3 show ferromagnetic-metallic properties. In particular, we found that, in semiconducting heterostructures, the band gap increases nontrivially with increasing the absolute value of the applied perpendicular electric field. This work is useful for designing heterojunctions and heterostructures made of graphene and other two-dimensional materials such as those proposed in recent experiments [X. Liu and M. C. Hersam Sci. Adv. 5, 6444 (2019)].