M. Farmanbar

Germanene: the germanium analogue of graphene

Recently, several research groups have reported the growth of germanene, a new member of the graphene family. Germanene is in many aspects very similar to graphene, but in contrast to the planar graphene lattice, the germanene honeycomb lattice is buckled and composed of two vertically displaced sub-lattices. Density functional theory calculations have revealed that free-standing germanene is a 2D Dirac fermion system, i.e. the electrons behave as massless relativistic particles that are described by the Dirac equation, which is the relativistic variant of the Schrödinger equation. Germanene is a very appealing 2D material. The spin-orbit gap in germanene (~24 meV) is much larger than in graphene (<0.05 meV), which makes germanene the ideal candidate to exhibit the quantum spin Hall effect at experimentally accessible temperatures. Additionally, the germanene lattice offers the possibility to open a band gap via for instance an externally applied electrical field, adsorption of foreign atoms or coupling with a substrate. This opening of the band gap paves the way to the realization of germanene based field-effect devices. In this topical review we will (1) address the various methods to synthesize germanene (2) provide a brief overview of the key results that have been obtained by density functional theory calculations and (3) discuss the potential of germanene for future applications as well for fundamentally oriented studies.

Controlling the Schottky barrier at MoS 2/metal contacts by inserting a BN monolayer

Making a metal contact to the two-dimensional semiconductor MoS 2 without creating a Schottky barrier is a challenge. Using density functional calculations we show that, although the Schottky barrier for electrons obeys the Schottky-Mott rule for high work function (≳4.7 eV) metals, the Fermi level is pinned at 0.1–0.3 eV below the conduction band edge of MoS 2 for low work function metals, due to the metal-MoS 2 interaction. Inserting a boron nitride (BN) monolayer between the metal and the MoS 2 disrupts this interaction, and restores the MoS 2 electronic structure. Moreover, a BN layer decreases the metal work function of Co and Ni by ∼2 eV, and enables a lineup of the Fermi level with the MoS 2 conduction band. Surface modification by adsorbing a single BN layer is a practical method to attain vanishing Schottky barrier heights.

First-principles study of van der Waals interactions and lattice mismatch at MoS2/metal interfaces

We explore the adsorption of MoS 2 on a range of metal substrates by means of first-principles density functional theory calculations. Including van der Waals forces in the density functional is essential to capture the interaction between MoS 2 and a metal surface, and obtain reliable interface potential steps and Schottky barriers. Special care is taken to construct interface structures that have a mismatch between the MoS 2 and the metal lattices of <1% . MoS 2 is chemisorbed on the early transition metal Ti, which leads to a strong perturbation of its (electronic) structure and a pinning of the Fermi level 0.54 eV below the MoS 2 conduction band due to interface states. MoS 2 is physisorbed on Au, where the bonding hardly perturbs the electronic structure. The bonding of MoS 2 on other metals lies between these two extreme cases, with interface interactions for the late 3d transition metals Co, Ni, Cu and the simple metal Mg that are somewhat stronger than for the late 4d/5d transition metals Pd, Ag, Pt and the simple metal Al. Even a weak interaction, such as in the case of Al, gives interface states, however, with energies inside the MoS 2 band gap, which pin the Fermi level below the conduction band.

Coulomb drag in anisotropic systems: a theoretical study on a double-layer phosphorene

We theoretically study the Coulomb drag resistivity in a double-layer electron system with highly anisotropic parabolic band structure using Boltzmann transport theory. As an example, we consider a double-layer phosphorene on which we apply our formalism. This approach, in principle, can be tuned for other double-layered systems with paraboloidal band structures. Our calculations show the rotation of one layer with respect to another layer can be considered a way of controlling the drag resistivity in such systems. As a result of rotation, the off-diagonal elements of the drag resistivity tensor have non-zero values at any temperature. In addition, we show that the anisotropic drag resistivity is very sensitive to the direction of momentum transfer between two layers due to highly anisotropic inter-layer electron-electron interaction and also the plasmon modes. In particular, the drag anisotropy ratio, [Formula: see text], can reach up to [Formula: see text]3 by changing the temperature. Furthermore, our calculations suggest that including the local field correction in the dielectric function changes the results significantly. Finally, We examine the dependence of drag resistivity and its anisotropy ratio on various parameters like inter-layer separation, electron density, short-range interaction and insulating substrate/spacer.

Anisotropic hybrid excitation modes in monolayer and double-layer phosphorene on polar substrates

We investigate the anisotropic hybrid plasmon-SO phonon dispersion relations in monolayer and double-layer phosphorene systems located on the polar substrates, such as SiO2, h-BN and Al2O3. We calculate these hybrid modes with using the dynamical dielectric function in the RPA by considering the electron-electron interaction and long-range electric field generated by the substrate SO phonons via Frohlich interaction. In the long-wavelength limit, we obtain some analytical expressions for the hybrid plasmon-SO phonon dispersion relations which represent the behavior of these modes akin to the modes obtaining from the loss function. Our results indicate a strong anisotropy in plasmon-SO phonon modes, whereas they are stronger along the light-mass direction in our heterostructures. Furthermore, we find that the type of substrate has a significant effect on the dispersion relations of the coupled modes. Also, by tuning the misalignment and separation between layers in double-layer phosphorene on polar substrates, we can engineer the hybrid modes.

Strong anisotropic optical conductivity in two-dimensional puckered structures: The role of the Rashba effect

We calculate the optical conductivity of an anisotropic two-dimensional system with Rashba spin-flip excitation within the Kubo formalism. We show that the anisotropic Rashba effect caused by an external field changes significantly the magnitude of the spin splitting. Furthermore, we obtain an analytical expression for the longitudinal optical conductivity associated with inter-band transitions as a function of the frequency for an arbitrary polarization angle. We find that the diagonal components of the optical conductivity tensor are direction-dependent and the spectrum of optical absorption is strongly anisotropic with an absorption window. The height and width of this absorption window are very sensitive to the system anisotropy. While the height of absorption peak increases with increasing effective mass anisotropy ratio, the peak intensity is larger when the light polarization is along the armchair direction. Moreover, the absorption peak width becomes broader as the density of state mass or Rashba interaction is enhanced. These features can be used to determine parameters relevant for spintronics through the optical absorption spectrum.

Interfering Bloch waves in a 1D electron system

Using low-temperature scanning tunnelling spectroscopy we have studied the spatial variation of confined electronic states between neighbouring atomic chains on a Ge(001)/Pt surface. The quasi-one-dimensional electronic states reside in the troughs between the atomic chains and exhibit a profound Bloch character along the chain direction. In the proximity of defects an enhancement of the oscillatory standing wave pattern in the density of states is found. The spatial variation of the standing wave pattern can be explained by an interference of incoming and reflected Bloch waves.

Green's function approach to edge states in transition metal dichalcogenides

The semiconducting two-dimensional transition metal dichalcogenides MX 2 show an abundance of one-dimensional metallic edges and grain boundaries. Standard techniques for calculating edge states typically model nanoribbons, and require the use of supercells. In this paper, we formulate a Greens function technique for calculating edge states of (semi-)infinite two-dimensional systems with a single well-defined edge or grain boundary. We express Greens functions in terms of Bloch matrices, constructed from the solutions of a quadratic eigenvalue equation. The technique can be applied to any localized basis representation of the Hamiltonian. Here, we use it to calculate edge states of MX 2 monolayers by means of tight-binding models. Aside from the basic zigzag and armchair edges, we study edges with a more general orientation, structurally modifed edges, and grain boundaries. A simple three-band model captures an important part of the edge electronic structures. An 11-band model comprising all valence orbitals of the M and X atoms is required to obtain all edge states with energies in the MX 2 band gap. Here, states of odd symmetry with respect to a mirror plane through the layer of M atoms have a dangling-bond character, and tend to pin the Fermi level.

Plasmon modes in monolayer and double-layer black phosphorus under applied uniaxial strain

We study the effects of an applied in-plane uniaxial strain on the plasmon dispersions of monolayer, bilayer and double-layer phosphorene structures in the long-wavelength limit within the linear elasticity theory. In the low energy limit, these effects can be modeled through the change in the curvature of the anisotropic energy band along the armchair and zigzag directions. We derive analytical relations for the plasmon modes under uniaxial strain and show that the direction of the applied strain is important. Moreover, we observe that along the armchair direction, the changes of the plasmon dispersion with strain are different and larger than those along the zigzag direction. Using the analytical relations for two-layer phosphorene systems, we find that the strain-dependent orientation factor of layers could be considered as a means to control the variations of the plasmon energy. Furthermore, our study shows that the plasmonic collective modes are more affected when the strain is applied equally to the layers compared to the case in which the strain is applied asymmetrically to the layers. We also calculate the effect of strain on the drag resistivity in a double-layer phosphorene structure and obtain that the changes in the plasmonic excitations, due to an applied strain, are mainly responsible for the predicted results. This study can be easily extended to other anisotropic two-dimensional materials.