A decade of intense research on two-dimensional (2D) atomic crystals has revealed that their properties can differ greatly from those of the parent compound. These differences are governed by changes in the band structure due to quantum confinement and are most profound if the underlying lattice symmetry changes. Here we report a high-quality 2D electron gas in few-layer InSe encapsulated in hexagonal boron nitride under an inert atmosphere. Carrier mobilities are found to exceed 10 cm V s and 10 cm V s at room and liquid-helium temperatures, respectively, allowing the observation of the fully developed quantum Hall effect. The conduction electrons occupy a single 2D subband and have a small effective mass. Photoluminescence spectroscopy reveals that the bandgap increases by more than 0.5 eV with decreasing the thickness from bulk to bilayer InSe. The band-edge optical response vanishes in monolayer InSe, which is attributed to the monolayer's mirror-plane symmetry. Encapsulated 2D InSe expands the family of graphene-like semiconductors and, in terms of quality, is competitive with atomically thin dichalcogenides and black phosphorus.

We present k· p Hamiltonians parametrised by ab initio density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the K, Q, Γ, and M points of the hexagonal Brillouin zone) in atomic crystals of semiconducting monolayer transition metal dichalcogenides. We discuss the parametrisation of the essential parts of the k· p Hamiltonians for MoS 2 , MoSe 2 , MoTe 2 , WS 2 , WSe 2 , and WTe 2 , including the spin-splitting and spin-polarisation of the bands, and we briefly review the vibrational properties of these materials. We then use k· p theory to analyse optical transitions in two-dimensional transition metal dichalcogenides over a broad spectral range that covers the Van Hove singularities in the band structure (the M points). We also discuss the visualisation of scanning tunnelling microscopy maps. PACS numbers:Contents 1 Introduction 2 2 Lattice parameters, band-structure calculations and vibrational properties 43 Band-edge energy differences and spin-splittings 7 4 Valence band width D vb 9 arXiv:1410.6666v3 [cond-mat.mes-hall] 6 Apr 2015 k · p theory for 2D TMDCs to be studied without constructing slabs in three-dimensionally periodic cells and the resulting electronic spectra are free of plane-wave continua. All our fleur calculations were carried out with a cut-off k max of 10.6 eV −1 for the plane-wave basis set and 144 k points corresponding to a 12 × 12 × 1 Monkhorst-Pack grid in the irreducible wedge of the BZ. Muffin-tin radii of 1.0, 1.21, 1.27, 1.27, and 1.27Å were used for S, Se, Te, Mo, and W, respectively. We note that considering local orbitals for Mo (s, p), Se (s, p, d), and W (s, p, f ) to improve the linearised augmented plane-wave basis proved to be crucial for a correct description of the excited states. We used the Perdew-Burke-Ernzerhof (PBE) generalised gradient approximation [83] to the exchange-correlation potential. The structures were relaxed (with the effects of SOC included) until the forces were less than 0.0005 eV/Å. The calculated values of a 0 and d S−S for monolayer TMDCs are shown in Table 1 and compared to measured values for the corresponding bulk materials. The lattice parameters obtained from the first of the DFT approaches described above are shown in the rows labelled by "(HSE)", the ones from the second approach are in the rows labelled by "(PBE)". "(Exp)" indicates experimental results found in the literature. Although there is some scatter in the experimental data, Table 1 suggests that using the HSE06 functional to relax the monolayer crystal structure leads to a good agreement with the room-temperature empirical bulk a 0 values. On the other hand, the PBE functional seems to slightly overestimates a 0 . However, the situation is less clear in the case of d X−X . We note that both the HSE06 and the PBE results are in good agreement with Reference [84].Recent experiments show that the energy of the photoluminescence peak is quite sensitive to the temperature [5,85,86], which can be understood in terms of th...

We report calculations of the electronic structure of silicene and the stability of its weakly buckled honeycomb lattice in an external electric field oriented perpendicular to the monolayer of Si atoms. The electric field produces a tunable band gap in the Dirac-type electronic spectrum, the gap being suppressed by a factor of about eight by the high polarizability of the system. At low electric fields, the interplay between this tunable band gap, which is specific to electrons on a honeycomb lattice, and the Kane-Mele spin-orbit coupling induces a transition from a topological to a band insulator, whereas at much higher electric fields silicene becomes a semimetal.

Using polarization-resolved photoluminescence spectroscopy, we investigate breaking of valley degeneracy by out-of-plane magnetic field in back-gated monolayer MoSe2 devices. We observe a linear splitting of −0.22 meV T between luminescence peak energies in σ+ and σ− emission for both neutral and charged excitons. The optical selection rules of monolayer MoSe2 couple photon handedness to the exciton valley degree of freedom, so this splitting demonstrates valley degeneracy breaking. In addition, we find that the luminescence handedness can be controlled with magnetic field, to a degree that depends on the back-gate voltage. An applied magnetic field therefore provides effective strategies for control over the valley degree of freedom.