Landau levels (LLs) are modified by the Fröhlich interaction which we investigate within the improved Wigner-Brillouin theory for energies both below and above the longitudinal-optical-continuum in monolayer MoS2, WS2, MoSe2, and WSe2. Polaron corrections to the LLs are enhanced in monolayer MoS2 as compared to WS2. A series of levels are found at ℏωLO+lℏωc, and in addition, the Fröhlich interaction lifts the degeneracy between the levels nℏωc and ℏωLO+lℏωc resulting in an anticrossing. The screening effect due to the environment plays an important role in the polaron energy corrections, which are also affected by the effective thickness reff parameter. The polaron anticrossing energy gap Egap decreases with increasing effective thickness reff.
Using the tight-binding approach, we investigate the energy spectrum of square, triangular and hexagonal MoS2 quantum dots (QDs) in the presence of a perpendicular magnetic field. Novel edge states emerge in MoS2 QDs, which are distributed over the whole edge which we call ring states. The ring states are robust in the presence of spin-orbit coupling (SOC). The corresponding energy levels of the ring states oscillate as function of the perpendicular magnetic field which are related to Aharonov-Bohm oscillations. Oscillations in the magnetic field dependence of the energy levels and the peaks in the magneto-optical spectrum emerge (disappear) as the ring states are formed (collapsed). The period and the amplitude of the oscillation decreases with the size of the MoS2 QDs. I. INTRODUCTIONAfter the initial boom in graphene research, recent years have seen a surge of interest in other two-dimensional (2D) atomic crystals[1]. Among them, molybdenium disulfide (MoS 2 ), a prototypical transition metal dichalcogenide (TMD), has attracted significant interest due to their extraordinary electronic and optical properties. Together with the excellent electrostatic control inherent of 2D materials, the large band gap and high carrier mobility makes them well suited for low power electronics and optoelectronic applications [2][3][4][5]. MoS 2 can be fabricated by, for example, mechanical exfoliation[6], chemical vapor deposition(CVD) [7] or by direct growth methods [8].Monolayer MoS 2 is in many ways similar to graphene, but it also has crucial differences, such as metal d bands around the Fermi level, a direct band gap, and a lack of inversion symmetry[9]. Transition-metal d orbitals lead to strong spin-orbit coupling (SOC) effects [10]. Coupled with the lack of inversion symmetry, SOC leads to a large spin splitting of the valence bands at the corners of the Brillouin zone. The splittings have opposite signs at K and K points, which gives rise to valley-dependent optical transitions [10]. This has been verified by experiment using dynamical pumping of valley polarization by circularly polarized light in monolayers of MoS 2 [11][12][13]. In addition, electrons and holes have valley degrees of freedom, which may be used for information encoding and processing [14][15][16]. Recently, control of the valley pseudospin via an external magnetic field was demonstrated experimentally, which works by breaking the degeneracy of energy states at ±K valleys [17,18]. These results suggest that monolayer MoS 2 can be used as a possible host for integrated spintronics and valleytronics.Quantum dots (QDs) in novel low-dimensional structures, such as graphene [19][20][21][22][23] and black phosphorene [24][25][26][27][28], are actively studied and the applicability of these structures for hosting qubits has also been discussed. To date, several strategies have been developed for preparation of MoS 2 QDs, including lithium intercalation [29], liquid exfoliation in organic solvents [30], hydrothermal synthesis[31], electrochemical etching[32],...
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