Exciton Diamagnetic Shifts and Valley Zeeman Effects in Monolayer WS2_2 and MoS2_2 to 65 Tesla

We report circularly-polarized optical reflection spectroscopy of monolayer WS$_2$ and MoS$_2$ at low temperatures (4~K) and in high magnetic fields to 65~T. Both the A and the B exciton transitions exhibit a clear and very similar Zeeman splitting of approximately $-$230~$\mu$eV/T ($g\simeq -4$), providing the first measurements of the valley Zeeman effect and associated $g$-factors in monolayer transition-metal disulphides. These results complement and are compared with recent low-field photoluminescence measurements of valley degeneracy breaking in the monolayer diselenides MoSe$_2$ and WSe$_2$. Further, the very large magnetic fields used in our studies allows us to observe the small quadratic diamagnetic shifts of the A and B excitons in monolayer WS$_2$ (0.32 and 0.11~$\mu$eV/T$^2$, respectively), from which we calculate exciton radii of 1.53~nm and 1.16~nm. When analyzed within a model of non-local dielectric screening in monolayer semiconductors, these diamagnetic shifts also constrain and provide estimates of the exciton binding energies (410~meV and 470~meV for the A and B excitons, respectively), further highlighting the utility of high magnetic fields for understanding new 2D materials.Comment: 9 pages, 5 figure

Magneto-reflection spectroscopy of monolayer transition-metal dichalcogenide semiconductors in pulsed magnetic fields

We describe recent experimental efforts to perform polarization-resolved optical spectroscopy of monolayer transition-metal dichalcogenide semiconductors in very large pulsed magnetic fields to 65 tesla. The experimental setup and technical challenges are discussed in detail, and temperature-dependent magneto-reflection spectra from atomically thin tungsten disulphide (WS$_2$) are presented. The data clearly reveal not only the valley Zeeman effect in these 2D semiconductors, but also the small quadratic exciton diamagnetic shift from which the very small exciton size can be directly inferred. Finally, we present model calculations that demonstrate how the measured diamagnetic shifts can be used to constrain estimates of the exciton binding energy in this new family of monolayer semiconductors.Comment: PCSI-43 conference (Jan. 2016; Palm Springs, CA

Magneto-Optics of Exciton Rydberg States in a Monolayer Semiconductor

We report 65 tesla magneto-absorption spectroscopy of exciton Rydberg states in the archetypal monolayer semiconductor WSe$_2$. The strongly field-dependent and distinct energy shifts of the 2s, 3s, and 4s excited neutral excitons permits their unambiguous identification and allows for quantitative comparison with leading theoretical models. Both the sizes (via low-field diamagnetic shifts) and the energies of the $ns$ exciton states agree remarkably well with detailed numerical simulations using the non-hydrogenic screened Keldysh potential for 2D semiconductors. Moreover, at the highest magnetic fields the nearly-linear diamagnetic shifts of the weakly-bound 3s and 4s excitons provide a direct experimental measure of the exciton's reduced mass, $m_r = 0.20 \pm 0.01~m_0$.Comment: To appear in Phys. Rev. Lett. Updated version (25 jan 2018) now includes detailed supplemental discussion of Landau levels, Rydberg exciton energies, exciton mass, Dirac Hamiltonian, nonparabolicity, and dielectric effect

System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion

The design of route-guidance systems faces a well-known dilemma. The approach that theoretically yields the system-optimal traffic pattern may discriminate against some users, for the sake of favoring others. Proposed alternate models, however, do not directly address the system perspective and may result in inferior performance. We propose a novel model and corresponding algorithms to resolve this dilemma. We present computational results on real-world instances and compare the new approach with the well-established traffic assignment model. The quintessence is that system-optimal routing of traffic flow with explicit integration of user constraints leads to a better performance than the user equilibrium while simultaneously guaranteeing a superior fairness compared to the pure system optimum

Probing the Dark Exciton in Monolayer MoS2_2 by Quantum Interference in Second Harmonic Generation Spectroscopy

We report resonant second harmonic generation (SHG) spectroscopy of an hBN-encapsulated monolayer of MoS$_2$. By tuning the energy of the excitation laser, we identify a dark state transition (D) that is blue detuned by +25 meV from the neutral exciton X$^0$. We observe a splitting of the SHG spectrum into two distinct peaks and a clear anticrossing between them as the SHG resonance is tuned through the energy of the dark exciton D. This observation is indicative of quantum interference arising from the strong two-photon light-matter interaction. We further probe the incoherent relaxation from the dark state to the bright excitons, including X$^0$ and localized excitons LX, by the resonant enhancement of their intensities at the SHG-D resonance. The relaxation of D to bright excitons is strongly suppressed on the bare substrate whilst enabled when the hBN/MoS$_2$/hBN heterostructure is integrated in a nanobeam cavity. The relaxation enabled by the cavity is explained by the phonon scattering enhanced by the cavity phononic effects. Our work reveals the two-photon quantum interference with long-lived dark states and enables the control through nanostructuring of the substrate. These results indicate the great potential of dark excitons in 2D-material based nonlinear quantum devices

Selective Exciton-Phonon-Phonon Coupling and Anharmonicity with Cavity Vibrational Phonons and MoS2_2 Lattice Phonons in Hybrid Nanobeam Cavities

We report selective coupling between neutral excitons X$^0$, vibrational phonon modes of a freestanding nanobeam cavity and lattice phonons of a MoS$_2$ monolayer fully encapsulated by hBN. Our experimental findings demonstrate that the cavity vibrational phonons selectively couple to neutral excitons (X$^0$), and the coupling to negatively charged trion (X$^-$) being significantly weaker. We establish this result by studying the lattice temperature induced broadening of exciton linewidths, where the contribution from the X$^0$-cavity phonon coupling is clearly observed while the X$^-$-cavity phonon coupling is not. Furthermore, when the Raman modes of MoS$_2$ lattice phonons A$_{1g}$ and 2LA are tuned into an outgoing resonance with exciton emissions, we observe the X$^0$-cavity phonon-lattice phonon coupling which inherits the characteristics rule the of X$^0$-cavity phonon coupling. As a result, X$^0$-induced Raman scatterings are enhanced, while X$^-$-induced scatterings are suppressed, revealed by the detuning-dependent Raman intensities and the ratio of X$^-$/X$^0$ emission intensities. The phonon anharmonicity from the coupling between cavity vibrational phonons and MoS$_2$ lattice phonons is further demonstrated by the observed Raman linewidth. Such hybrid couplings between materials and nanostructures enable the control of phonon-induced processes in nanophotonic and nanomechanical systems incorporating 2D semiconductors

Charged exciton kinetics in monolayer MoSe2_2 near ferroelectric domain walls in periodically poled LiNbO3_3

Monolayers of semiconducting transition metal dichalcogenides are a strongly emergent platform for exploring quantum phenomena in condensed matter, building novel opto-electronic devices with enhanced functionalities. Due to their atomic thickness, their excitonic optical response is highly sensitive to their dielectric environment. In this work, we explore the optical properties of monolayer thick MoSe$_2$ straddling domain wall boundaries in periodically poled LiNbO$_3$. Spatially-resolved photoluminescence experiments reveal spatial sorting of charge and photo-generated neutral and charged excitons across the boundary. Our results reveal evidence for extremely large in-plane electric fields of 3000\,kV/cm at the domain wall whose effect is manifested in exciton dissociation and routing of free charges and trions toward oppositely poled domains and a non-intuitive spatial intensity dependence. By modeling our result using drift-diffusion and continuity equations, we obtain excellent qualitative agreement with our observations and have explained the observed spatial luminescence modulation using realistic material parameters.Comment: 29 pages, 6 figures, submetted materia