Probing negatively charged and neutral excitons in MoS2/hBN and hBN/MoS2/hBN van der Waals heterostructures.

High-quality van der Waals heterostructures assembled from hBN-encapsulated monolayer transition metal dichalcogenides enable observations of subtle optical and spin-valley properties whose identification was beyond the reach of structures exfoliated directly on standard SiO2/Si substrates. Here, we describe different van der Waals heterostructures based on uncapped single-layer MoS2 stacked onto hBN layers of different thicknesses and hBN-encapsulated monolayers. Depending on the doping level, they reveal the fine structure of excitonic complexes, i.e. neutral and charged excitons. In the emission spectra of a particular MoS2/hBN heterostructure without an hBN cap we resolve two trion peaks, T1 and T2, energetically split by about 10 meV, resembling the pair of singlet and triplet trion peaks (T S and T T ) in tungsten-based materials. The existence of these trion features suggests that monolayer MoS2 has a dark excitonic ground state, despite having a 'bright' single-particle arrangement of spin-polarized conduction bands. In addition, we show that the effective excitonic g-factor significantly depends on the electron concentration and reaches the lowest value of -2.47 for hBN-encapsulated structures, which reveals a nearly neutral doping regime. In the uncapped MoS2 structures, the excitonic g-factor varies from -1.15 to -1.39 depending on the thickness of the bottom hBN layer and decreases as a function of rising temperature.

Probing of free and localized excitons and trions in atomically thin WSe2, WS2, MoSe2 and MoS2 in photoluminescence and reflectivity experiments.

We report on detailed temperature dependent (T = 7-295 K) optical spectroscopy studies of WSe2, WS2, MoSe2 and MoS2 monolayers exfoliated onto the same SiO2/Si substrate. In the high energy region of absorption type (reflectivity contrast-RC) and emission (photo-luminescence-PL) spectra of all the monolayers resonances related to the neutral and charged excitons (X and T) are detected in the entire measured temperature range. The optical amplitudes of excitons and trions strongly depend on the temperature and two dimensional carrier gas (2DCG) concentration. In the low energy PL spectra of WSe2 and WS2 we detect a group of lines (L) which dominates the spectra at low temperatures but rapidly quenches with the increase in the temperature. Interestingly, in the same energy range of the RC spectra recorded for WS2, we observe an additional line (L 0), which behaves in the same way as the L lines in the PL spectra. The optical amplitude of L 0 and T resonances in the RC spectra strongly increases with the growth of the 2DCG concentration. On the base of these observations we identify the L 0 resonance in the RC spectra as arising from the fine structure of the trion. We also propose that the line interpreted previously in PL spectra of WSe2 and WS2 as related to the biexciton emission is a superposition of the biexciton, trion and localized exciton emission. We find that with the temperature increase from 7-295 K the total PL intensity decreases moderately in WSe2 and WS2, strongly in MoS2 and dramatically in MoSe2.

Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect.

The spin transitions in the fractional quantum Hall effect provide a direct measure of the tiny energy differences between differently spin-polarized states and thereby serve as an extremely sensitive test of the quantitative accuracy of the theory of the fractional quantum Hall effect, and, in particular, of the role of Landau-level mixing in lifting the particle-hole symmetry. We report on an accurate quantitative study of this physics, evaluating the effect of Landau-level mixing in a nonperturbative manner using a fixed-phase diffusion Monte Carlo method. We find excellent agreement between our calculated critical Zeeman energies and the experimentally measured values. In particular, we find, as also do experiments, that the critical Zeeman energies for fractional quantum Hall states at filling factors ν=2-n/(2n±1) are significantly higher than those for ν=n/(2n±1), a quantitative signature of the lifting of particle-hole symmetry due to Landau-level mixing.

Fractionally charged skyrmions in fractional quantum Hall effect.

The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.

Unpaired composite fermion, topological exciton, and zero mode.

The paired state of composite fermions is expected to support two kinds of excitations: vortices and unpaired composite fermions. We construct an explicit microscopic description of the unpaired composite fermions, which we demonstrate to be accurate for a 3-body model interaction and, possibly, adiabatically connected to the Coulomb solution. This understanding reveals that an unpaired composite fermion carries with it a charge-neutral "topological" exciton, which, in turn, helps provide microscopic insight into the origin of zero modes, fusion rules, and energetics.

Bipartite composite fermion States.

We study a class of ansatz wave functions in which composite fermions form two correlated "partitions." These "bipartite" composite fermion states are demonstrated to be very accurate for electrons in a strong magnetic field interacting via a short-range 3-body interaction potential over a broad range of filling factors. Furthermore, this approach gives accurate approximations for the exact Coulomb ground state at 2+3/5 and 2+4/7 and is thus a promising candidate for the observed fractional quantum Hall states at the hole conjugate fractions at 2+2/5 and 2+3/7.