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

Asymmetric magnetic proximity interactions in MoSe2_{2}/CrBr3_{3} van der Waals heterostructures

Magnetic proximity interactions (MPIs) between atomically-thin semiconductors and two-dimensional magnets provide a means to manipulate spin and valley degrees of freedom in nonmagnetic monolayers, without the use of applied magnetic fields. In such van der Waals (vdW) heterostructures, MPIs originate in the nanometer-scale coupling between the spin-dependent electronic wavefunctions in the two materials, and typically their overall effect is regarded as an effective magnetic field acting on the semiconductor monolayer. Here we demonstrate that this picture, while appealing, is incomplete: The effects of MPIs in vdW heterostructures can be markedly asymmetric, in contrast to that from an applied magnetic field. Valley-resolved optical reflection spectroscopy of MoSe$_{2}$/CrBr$_{3}$ vdW structures reveals strikingly different energy shifts in the $K$ and $K'$ valleys of the MoSe$_2$, due to ferromagnetism in the CrBr$_3$ layer. Strong asymmetry is observed at both the A- and B-exciton resonances. Density-functional calculations indicate that valley-asymmetric MPIs depend sensitively on the spin-dependent hybridization of overlapping bands, and as such are likely a general feature of such hybrid vdW structures. These studies suggest routes to selectively control \textit{specific} spin and valley states in monolayer semiconductors.Comment: 12 pages total (including 4 figures + 7 Supplemental Figures

Spin noise spectroscopy to probe quantum states of ultracold fermionic atomic gases

Ultracold alkali atoms provide experimentally accessible model systems for probing quantum states that manifest themselves at the macroscopic scale. Recent experimental realizations of superfluidity in dilute gases of ultracold fermionic (half-integer spin) atoms offer exciting opportunities to directly test theoretical models of related many-body fermion systems that are inaccessible to experimental manipulation, such as neutron stars and quark-gluon plasmas. However, the microscopic interactions between fermions are potentially quite complex, and experiments in ultracold gases to date cannot clearly distinguish between the qualitatively different microscopic models that have been proposed. Here, we theoretically demonstrate that optical measurements of electron spin noise -- the intrinsic, random fluctuations of spin -- can probe the entangled quantum states of ultracold fermionic atomic gases and unambiguously reveal the detailed nature of the interatomic interactions. We show that different models predict different sets of resonances in the noise spectrum, and once the correct effective interatomic interaction model is identified, the line-shapes of the spin noise can be used to constrain this model. Further, experimental measurements of spin noise in classical (Boltzmann) alkali vapors are used to estimate the expected signal magnitudes for spin noise measurements in ultracold atom systems and to show that these measurements are feasible

A quantitative study of spin noise spectroscopy in a classical gas of 41^{41}K atoms

We present a general derivation of the electron spin noise power spectrum in alkali gases as measured by optical Faraday rotation, which applies to both classical gases at high temperatures as well as ultracold quantum gases. We show that the spin-noise power spectrum is determined by an electron spin-spin correlation function, and we find that measurements of the spin-noise power spectra for a classical gas of $^{41}$K atoms are in good agreement with the predicted values. Experimental and theoretical spin noise spectra are directly and quantitatively compared in both longitudinal and transverse magnetic fields up to the high magnetic field regime (where Zeeman energies exceed the intrinsic hyperfine energy splitting of the $^{41}$K ground state)