Through our work, we demonstrated a way to map out the Berry curvature distribution over the Brillouin zone and provide a direct probe of the topological character of strongly spin-orbit-coupled materials. This stands in contrast with transport measurement of spin and charge which reflect the global momentum-space average of the Berry curvature. In this regards, CD-ARPES can be a useful experimental tool to investigate certain aspects of the phase in electron wave functions if one can disentangle different contributions in the CD-ARPES. This work was supported by Research Resettlement Fund for the new faculty of Seoul National University and the research program of Institute for Basic Science . S. R. P. acknowledges support from the National Research Foundation of Korea . The Advanced Light Source is supported by the Office of Basic Energy Sciences of the U.S. DOE under Contract No. DE-AC02-05CH11231.In the momentum space of atomically thin transition metal dichalcogenides , a pair of degenerate exciton states are present at the K and K’-valleys, producing a valley degree of freedom that is analogous to the electron spin. The electrons in the K and K’-valleys acquire a finite Berry phase when they traverse in a loop around the band extrema, with the phase equal in magnitude but opposite in sign at the K and K’-valleys, as required by the time-reversal symmetry. The Berry phase not only has close connections to the optical selection rules that allow optical generation and detection of the valley-polarized carriers by circularly polarized photons, dutch bucket for tomatoes but also plays a central role in novel electron dynamics and transport phenomena in TMD and graphene layers, such as the valley Hall effect.
In principle the Berry phase, together with other effects from inversion symmetry breaking, can have profound consequences for the wave function and energy spectrum of the excited states in two-dimensional materials. TMD monolayers are known to host strongly bound excitons with a remarkably large exciton binding energy due to enhanced Coulomb interactions in 2D. It was recently predicted that the Berry curvature of Bloch states can add an anomalous term to the group velocity of electrons and holes and creates an energy splitting between exciton states with opposite angular momentum. Fig. 1a shows a simplified exciton energy spectrum illustrating the exciton fine structure based on our ab initio GW-Bethe-Salpeter equation calculations. The 2p+ and 2p− exciton states are split in energy with opposite order for the K and K’ valleys due to the opposite chirality in the two valleys. Such novel exciton fine structure, which embodies important wave function properties arising from the Bloch band geometry, can strongly modify the intraexcitonic light-matter interactions. Experimental observation of this predicted exciton spectrum, however, has been challenging, because it requires new spectroscopic probe that can distinguish both the momentum valley and the exciton angular momentum. Here, we report the first observation of the Berry-phase effect in the exciton spectrum of MoSe2 monolayer using intraexciton optical Stark spectroscopy. We demonstrate that the degeneracy between the 2p±-exciton states is lifted by the Berry phase effect, and enabling a valley-dependent Autler-Townes doublet from strong intraexciton light-matter coupling.
We coherently drive the intraexciton transitions using circularly-polarized infrared radiation, which couples the 1s exciton to the 2p+ or 2p− states selectively through the pumpphoton polarization . The pump-induced changes in the 1s exciton transition are detected by circularly polarized probes, which selectively measure the K or K’-valley excitons. Independent control of pump and probe photon polarization enables us to distinguish the exciton fine structures in the K and K’-valleys. We determine an energy splitting of 14 meV between the 2p+ and 2p− exciton states within a single valley, and this energy splitting changes sign between K and K’-valleys. We determine the 1s-2p transition dipole moment to be 55±6 Debye. This leads to an optical Stark shift that is almost 40 times larger than the interband counterpart under the same pump detuning and driving optical field strength. Such strong and valley-dependent intraexciton transitions open-up new pathways for the coherent manipulation of quantum states in 2D semiconducting materials using infrared radiation. To investigate the fine structure of the excitonic p-manifold, we fabricated a high quality MoSe2 monolayer that is encapsulated in hexagonal boron nitride layers using mechanical exfoliation and stacking following Ref. 21. The sandwiched hBN-MoSe2-hBN heterostructure was then transferred to an alumina-coated silver surface . The device was kept in vacuum at 77K for all optical measurements. This Aexciton peak arises from the optical transition between the ground state and the lowest energy 1s exciton state in MoSe2 monolayer, which is well-separated from the higher-lying exciton states due to strong Coulomb interactions in TMD monolayers10,11,20,24. We use intraexciton optical Stark spectroscopy with helicity-defined pump and probe light to selectively access the 2p+ or 2p− exciton states in the K and K’-valleys.
Quantum-mechanical coupling between the infrared photon field and the 1s-2p+ electronic transition leads to an avoided-crossing behavior that modifies the 1s-exciton state systematically with the changing infrared photon energy, as illustrated in Fig. 1d. When the infrared photon energy is below the 1s-2p+ resonance, the non-resonant hybridization leads to a decreased energy for the 1s exciton state.Since the infrared pump photon energy is much lower than the transition energy of 1s exciton, our measurement scheme probes only the coherent optical Stark effects without non-coherent contribution from real carrier generation. The colors in Fig. 2a-c represent the pump-induced change of the probe reflectivity Δ R, which is directly proportional to the change of absorption. The positive Δ R, is proportional to the decrease of absorption. The horizontal and vertical axes show the probe energy and pump-probe time delay, respectively. Strong transient signals are present for pump-probe delay closed to zero and they become negligible at pump-probe delays larger than 500fs. These instantaneous signals confirm the optical responses arise from coherent optical Stark effects.The evolution of the 1s exciton absorption in monolayer MoSe2 under coherent infrared driving can be better visualized directly from the optical absorption spectra characterized by the imaginary part of optical susceptibility.It shows clearly that the 1s exciton transition exhibits avoided-crossing behavior in both valleys, which evolves gradually from energy blueshift to splitting and then to redshift as the pump photon energy is decreased. It shows that the 1s-2 p+ intraexciton transition energy differs by 14 meV for the K and K’ valleys. Due to the time-reversal symmetry between K and K’-valleys in MoSe2 monolayer, this observation also indicates that the 2p+ and 2p− exciton states are non-degenerate and has an energy difference of 14 meV in a single valley. We further plot the blue- and red-shifted 1s resonance as a function of the infrared pump photon energy in Fig. 3b. We find that the energy shifts induced by the intraexciton optical Stark effect are almost 40 times larger than its interband counterpart at the same pump intensity and resonance detuning. To better understand the experimental results, we performed ab initio GW-BSE calculations using the BerkeleyGW package to determine the exciton energy levels and optical selection rules of exciton and intraexciton transitions in monolayer MoSe2. In these calculations, blueberry grow pot environmental screening effects from the hexagonal boron nitride encapsulation layers are included from first-principles . The simulation confirms the energy level diagram of the 1s, 2p+, and 2p− excitons and the optical selection rules in K and K’- valleys in Fig. 1a. Our calculations find that the energies of the 1s and 2p− exciton states are separated by 117 meV, with 2p+ exciton states further separated by 7 meV in K-valley. The energetic order of 2p+ , and 2p− excitons states is opposite in the K’-valley, as a result of time-reversal symmetry. Although the 2p± excitons are dark in linear optics, they are optically active when coupled to the 1s exciton with circularly-polarized light . The 1s-2p− intraexciton transition, on the other hand, coupled exclusively to the right-handed circularly polarized light. The experimentally observed intraexciton dipole moment and valley-dependent exciton fine structure match reasonably well with the ab initio GW-BSE calculations. The combination of 2p±-exciton splitting and extremely strong intraexcitonic light-matter interaction allow us to observe valley-dependent Autler-Townes doublets at higher pump intensity in MoSe2 monolayer. Towards this goal, we fabricated a hBN-encapsulated MoSe2 heterostructure on a zinc-sulphide substrate, where the local field factor on the sample for the infrared pump light is more favorable than that for MoSe2 on alumina coated silver substrate . In this device the 1s-2p+ intraexciton transition energies for the K and K’-valleys are determined to be 150 meV and 138 meV, respectively .This Autler-Townes doublet leads to a valleydependent electromagnetically induced transparency in the 1s exciton transition, where the absorption at the 1s exciton resonance is reduced by more than 10-fold compared to the undriven exciton . Our findings offer a new and effective pathway to coherently manipulate the quantum states and excitonic excitations using infrared radiation coupled to the 1s-2p+ intraexciton transition.Sample Fabrication. The MoSe2 monolayer encapsulated in hBN flakes were prepared with a polyethylene terephthalate stamp by a dry transfer method21. Monolayer MoSe2 and hBN flakes were first exfoliated onto silicon substrate with a 90 nm oxide layer. We used PET stamp to pick-up the top hBN flake, monolayer MoSe2, and bottom hBN flake in sequence with accurate alignment based on an optical microscope. The hBN/MoSe2/hBN heterostructure was then stamped on a silver substrate coated with a 85 nm alumina layer or on a zinc sulphide substrate.
Polymer and samples were heated to 60oC for the pickup and 130oC for the stamping process. Finally, the PET was dissolved in dichloromethane for 12 hours at room temperature. The sample temperature was kept at 77 K in a liquidnitrogen cooled cryostat equipped with BaF2 window during optical measurements. Intraexciton Optical Stark Spectroscopy. Pump-probe spectroscopy study is based on a regenerative amplifier seed by a mode-locked oscillator . The regenerative amplifier delivers femoto second pulses at a repetition rate of 150 kHz and a pulse duration of 250 fs, which were split into two beams. One beam was used to pump an optical parametric amplifier and the other beam was focused onto a sapphire crystal to generate super continuum light for probe pulses. Femto second mid-infrared pump pulses with tunable photon energies were generated via difference frequency mixing of the idler pulses from the optical parametric amplifier and residual of fundamental output from regenerative amplifier in a 1 mm thick silver gallium sulphide crystal. The mid-infrared pulse duration is ~350 fs. The pump-probe time delay was controlled by a motorized delay stage. The helicity of pump and probe pulses was independently controlled using Fresnel rhomb and broadband quarter-wave plates, respectively. The experiment followed a reflection configuration with a normal incidence and collinear pump-probe geometry, where the absorption spectra are extracted from the reflectance contrast as described in the supporting information.This work was primarily supported by the Center for Computational Study of Excited State Phenomena in Energy Materials, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05CH11231, as part of the Computational Materials Sciences Program which provided the experimental measurements and GW-BSE calculations. The sample fabrication and linear optical spectroscopy was supported by the US Army Research Office under MURI award W911NF-17-1-0312. The pump-probe setup was supported by the ARO MURI award W911NF- 15-1-0447. This research used resources of the National Energy Research Scientific Computing Center , a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, and the Extreme Science and Engineering Discovery Environment , which is supported by National Science Foundation grant number ACI-1548562. S.T. acknowledges support from NSF DMR-1552220. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST , JST. E.C.R acknowledges support from the Department of Defense through the National Defense Science & Engineering Graduate Fellowship Program. C.-K.Y. and C.S.O. acknowledges useful discussion with Prof. Ajit Srivastava. Viruses are obligate intracellular pathogens that require living host cells to replicate and spread in the infected plant. During compatible interactions, viruses overcome the plant immune system and hijack host cellular processes to establish active infections .