Chirality characterizes an object that is not identical to its mirror image. In condensed matter physics, Fermions have been demonstrated to obtain chirality through structural and time-reversal symmetry breaking. These systems display unconventional electronic transport phenomena such as the quantum Hall effect and Weyl semimetals. However, for bosonic collective excitations in atomic lattices, chirality was only theoretically predicted and has never been observed. We experimentally show that phonons can exhibit intrinsic chirality in monolayer tungsten diselenide, whose lattice breaks the inversion symmetry and enables inequivalent electronic K and -K valley states. The time-reversal symmetry is also broken when we selectively excite the valley polarized holes by circularly polarized light. Brillouin-zone-boundary phonons are then optically created by the indirect infrared absorption through the hole-phonon interactions. The unidirectional intervalley transfer of holes ensures that only the phonon modes in one valley are excited. We found that such photons are chiral through the transient infrared circular dichroism, which proves the valley phonons responsible to the indirect absorption has non-zero pseudo-angular momentum. From the spectrum we further deduce the energy transferred to the phonons that agrees with both the first principle calculation and the double-resonance Raman spectroscopy. The chiral phonons have significant implications for electron-phonon coupling in solids, lattice-driven topological states, and energy efficient information processing.
The interaction of macroscopic mechanical object with electron charge and spin plays a vital role in today’s information technology and fundamental studies of the quantum-classical boundary. Recently emerged valleytronics encodes information to the valley degree-of-freedom and promises exciting applications in communication and computation. Exploring the interplay between the valley physics and macroscopic mechanics will bring new perspectives for valley information processing and exploration of the quantum-classical boundary.
Recently discovered two-dimensional (2D) transition metal dichalcogenides (TMDs) provide an appealing platform to explore valley-mechanical interaction. Their honeycomb lattice supports two valleys (namely K and K’) and thus forms a spin-like binary system called valley-pseudospin. The broken inversion symmetry together with the strong spin-orbit coupling give rise to a unique optical selection rule, which provides a powerful tool for optical generation and manipulation of the valley. On the other hand, nano-mechanical systems made of 2D materials have shown high mechanical strength, high quality-factor, and extraordinary mass and force sensitivities. Their extremely small mass also leads to large quantum zero-point motion and thus facilitates its use in quantum system.
Because of the broken inversion symmetry in monolayer TMDs, electrons in the K and K’ valleys possess total magnetic moments that are equal in magnitude but opposite in sign. When a magnetic field gradient is applied perpendicular to the monolayer, it experiences a net force whose direction depends on which valley is populated and therefore allows transduction of the valley information (K or K’) into the mechanical motion (upward or downward displacement).
We fabricate the valley-resonators by dry-transferring an exfoliated monolayer MoS2 onto pre-patterned square hole structures, which are conformally coated with a film of high permeability permalloy (Ni/Fe). Under an external magnetic field, the permalloy film distorts the field and generates a strong local magnetic field gradient. For an applied magnetic field of 26 mT, the magnetic field gradient in the central region of the suspended MoS2 reaches ~4000 T/m. The monolayer nature of the MoS2 membrane is confirmed by Raman and photoluminescence (PL) spectroscopy. A PL scan across the sample shows that the emission from the suspended regions is much stronger than that from the metal substrate, which confirms that the membrane is freestanding. The square structure has a lateral dimension of 5.2 × 5.2 um^2 and the resonator has an effective mass of 21 fg. The mechanical resonance frequency is ~35.7 MHz and the quality factor is 22,000 at 30 K.
We observe the valley-mechanical actuation of the monolayer MoS2 at low temperature. We detect the resonator motion by an optical interferometric scheme using a probe laser (654 nm) and excite the K and K’ valleys alternatingly by modulating the polarization of the pump laser (633 nm) between left- and right-circular (LCP and RCP) while keeping the optical intensity constant. This exerts an oscillating push-pull force to drive the resonator. The measured displacement of the resonator shows a clear Lorentzian response. Meanwhile, a linearly-polarized pump light shows no driving effect because it equally populates both valleys and thus results in zero net force. The mechanical displacement shows an opposite phase when the pump laser polarization is switched to opposite helicity, which confirms that the excitation of carriers at different valleys exerts opposite forces onto the monolayer. In the measurement, the polarization modulation frequency is close to the mechanical resonance (~35.7 MHz) which is much slower than the decay of the valley carriers, whose timescale is in the range of picoseconds to a few nanoseconds. Therefore, the valley carrier population adiabatically follows the polarization modulation. The probe light is kept linearly-polarized throughout the measurement to eliminate its effect on the net valley population.
Utilizing the fact that the direction of the force depends on which valley is populated, we demonstrate transduction of the valley information into the mechanical state of the nano-resonator. We examine the mechanical quadratures of the device when it is resonantly driven by opposite valley population. Two distinct mechanical states of opposite phase are clearly resolved within the measurement uncertainty and the confidence level of differentiating the two states is close to 100%. This result demonstrates that the valley information of the monolayer is unambiguously transferred into the mechanical states.
In conclusion, our experiment demonstrates direct transduction of valley information to mechanical states of a MoS2 monolayer resonator. The valley-mechanical interaction lays the foundation for a new class of valley-controlled mechanical devices. It also facilitates hybridization of valley pseudospin with other quantum information carriers such as two-level qubits and microwave photons.
Metamaterials offer unprecedented opportunity to engineer fundamental band dispersions which enable novel optoelectronic functionalities and devices. Precise control of photonic degrees of freedom can always succeed to manipulate the flow of light. For example, photonic net spin flows such as one-way transports and spin-directional locking have been realized at the boundary of topologically-protected photonic metacrystals. But this is not the only way to achieve net spin flow in solid state systems. Valley degree of freedom may provide a new route to modulate the spin flow in bulk crystals without the assist of boundary. Here, we show the molding of spin flow of light in valley photonic crystals. The coupled valley and spin physics is illustrated analytically. The associated photonic valley Hall effect and unidirectional net spin flow are well demonstrated inside the bulk crystals, instead of the assist of topologically non-triviality. We also show the independent control of valley and topology, resulting in a topologically protected flat edge state. Valley photonic crystals may open up a new route towards the discovery of fundamentally novel states of light and possible revolutionary applications.
Layered transition metal dichalcogenide (TMDC) with hexagonal lattice structure has six valleys at corners of the Brillouin zone. The nontrivial Berry curvature distribution renders the adjacent valleys with distinguishable valley angular momentum, which enables itself as an ideal 2D valleytronic platform. Recent studies reported strong excitonic effect in monolayer WS2 and each excitonic state is identified with a well-defined orbital angular momentum, however the anticipated selection rules involve nonlinear optical processes are not clear. Here we show valley angular momentum (VAM) together with exciton angular momentum (EAM) impose different valley-exciton locked selection rules for second harmonic generation (SHG) and two photon luminescence (TPL) in monolayer WS2. Moreover, the two-photon induced valley populations yield net circular polarized photoluminescence after a sub-ps interexciton relaxation. The work demonstrates a new approach to control valley population at different excitonic states for next generation of optical circuits and quantum information computing.
The second harmonic generation (SHG) produced from two-dimensional atomic crystals have been utilized recently in studying the grain boundaries and electronic structure of such ultra-thin materials. However, the SHG in many of these crystals, such as transition metal dichalcogenides (TMDCs), only occur in odd numbered layers with limited intensity due to their noncentrosymmetric nature. Here, we probe the SHG from the bulk noncentrosymmetric molybdenum disulfide (MoS2). Whereas the commonly studied 2H crystal phase’s anti-parallel nonlinear dipoles in adjacent layers give an oscillatory SH response, the parallel nonlinear dipoles of each atomic layer in the 3R phase constructively interfere to amplify the nonlinear light. Due to this interference, we observed the atomically phase-matched condition yielding a quadratic dependence between the intensity and layer number. Additionally, we probed the layer evolution of the A and B excitonic transitions in 3R-MoS2 using SHG spectroscopy and found distinct electronic structure differences arising from the crystal geometry. These findings demonstrate the dramatic effect of the symmetry and layer stacking of these atomic crystals.