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.