When two physical systems share the quantum property of entanglement, measurements of one system appear to determine the state of the other. This peculiar property is used in optical, atomic, and electrical systems in an effort to exceed classical bounds when processing information. We extended the domain of this quantum resource by entangling the motion of a macroscopic mechanical oscillator with a propagating electrical signal and by storing one half of the entangled state in the mechanical oscillator. This result demonstrates an essential requirement for using compact and low-loss micromechanical oscillators in a quantum processor, can be extended to sense forces beyond the standard quantum limit, and may enable tests of quantum theory.

A ferroelectric is a material with a polar structure whose polarity can be reversed (switched) by applying an electric field. In metals, itinerant electrons screen electrostatic forces between ions, which explains in part why polar metals are very rare. Screening also excludes external electric fields, apparently ruling out the possibility of ferroelectric switching. However, in principle, a thin enough polar metal could be sufficiently penetrated by an electric field to have its polarity switched. Here we show that the topological semimetal WTe provides an embodiment of this principle. Although monolayer WTe is centro-symmetric and thus non-polar, the stacked bulk structure is polar. We find that two- or three-layer WTe exhibits spontaneous out-of-plane electric polarization that can be switched using gate electrodes. We directly detect and quantify the polarization using graphene as an electric-field sensor. Moreover, the polarization states can be differentiated by conductivity and the carrier density can be varied to modify the properties. The temperature at which polarization vanishes is above 350 kelvin, and even when WTe is sandwiched between graphene layers it retains its switching capability at room temperature, demonstrating a robustness suitable for applications in combination with other two-dimensional materials.

A two-dimensional topological insulator (2DTI) is guaranteed to have a helical 1D edge mode 1-11 in which spin is locked to momentum, producing the quantum spin Hall effect and prohibiting elastic backscattering at zero magnetic field. No monolayer material has yet been shown to be a 2DTI, but recently the Weyl semimetal WTe 2 was predicted 12 to become a 2DTI in monolayer form if a bulk gap opens. Here, we report that at temperatures below about 100 K monolayer WTe 2 does become insulating in its interior, while the edges still conduct. The edge conduction is strongly suppressed by in-plane magnetic field and is independent of gate voltage, save for mesoscopic fluctuations that grow on cooling due to a zero-bias anomaly which reduces the linear-response conductance. Bilayer WTe 2 also becomes insulating at low temperatures but does not show edge conduction. Many of these observations are consistent with monolayer WTe 2 being a 2DTI. However, the low temperature edge conductance, for contacts spacings down to 150 nm, is below the quantized value, at odds with the prediction that elastic scattering is completely absent in the helical edge.Experimental work on 2DTIs to date has focused on quantum wells in Hg/CdTe 4-7 and InAs/GaSb 9-11 designed to achieve an inverted band gap. These heterostructures show edge conduction as anticipated 13,14 , but they also present some puzzles. One is that the conductance at low temperatures is not perfectly quantized, becoming small in long edges 13 and showing mesoscopic fluctuations as a function of gate voltage 5,7,10 . This is inconsistent with the predicted absence of elastic backscattering at zero magnetic field, although several possible explanations have been put forward for the discrepancy [15][16][17][18][19][20] . Another is that the edges show signs of conducting even at high magnetic field 21,22 , contrary to expectations that helical modes, protected by timereversal (TR) symmetry at zero field, should Anderson-localize once this symmetry is broken. An additional complication is that non-helical edge conduction may also be present, due for instance to band bending when a gate voltage is applied 23 .Identification of a natural monolayer 2DTI, which lacked some of these discrepancies and which could be probed, manipulated, and coupled with other materials more easily than quantum wells, would be helpful for elucidating and exploiting TI physics. Band structure calculations predict that certain monolayer materials are intrinsically topologically nontrivial 12 . An example is monolayer WTe2, which has the T′ structure illustrated in Fig. 1a. Three-dimensional WTe2, in which such monolayers are stacked in the orthorhombic Td structure, has recently attracted attention as a type-II Weyl semimetal 24,25 that exhibits extreme non-saturating magnetoresistance 26,27 related to the closely balanced electron and hole densities [28][29][30] . Calculations suggest that the monolayer will be likewise a semimetal 12,30 , its Fermi surface comprising two electron pockets (green) an...