Nanomechanical detection of vortices in an electron fluid

Abstract

Electron vortices are the quintessential signature of a viscous electron fluid. For decades, their detection relied on indirect transport measurements with persistently debated interpretations. Recently, scanning magnetometry enabled direct visualization, yet these techniques demand considerable sophistication. Here we introduce a conceptually different and inherently simpler paradigm based on nanomechanics. By integrating a circular cavity into a suspended resonator, we create a vortex whose circulating current generates a magnetic moment. In an in-plane magnetic field, this moment experiences a torque, driving vibrations that directly reveal the vortex's presence and nature. We detect ballistic and hydrodynamic vortices and trace their temperature-driven crossover. Our work establishes nanomechanics as a platform for electron hydrodynamics, showing that viscosity - subtle in transport - is one of the dominant factors shaping nanoelectromechanical response.

Figures (4)

• Figure 1: Comparative experiment confirming the vortex presence (A), Scanning electron microscope image of a studied device ($\underline{\mathrm{O}}$-device) - a nanomechanical cantilever-like resonator hosting a circular electron cavity attached to a straight conductive channel. (B), A current flowing through the channel can induce an electron vortex in the cavity accompanied by a counterflow at the free edge. In an in-plane magnetic field $\vec{B}$, Lorentz force $\vec{F}_\mathrm{L}$ contributes to driving of mechanical oscillations (the calculated shape of the first mode is displayed, color shows the displacement). (C), Image of a reference sample ($\Omega$-device), where the vortex formation is geometrically suppressed by an additional etched trench. The common measurement scheme is shown; mechanical oscillations are detected by measuring the conductance response $\delta G$ of a constriction in a two-dimensional electron gas (detector) using heterodyne down-mixing. (D), Co-flow at the free edge leads to a Lorentz force opposite to that in $\underline{\mathrm{O}}$-device sample. (E-H), Amplitude $\delta G_0$ and phase of the measured response as functions of the driving frequency $\Omega/2\pi$ at various magnetic fields. Phase curves are horizontally offset by 200 Hz for clarity. Top panels: $\underline{\mathrm{O}}$-device; bottom panels: $\Omega$-device. The magnetic field leads to opposite effects in samples supporting and preventing vortex formation. Insets in panels E,F show the resonant amplitude as a function of magnetic field.
• Figure 2: Temperature evolution of vortices (A) Temperature dependence of coefficient $\Gamma\propto\Lambda$ characterizing the influence of the spatial current distribution on the Lorentz force $F_\mathrm{L}=\Lambda BI$. Hydrodynamic fits based on Stokes equation solution are shown. In $\underline{\mathrm{O}}$-device, additional ballistic component is needed to fit the data at low temperatures. (B-E), Calculated current distributions corresponding to low (left panels) and high (right panels) temperatures. The corresponding points are labeled in panel (A).
• Figure S1: Gate voltage dependence of the measured signal. Amplitudes (A,B) and resonant frequencies (C,D) measured as functions of the dc component of the gate voltage. Negative amplitude values correspond to a 180$^\circ$ phase shift. Top and bottom panels correspond to $\underline{\mathrm{O}}$- and $\Omega$-devices, respectively.
• Figure S2: Transport parameters. (A), Electron mobility measured in 50$\times$20 $\mu$m suspended Hall bars. (B) Characteristic transport length scales extracted from the measurements.