Magnetic electron collimation in three-dimensional semi-metals

Generating and controlling electron beams by electric and magnetic fields has enabled technologies such as cathode-ray tubes and electron microscopes. Translating electron optics concepts into solid-state devices is challenging because free-space-like motion requires long mean free paths (high mobility, clean materials), yet electric fields are screened in good conductors, limiting field-based beam shaping. Prior approaches in ballistic devices use geometric constrictions (pinhole-like) to collimate electrons, with two-dimensional electron gases (2DEGs) offering long mean free paths and geometric control. However, restricting motion to 2D reduces the richness of electron dynamics: in 2DEGs the orbital motion depends only on the out-of-plane field component, making the magnetic field effectively scalar and the beam shape fixed by fabrication, precluding steering by field direction. This work aims to demonstrate experimentally that in three-dimensional (3D) semimetals, in-plane magnetic fields induce an out-of-plane Hall component and a strong transport anisotropy that can be exploited to generate, steer, and control narrow, long-range electron beams (“current jets”) using micro-fabricated constrictions. The study highlights the additional degrees of freedom in 3D that enable field-guided electron beam control not available in 2D systems.

Materials and device fabrication: High-quality single crystals of the Dirac semimetal Cd3As2 were grown by flux methods. Crystal orientation was determined by X-ray diffraction so that the crystalline c-axis is perpendicular to the device main face. Micrometer-scale devices were fabricated from slabs (approximately 150 µm × 50 µm × 2 µm) using focused ion beam (FIB) milling: FEI Helios G3 (Ga ions), FEI Helios PFIB (Xe ions), and ZEISS Crossbeam FIB for the multi-channel device. Coarse milling was performed at 30 kV (e.g., 60 nA; Xe PFIB) with finer steps at lower currents (e.g., 4 nA). The slab was transferred to a sapphire substrate using a micromanipulator and fixed with two-component araldite rapid epoxy. Low-ohmic contacts were formed by gold deposition after argon etching (200 V, 5 min), followed by Ti (5 nm) and Au (200 nm). The gold film was selectively removed by FIB (2 kV, 1.7 nA, Ga) to clear regions of interest. Final device shaping used 30 kV, 0.79 nA for coarse and 80 pA for fine milling (Ga), with final polishing at 7.7 pA. Six devices (S1–S6) with varying dimensions were produced. Typical devices were thick, bulk-like (thickness t ≈ 1.4 µm >> Fermi wavelength λF ≈ 17 nm) to ensure fully 3D transport, with a main cuboid body connected by ~1 µm-wide crystal bridges (“nozzles”) that serve as artificial constrictions; typical nozzle spacing d ≈ 2.0 µm and main body length L ≈ 11 µm. Transport measurements: Measurements were conducted in a PPMS with a 14 T superconducting magnet. A typical AC excitation current I_ac ≈ 10 µA at 177.77 Hz was sourced through one pair of top contacts (nozzles), and non-local voltages were measured between distant bottom contact pairs. Angular dependence was obtained by rotating the sample in the ab-plane from −90° to 90° using a rotator, acquiring data continuously. Finite-element simulations: Potential distributions were computed by solving the stationary Laplace equation using Comsol Multiphysics 5.3a on full 3D models matching device geometries, with current and voltage boundary conditions applied self-consistently. Conductivity was modeled using a Drude magnetoconductivity tensor for fields along z: σ = σ0/(1+(µB)^2) for components perpendicular to B, σ_parallel = σ0, with Hall components included; the in-plane field rotation was implemented by rotating the conductivity tensor with the appropriate rotation matrix R (tilt angle θ). Reported contact voltages were computed by averaging the potential over the contact surface. For quantitative comparisons, independently determined material parameters from square test devices were used (e.g., σ0 = 1.35 × 10^6 S m−1, µB = 36 at 12 T), without fitting; simulated amplitudes were scaled uniformly by a factor of 3 to match the measured magnitude. Material characterization: Magnetoconductivity for current parallel (σ||) and perpendicular (σ⊥) to B was measured to quantify anisotropy A = σ||/σ⊥. Quantum oscillations appearing at low fields (B ~ 1 T) with frequency F ~ 27 T indicated high mobility and low carrier density. Drude and Hall analyses yielded µ ≈ 1.84 m^2 V−1 s−1 and n = 6.54 × 10^24 m−3 at 2 K. Experimental configurations: Primary experiments used two opposing nozzle pairs: current injected at one pair, non-local voltage detected at the other. Magnetic field was rotated within the plane to steer current beams. A multi-contact device with two rows of four contacts (~1 µm wide, ~2 µm spacing) separated by a ~10 µm channel was used to demonstrate selective routing by field angle, serving as a demultiplexer-like function.

- Demonstration of controlled, magnetic-field-guided electron beams (“current jets”) in 3D Cd3As2 microdevices with engineered constrictions. Finite-element simulations and experiments show narrow beams that propagate along B and can be steered by rotating B. - Material parameters: High mobility and low carrier density confirmed by quantum oscillations (F ≈ 27 T). Drude/Hall analysis at 2 K gives µ ≈ 1.84 m^2 V−1 s−1 and n = 6.54 × 10^24 m−3. - Strong magnetoconductivity anisotropy: A = σ||/σ⊥ increases rapidly with field, reaching A ≈ 706 at 14 T, leading to pronounced current path reorientation and long-range non-local effects. - Angular response: At B = 12 T and 2 K, rotating in-plane field produces a characteristic W-shaped non-local voltage with sign reversal. For a device with nozzle spacing d = 2.0 µm and body length L ≈ 10.7–11.0 µm, a large positive maximum at θ = 0° occurs when both beams hit the opposite nozzles; a pronounced negative minimum appears near θ ≈ −11°, matching the geometric criterion tan(θg) ≈ d/L (θg ≈ 10.6°), indicating a single opposite-polarity beam hitting a diagonal contact; signals vanish at larger angles when beams miss contacts. - Quantitative modeling: Finite-element simulations using a Drude tensor (σ0 = 1.35 × 10^6 S m−1, µB = 36) reproduce the full angular dependence including the relative amplitude ratio (|Vmin| ≈ 0.5 Vmax), with a uniform amplitude scale factor of 3 to match experiment. - Temperature and field dependence: The W-shape persists above room temperature; at 350 K and 14 T, amplitude is ~20% of that at 2 K. At low T, signatures remain visible at B = 1 T. The collimation strength, quantified as ΔV = Vmax − Vmin, follows µ(T)B scaling trends, with deviations due to σ0(T) and material-specific magnetoresistance. - 3D Hall effect necessity: Simulations with σxy artificially set to zero (mimicking 2D behavior with in-plane anisotropy) yield only positive non-local voltages without minima, indicating that the out-of-plane Hall component and 3D helical motion are essential for beam formation and sign-inverted signals. - Multi-channel control: A device with two rows of contacts demonstrates angle-selective signal routing; at θ ≈ 17°, beams land on a specific detector pair (c, d) while the opposite pair (e, f) sees no signal. Geometry (contact width and spacing) tunes peak amplitude, angle positions, and asymmetry, enabling demultiplexer-like behavior and directional magnetic sensing.

The findings address the central question of whether 3D semimetals can support controllable, long-range, beam-like electron transport guided by magnetic fields. The experiments show that the large Hall conductivity and field-induced anisotropy in low-carrier-density, high-mobility 3D materials produce narrow current jets that can be steered by field direction, a capability absent in 2D systems where only the out-of-plane field component matters. The strong agreement between finite-element Drude-based simulations and measured non-local voltages validates a semiclassical picture of field-guided collimation in devices with engineered constrictions. The presence of sign-reversing angular features and their geometric scaling with device dimensions demonstrate precise, tunable control over non-local signal propagation. These results are significant for both fundamental and applied contexts. Fundamentally, they highlight that classical non-locality in 3D semimetals can be pronounced and must be accounted for when interpreting magnetotransport in topological materials (e.g., chiral anomaly-related negative longitudinal magnetoresistance and planar Hall effects). The demonstrated control over semiclassical transport provides a reference against which truly topological non-local phenomena (e.g., Weyl-orbit-mediated transport) must be contrasted in a unified theory incorporating both semiclassical and topological contributions. From an applications perspective, the ability to route and steer electron beams via magnetic field orientation and device geometry could enable devices for electron optics analogs, directional magnetic field sensing in extreme conditions, and neuromorphic architectures leveraging non-local interactions, potentially assisted by integrating magnetic thin films or spintronic elements to provide local fields.

This work demonstrates controlled generation, steering, and detection of narrow electron beams in 3D Cd3As2 microdevices by exploiting field-induced conductivity anisotropy and a large Hall response. Purpose-built constrictions create point-like injectors that, under in-plane magnetic fields, launch long-range, beam-like current jets whose trajectories are tunable by field angle and strength. Quantitative agreement between experiment and finite-element Drude simulations confirms a semiclassical mechanism, with key observables including W-shaped angular responses, sign reversals at geometry-determined angles, and strong field and temperature dependencies. The approach enables multi-contact architectures that function as magnetic demultiplexers and directional sensors. Future directions include: (i) materials optimization toward higher mobilities (e.g., elemental semimetals like Bi or Sb, or other topological semimetals) to reduce operating fields and enable room-temperature practicality; (ii) integrating on-chip magnetic layers or spintronic elements to eliminate external fields; (iii) developing comprehensive theories that jointly treat semiclassical non-locality and topological transport (e.g., Weyl orbits); and (iv) exploring device designs that leverage electron beam control for neuromorphic and electron-optics-inspired functionalities.

- Operating fields: In Cd3As2, room-temperature operation requires high magnetic fields; while effects persist at 350 K, fields remain impractically large for many applications. - Model simplifications: The Drude-based simulations assume field-independent mobility and temperature-independent carrier density, and neglect finite-size and complex magnetoresistance effects in Cd3As2, leading to small deviations; simulated amplitudes required a uniform scale factor (×3) to match experiment. - Contact and geometry sensitivity: Non-local signals depend sensitively on contact shapes, widths, and separations; imperfections or unintended point contacts can alter current paths. - Attribution in topological materials: Pronounced classical non-locality complicates interpreting putative topological magnetotransport signatures (e.g., negative longitudinal MR, planar Hall), necessitating careful disentanglement. - Thermal and fabrication constraints: Device performance depends on high mobility and precise microfabrication; FIB processes and substrate/support choices may introduce disorder or strain affecting mobility.