On-demand higher-harmonic generation through nonlinear Hall effects in curved nanomembranes

Botsz Huang, You-Ting Huang, Jan-Chi Yang, Tse-Ming Chen, Ali G. Moghaddam, and Ching-Hao Chang

Phys. Rev. B 109, 134419 – Published 12 April 2024

Abstract

The high-order Hall effects, which go beyond the ordinary, unlock more possibilities of electronic transport properties and functionalities. Pioneer works focus on the manufacture of complex nanostructures with low lattice symmetry to produce them. In this paper, we theoretically show that such high-order Hall effects can alternatively be generated by curving a conducting nanomembrane which is highly tunable and also enables anisotropy. Its Hall response can be tuned from first to fourth order by simply varying the direction and magnitude of the applied magnetic field. The dominant Hall current frequency can also be altered from zero to double, or even four times that of the applied alternating electric field. This phenomenon is critically dependent on the occurrence of high-order snake orbits associated with the effective magnetic-field dipoles and quadruples induced by the curved geometry. Our results offer pathways for spatially engineering magnetotransport, current rectification, and frequency multiplication in the bent conducting nanomembrane.

Received 25 September 2023
Accepted 12 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.134419

Physics Subject Headings (PhySH)

Electrical conductivity Magnetotransport

2-dimensional systems Flexible electronics Nanoribbon

Drude model Free-electron model Materials modeling Numerical techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Botsz Huang ^1,2, You-Ting Huang^1,2, Jan-Chi Yang ^1,2, Tse-Ming Chen^1,2, Ali G. Moghaddam ^3,4,*, and Ching-Hao Chang ^1,2,†

¹Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan
²Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan 70101, Taiwan
³Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
⁴Computational Physics Laboratory, Physics Unit, Faculty of Engineering and Natural Sciences, Tampere University, FI-33014 Tampere, Finland

^*a.ghorbanzade@gmail.com
^†cutygo@phys.ncku.edu.tw

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Issue

Vol. 109, Iss. 13 — 1 April 2024

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Images

Figure 1
Switching between ordinary and nonlinear Hall effect can be easily achieved by rotating the applied magnetic field $B$ . (a) shows a schematic of the proposed device. By applying an AC electric field with a frequency $f_{0}$ as shown in (b) we also get a transverse signal which can be dominated by ordinary linear Hall effect or nonlinear behavior depending on the magnetic field orientation as shown in (c) and (d), respectively. When $B$ is along the $z$ direction, the transverse signal almost follows the applied electric field with the same frequency (c), whereas for in-plane alignment as $B = B_{0} \hat{x}$ , the electronic gas in semicylindrical region feels like an effective $B$ dipole, and as a result we have a nonlinear response where higher harmonics dominate the transverse signal. Here $x, y,$ and $z$ are the axes of Cartesian coordinates on the curved nanomembrane.
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Figure 2
The frequencies of longitudinal and Hall current depend on the strength of applied magnetic field. (a) Simulation of the distribution and velocity of magnetic orbits in the nanomembrane as the function of time for the strong $B$ -field dipole. The dashed line indicates the position of $x / L = 0,$ where $B_{z} = 0$ . (b) Comparing with the frequency of AC voltage, the frequencies of longitudinal current $j_{x}$ is the same, and the major frequencies of Hall current $j_{y}$ are zero and two times. (c) Simulation of the distribution and velocity of magnetic orbits as the function of time for the moderate field. The solid green line shows the snake orbits [48, 49]. (d) Comparing with the frequency of AC voltage, the major frequencies of longitudinal current $j_{x}$ are one and three times, and the major frequencies of Hall current $j_{y}$ are two and four times.
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Figure 3
(a) The high order Hall effects due to the $B$ -field dipole, following the nature of the ordinary Hall effect, drive the current with zero, double and four times of frequencies. (b) The formation of drift orbits (snake orbits) in the $B$ -field dipole contributes to the Hall current with a frequency that is two (four) times of that of AC electric field. Finally, the Hall current flows along the $+ y$ direction whether the applied field is along the $+ x$ (upper panel) or $- x$ (lower panel) directions.
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Figure 4
The relative weight of the different harmonics contributions in the Hall response as a function of the orientation of applied magnetic field ( $θ$ ). The blue, red, yellow, and purple line presents the percentage of (a) second-harmonic Hall current and (b) fourth-harmonic Hall currents in the alternating Hall current driven by magnetic fields of different strengths $B_{0} = 0.8, 1.2, 3,$ and 7 T, respectively. The alternating Hall current is estimated approximately by summing the Hall response from linear to fourth harmonic.
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Figure 5
The amplitude of high-order Hall current decreases and increases with the radius of curvature and tangent angle, respectively. The applied field strength is $B_{0} = 0.8$ T.
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