Pseudomagnetic Fields Enabled Manipulation of On-Chip Elastic Waves

Mou Yan, Weiyin Deng, Xueqin Huang, Ying Wu, Yating Yang, Jiuyang Lu, Feng Li, and Zhengyou Liu

Phys. Rev. Lett. 127, 136401 – Published 23 September 2021

Abstract

The physical realization of pseudomagnetic fields (PMFs) is an engaging frontier of research. As in graphene, elastic PMF can be realized by the structural modulations of Dirac materials. We show that, in the presence of PMFs, the conical dispersions split into elastic Landau levels, and the elastic modes robustly propagate along the edges, similar to the quantum Hall edge transports. In particular, we reveal unique elastic snake states in an on-chip heterostructure with two opposite PMFs. The flexibility in the micromanufacture of silicon chips and the low loss of elastic waves provide an unprecedented opportunity to demonstrate various fascinating topological transports of the edge states under PMFs. These properties open new possibilities for designing functional elastic wave devices in miniature and compact scales.

Received 5 May 2021
Accepted 27 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.136401

Physics Subject Headings (PhySH)

Acoustic metamaterials Geometric & topological phases Mechanical & acoustical properties

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Mou Yan¹, Weiyin Deng ¹, Xueqin Huang¹, Ying Wu¹, Yating Yang¹, Jiuyang Lu ^1,*, Feng Li ^1,†, and Zhengyou Liu^2,3,‡

¹School of Physics and Optoelectronics, South China University of Technology, Guangzhou, Guangdong 510640, China
²Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
³Institute for Advanced Studies, Wuhan University, Wuhan 430072, China

^*Corresponding author. phjylu@scut.edu.cn
^†Corresponding author. jilinhubei@gmail.com
^‡Corresponding author. zyliu@whu.edu.cn

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Issue

Vol. 127, Iss. 13 — 24 September 2021

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Images

Figure 1
PMF on a silicon chip. (a) Schematic of the PC with a lattice constant $a = 400 μ m$ , plate thickness $d = 80 μ m$ , and height of triangular scatterers $h = 240 μ m$ . (b) Photograph of the silicon chip. PMF is engineered by deforming the triangular pillars etched on the top surface of the chip. The dashed green line indicates the baseline of the Landau gauge, where triangular pillars are undeformed. The dashed yellow lines denote boundaries of cladding layers. The insets show the scanning tunneling microscope images near the top and bottom boundaries outlined by the red and blue boxes, respectively. Scale bar, $400 μ m$ .
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Figure 2
Deformation-induced PMF and elastic LLs. (a) Shape deformations of triangular pillars and their effects on the shifts $δ k$ of Dirac cones located originally at $K$ and $K^{'}$ points. The deformation is identified by a deviation rate $ξ$ characterizing the deformed side length relative to the original side length (with side length $l_{0} = 276 μ m$ ). (b) Simulated Dirac cone shifts (black circles) and deviation rates (red circles) along the $y$ direction. They both exhibit good linearity with respect to coordinate $y$ with the black and red lines being fitting lines of the simulated data. (c) Simulated (left panel) and measured (right panel) dispersions, showing Landau splitting of elastic waves.
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Figure 3
Elastic edge states under PMFs. (a) Measured displacement field $| u_{z} |$ of the edge states at a frequency of 1.38 MHz, excited by a source (green star) in the top left corner near the cladding layer. (c) Circular propagations in a hexagonal PC with PMF. Inset shows a photo of this PC. (b) and (d) Spatial Fourier spectra of the displacement fields in (a) and (c), respectively.
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Figure 4
Elastic snake states. (a) Photograph of a PC consisting of two opposite PMFs and a narrow transition region (denoted in yellow). Inset shows an enlarged image of the region in a black box. (b) Measured $| u_{z} |$ of the snake states at a frequency of approximately 1.42 MHz. (c) Measured (left panel) and simulated (middle panel) dispersions along the $k_{x}$ direction for this PC. Right panel: enlarged view of the dispersions in the orange box. Gray region denotes available frequencies for the snake states. (d) Top panel: real parts of field distributions for the eigenstates marked by red ( $u_{1}$ ) and blue ( $u_{2}$ ) dots in (c). Inset: enlarged view of the region in the dashed box. Bottom panel: rearranged displacement fields. The envelope curves (dark green and purple) are obtained by polynomial fitting of all the peaks.
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