image: This schematic illustrates how to reshape high-order Landau modes. By constructing artificial gauge fields and imaginary momentum, the inherently diffuse and multi-peak wave packets are successfully separated by energy and reshaped into different patterns on demand.
Credit: ©Science Bulletin
When charged particles are subjected to strong magnetic fields, they form discrete energy levels known as Landau levels. The Landau levels consist of a series of degenerate states, making them a promising platform for large-capacity information processing. However, previous studies have predominantly focused on the zero-order Landau modes. In contrast, high-order Landau modes exhibit rich multi-peak profiles, offering more opportunities for mode reshaping. Moreover, high-order Landau modes provide a much broader operational bandwidth due to the infinite Landau level index. The absence of a universal method hinders the manipulation of these high-order Landau modes.
Recently, a joint team from Beijing Institute of Technology, the University of Hong Kong, Tsinghua University and Tongji University proposed introducing imaginary momentum. By constructing a synergistic mechanism of imaginary momentum, pseudomagnetic fields and pseudoelectric fields, the team realized reshaping of high-order Landau modes. In their theoretical model, the electric field breaks the degeneracy of the Landau levels, spatially separating the modes based on their energy. Concurrently, the introduction of imaginary momentum reshapes the wave packet envelopes on demand. Experimentally, the researchers constructed a non-Hermitian circuit platform to implement these phenomena. First, a pseudo-magnetic field (PMF) is generated along the y direction via the gradient variation of capacitance between nodes. Second, a graded on-site potential is introduced by the linear increase of nodal capacitance along the x direction, which further realizes the pseudo-electric field (PEF). Finally, non-reciprocal coupling is achieved at the node junctions using voltage followers, thereby introducing the imaginary momentum. Based on this platform, the researchers directly observed the frequency-dependent spatial localization phenomenon of the high-order Landau modes on a non-Hermitian electric circuit platform.
The underlying physical mechanism is highly universal and can be extended to other platforms, such as photonic, acoustic, and elastic systems. By demonstrating that the combination of artificial gauge fields and non-Hermiticity can be used to tailor Landau modes, this work furnishes a robust topological platform for exploring future applications in frequency multiplexing and wave packet reshaping.