Landau levels induced by synthetic strain in plasmonic metasurface

The quantum Hall effect arises when electrons in a two-dimensional plane are subjected to a magnetic field, causing them to undergo cyclotron motion and form discrete energy levels, known as Landau levels. These levels play a critical role in condensed matter physics. However, practical limitations of applying a magnetic field have led to the introduction of pseudomagnetic fields, which can similarly induce Landau levels. Such pseudomagnetic fields are typically generated through synthetic strain, achieved by deforming geometric patterns, and have been applied to systems like graphene, photons, and phonon crystals. Building on previous research in electronics and optics, we present a plasmonic metasurface that induces Landau levels via synthetic strain in the microwave frequency range. This strain is realized by printing metal structures of specific shapes on a dielectric substrate using printed circuit board technology. The fundamental unit of the plasmonic metasurface is a C6 symmetric structure composed of six localized surface plasmon patches. By applying a displacement function along the transmission direction, we discretize the dispersion curve, leading to band degeneration and the emergence of edge states. The distribution of these edge states is influenced by the strength of the pseudomagnetic field, which is controlled by the magnitude of the displacement function. We validate our design through fabricated models and demonstrate the existence of edge states using near-field scanning experiments. Our work, which combines synthetic magnetic fields and plasmonic metasurface, provides valuable insights for the development and application of integrated photonic devices.