Disorder and waves have an uneasy relationship. In everyday life, a muddy room muffles sound and makes it hard for a whisper to travel. In quantum materials, randomness can trap electrons, a phenomenon known as Anderson localization. For a long time, physicists have understood that in one- and two-dimensional systems, any amount of uncorrelated disorder tends to localize waves. In three dimensions, a mobility edge can separate localized states from extended ones, with a localization length that diverges near the transition. The story grows richer when the landscape isn’t strictly Hermitian (the standard assumption where energy is real and probabilities conserve) or when the disorder is quasiperiodic, a nearly-but-not-quite repeating pattern. The new work in this paper pushes the frontier by placing a non-Hermitian, quasiperiodic potential onto a highly special one-dimensional lattice called a flat-band lattice, and then tracking how localization behaves in the complex energy plane. The result isn’t just a nuance; it’s a reimagining of how localized and extended waves can organize themselves when gain, loss, and unusual band structure interact.
The study, conducted by researchers affiliated with Guangzhou University and South China Normal University in China, led by Yi-Cai Zhang (with colleagues Guang-Xin Pang, Zhi Li, Shan-Zhong Li, Yan-Yang Zhang, and Jun-Feng Liu), maps the exact boundaries between localized and extended states in a complex energy landscape. In other words, they don’t just say where localization happens; they show the precise geometry of where extended states live in the complex plane, and how those regions rearrange when non-Hermiticity enters the game. The terms “mobility edges,” “mobility lines,” and “mobility rings” become literal shapes in the math, and the shapes tell a vivid story about how quantum states traverse disordered, non-conservative worlds.
To situate the drama, think of a lattice that’s not just a simple line of atoms but a compact three-site motif—a capital A, B, and C—that fuses two diamonds into a flat, energy-flat plateau in the middle of its spectrum. In such a flat-band lattice, there’s a unique opportunity: localization can coexist with extended states in striking ways, and the transitions between these kinds of states can be triggered not only by how strong the disorder is, but by how the potential bends and twists in a non-Hermitian, quasiperiodic landscape. The researchers ask a bold question: what happens to the classic idea of critical states—those delicate, patchwork states sitting between localization and extension—when the potential is non-Hermitian? The answer unfolds with elegance and a touch of mathematical artistry.
Behind the science, the paper grounds its analysis in a lattice model built from three sublattices (A, B, C) arranged as two intersecting diamond lattices. When the on-site potential vanishes, the model reveals three energy bands: a lower band, a middle flat band at zero energy, and an upper band. The flat band is the stage where localization physics can play out in surprising ways, because the dispersionless middle band allows localized and extended states to mingle in nontrivial fashions. Introducing a non-Hermitian, quasiperiodic on-site potential—one that carries both a real phase and an imaginary component—acts like a breeze stirring the sea of states. What follows is a precise, almost geometric map of where waves can roam freely and where they must be confined, with the added twist that those boundaries live in a complex energy plane. The work’s authors—Pang, Li, Li, Zhang, Liu, and Zhang—are backed by several Chinese institutions and led by Yi-Cai Zhang in this distinctive foray into non-Hermitian flat-band physics.
