Localization transition in one-dimensional non-Hermitian Anderson systems

When a wave, such as sound, light, microwave, or electronic quantum wave,
propagates through a region densely filled with randomly arranged scatterers, it may
reach a status called Anderson localization, in which the propagation comes to a
complete stop and the wave’s energy is exponentially trapped in the specimen. Anderson
localization is responsible for many phenomena, ranging from conductor-insulator
transition to confinement of light. It is the underlying principle of several applications,
such as random lasers and perfect-absorbing solar cells. The scaling theory of
localization shows that, in one-dimensional (1D) systems, all modes are localized modes,
even in the presence of a very small amount of disorder. However, such a rule no longer
holds when the system becomes non-Hermitian, i.e., the Anderson transition can occur
in non-Hermitian 1D disordered systems, and propagative and localized modes can
coexist. Hermitian models commonly seen in textbooks handle closed and conservative
systems. In contrast, non-Hermitian formalism is a new regime of physics research that
permits the energy or particle exchange between a physical system and the
surroundings. By incorporating non-Hermitian parameters in the form of non-reciprocal
hopping, it has been shown that the energy spectrum of a 1D disordered ring can become
complex-valued, and the corresponding modes cease to be localized and become
propagative. This non-Hermitian localization transition is the inspiration for this
project.
Recent advancements in non-Hermitian physics have uncovered two important and
interconnected aspects: topological phases enriched by non-Hermiticity, and nonHermitian skin effect. Together, they open a completely new frontier of physics research.
Our project will assimilate these new developments and apply them to analyze 1D nonHermitian Anderson systems, including disordered lattices and quasicrystals. For
disordered systems, we will explore beyond the Hatano-Nelson model by studying the
roles of spectral topology and non-Hermitian universality classes in Anderson
transitions. As a different type of Anderson model, localization in 1D non-Hermitian
quasicrystals, i.e., incommensurate AAH models, will also be explored. Experimentally, we
will develop the active mechanical lattices, an experimental platform capable of realizing
non-Hermitian tight-binding models, to realize the non-Hermitian disordered systems
and quasicrystals with the aim of observing the localization transition and verifying
other findings.
The outcome of our project will advance the new area of non-Hermitian physics and
rejuvenate the study of Anderson localization. It will also bring new technological
advancements that may give rise to applications in photonics, acoustics, and other forms
of wave-based devices.