Higher-Order Topological Matter

During the past decades, topological quantum matter has not only fundamentally updated our knowledge of the phases of matter but has also become a major cutting-edge research direction in condensed matter physics. A bulk topological quantum system will phenomenologically distinguish from its non-topological counterpart by the emergence of robust gapless boundary states of codimension-1. Remarkably, such topological boundary modes hold great promise for achieving the next-generation electronics with ultralow dissipation and topological quantum information processing. Recently, the field of topological quantum matter has experienced a new intriguing higher-order twist. While a higher-order topological phase looks no different from a trivial system on its codimension-1 boundaries, it additionally features exotic topological hinge states or corner states on boundary manifolds of codimensions larger than one. As a rapidly growing field that attracts great attention, a central challenge is to understand, classify, and build higher-order topological phenomena in various quantum or even classical platforms.

This Research Topic is dedicated to the state-of-the-art theoretical and experimental developments of higher-order topological physics. The key areas we would like to address in this Research Topic include (but not limited to):
• Establishing new mathematical foundations for higher-order topological phases, including topological classification, topological invariant, field-theory description, etc.
• Designing new model paradigms for higher-order topological insulators and superconductors, with an emphasis on the experimental feasibility.
• Proposing new designs of topological electronics/spintronics/Majorana devices with higher-order topological physics.
• Experimental realization, manipulation and detection of higher-order topology in both quantum material-based condensed matter platforms and other classical physical systems such as acoustic crystals, photonic crystals, electric circuits, etc.

Manuscripts submitted for publication should be original and present a significant scientific contribution to the field of higher-order topological states. Review articles are also welcome. Topics of interest mainly include:
• Topological classification and topological invariants of higher-order topological phases;
• Theoretical proposals of higher-order topological states;
• Field theory description of higher-order topological phases;
• Design of higher-order topological materials based devices;
• Floquet higher-order topological phases;
• Higher-order topological states in metamaterials;
• Phase transitions of higher-order topological phases;
• Higher-order topology in disordered and quasiperiodic systems;
• Experimental realization and detection of higher order topology.