  Topology is a fundamental aspect of quantum physics, and it has led to key
breakthroughs and results in various fields of quantum materials. In condensed
matters, this has culminated in the recent discovery of symmetry-protected
topological phases. However, symmetry-based topological characterizations rely
heavily on symmetry analysis and are incapable of detecting the topological
phases in systems where the symmetry is broken, thus missing a large portion of
interesting topological physics. Here, we propose a new approach to
understanding the topological nature of quantum materials, which we call
feature spectrum topology. In this framework, the ground-state is separated
into different partitions by the eigenspectrum of a feature, a particular
chosen internal quantum degree of freedom, such as spin or pseudo-spin, and the
topological properties are determined by analysis of these ground-state
partitions. We show that bulk-boundary correspondence guarantees gapless
spectral flows in either one of the energy or feature spectrum. Most
importantly, such 'feature-energy duality' of gapless spectral flows serves as
a fundamental manifestation of a topological phase, thereby paving a new way
towards topological characterizations beyond symmetry considerations. Our
development reveals the topological nature of a quantum ground state hidden
outside symmetry-based characterizations, hence, providing a platform for a
more refined search of unconventional topological materials.

Materials Science