Topological Phases in Quantum Systems

Topological phases represent distinct states of matter that cannot be characterised by local order parameters or spontaneous symmetry breaking, but rather by global invariants that remain unchanged under continuous deformations. Such phases arose historically with the discovery of the quantum Hall effect and have since extended to a plethora of electronic, photonic and mechanical platforms. In these systems, the bulk spectrum exhibits an energy gap while supporting robust edge or surface states that are immune to disorder and perturbations. The classification of topological phases draws upon concepts such as Berry curvature, Chern numbers and symmetry classes, leading to a tenfold way of insulators and superconductors as well as generalisations to non-Hermitian and periodically driven (Floquet) settings. Practical realisations span two-dimensional electron gases, cold-atom lattices with synthetic gauge fields, photonic crystals and metamaterials. Beyond fundamental insight into quantum coherence and entanglement, topological phases promise applications in low-power electronics, fault-tolerant quantum computing and resilient information transport in photonic or acoustic networks. Their exploration continues to bridge condensed matter physics, materials science and engineered platforms, revealing new pathways to manipulate waves and quasiparticles with topological protection.

Research from Nature Portfolio

Recent studies have demonstrated unprecedented control of topological phases in integrated photonic and phononic circuits. A fully programmable topological photonic chip has been realised on a silicon-based platform, enabling on-chip adjustment of artificial atoms and interactions to induce dynamic transitions between distinct insulator phases and to probe disorder-induced topological Anderson transitions. This approach allows comprehensive statistical characterisation of topological robustness and reconfigurable functionalities for robust light transport. In parallel, advances in phononic metamaterials have yielded elastic-wave analogues of quantum spin-Hall effects, where dual-scale crystal slabs break mirror symmetries to emulate spin–orbit coupling for phonons. Such designs support backscattering-immune edge modes over a broad bandwidth, highlighting the versatility of topological protection in mechanical platforms and opening prospects for vibration isolation and acoustic signal processing.

Research from all publishers

Work outside the portfolio has greatly expanded the theoretical framework and experimental realisations of topological phases. A coherent classification of non-Hermitian topological phases has been established, revealing unique bulk spectra, novel winding invariants and a modified bulk-edge correspondence in dissipative systems. This framework unifies time-reversal and particle-hole symmetries to predict phases with no Hermitian counterpart. Foundational research on the tenfold classification of insulators and superconductors has elucidated how dimensional hierarchies and symmetry constraints determine the complete set of topological sectors, linking Chern–Simons and winding numbers to observable electromagnetic responses. Additionally, the development of purely dielectric photonic crystals has shown that conventional materials can host photonic topological states by exploiting crystal symmetry and pseudo-time-reversal invariance, giving rise to helical edge modes without magneto-optical components.

Topological Phases in Quantum Systems publication trend

The graph below shows the total number of articles in topological phases in quantum systems across all publications each year (not limited to Nature Index journals).

Technical terms

Topological phase: A state of matter characterised by global invariants rather than local order parameters.

Berry curvature: A geometric property of energy bands that underlies topological invariants in momentum space.

Chern number: An integer quantifying the net Berry curvature over a closed manifold, defining Hall conductance.

Bulk-edge correspondence: A principle linking bulk topological invariants to the number of protected boundary states.

Floquet system: A periodically driven quantum or classical system exhibiting effective Hamiltonians with engineered band topology.

References

1. A programmable topological photonic chip. Nature Materials (2024).
2. Scheme for Achieving a Topological Photonic Crystal by Using Dielectric Material. Physical Review Letters (2015).
3. Topological insulators and superconductors: tenfold way and dimensional hierarchy. New Journal of Physics (2010).
4. Topological Phases of Non-Hermitian Systems. Physical Review X (2018).
5. Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems. Physical Review X (2013).
6. Topologically protected elastic waves in phononic metamaterials. Nature Communications (2015).
7. Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields. Physical Review X (2014).