Custodial chiral symmetry in a Su-Schrieffer-Heeger electrical circuit with memory

Abstract

Custodial symmetries are common in the Standard Model of particle physics. They arise when quantum corrections to a parameter are proportional to the parameter itself. Here, we show that a custodial symmetry of the chiral type is also present in a classical Su-Schrieffer-Heeger (SSH) electrical circuit with memory (memcircuit). In the absence of memory, the SSH circuit supports a symmetry-protected topological edge state. Memory induces nonlinearities that break chiral symmetry explicitly and spreads the state across the circuit. However, the resulting state is still protected against perturbations by the ensuing custodial chiral symmetry. These predictions can be verified experimentally and demonstrate the interplay between symmetry and memory.

11 pages, 11 figures

References in corpus (5)

• Memory effects in complex materials and nanoscale systems
• Topological properties of linear circuit lattices
• New topological invariants in non-Hermitian systems
• Nonlinearity induced topological physics in momentum space and real space
• Observation of symmetry protected zero modes in topolectrical circuits

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• Non-Abelian inverse Anderson transitions
• Observation of inverse Anderson transitions in Aharonov-Bohm topolectrical circuits
• Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks
• Observation of type-III corner states induced by long-range interactions
• Engineering topological states and quantum-inspired information processing using classical circuits
• Memristive Ising Circuits