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

TL;DR

This paper demonstrates that a classical SSH electrical circuit with memory exhibits a custodial chiral symmetry that protects topological edge states even when memory-induced nonlinearities break the original symmetry.

Contribution

It reveals the presence of custodial chiral symmetry in a memristive SSH circuit, showing how memory effects influence topological protection.

Findings

Memory induces nonlinearities that break chiral symmetry.

Despite symmetry breaking, edge states remain protected.

Predictions are experimentally verifiable.

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.