Anomalous tunneling as a low-energy theorem for Nambu-Goldstone modes

TL;DR

This paper proves that anomalous tunneling of Nambu-Goldstone modes is a universal low-energy phenomenon governed solely by symmetry considerations, using an effective field theory approach.

Contribution

It establishes that anomalous tunneling is a universal low-energy theorem dictated by symmetry and scaling, clarified through an effective field theory framework.

Findings

Symmetry-preserving potentials do not affect NG mode tunneling at low energies.

Symmetry-breaking perturbations suppress NG mode tunneling.

Universal behavior demonstrated with superfluid phonons and magnons.

Abstract

Anomalous tunneling refers to the phenomenon in which the transmission coefficient through a potential barrier approaches unity as the energy of an incident particle or quasiparticle tends to zero. This counterintuitive effect has been reported in systems exhibiting spontaneous symmetry breaking (SSB), such as superfluids, yet the general conditions for its occurrence remain unclear. In this Letter, we establish that anomalous tunneling of Nambu-Goldstone (NG) modes is a universal low-energy theorem dictated solely by symmetry and scaling, using a low-energy effective field theory (EFT) framework. We formulate the scattering of NG modes by external potentials in terms of spatially dependent EFT coefficients and demonstrate that symmetry-preserving localized potentials are irrelevant in the long-wavelength limit, leading to perfect transmission. In contrast, symmetry-breaking perturbations are relevant and suppress transmission, resulting in the absence of anomalous tunneling. We illustrate this universal behavior with explicit examples of superfluid phonons and magnons.