[Paper Review] Meson Domain Wall as a Surface of Topological Insulator and Nonrelativistic Photons

Naoki Yamamoto|arXiv (Cornell University)|Dec 17, 2015

Quantum, superfluid, helium dynamics3 citations

TL;DR

The paper proposes that a meson domain wall in dense nuclear matter acts as a topological surface akin to that in topological insulators, leading to axion electrodynamics. In this effective theory, one photon helicity state exhibits a nonrelativistic, gapless dispersion relation ω ∼ k² at low momentum, while the other remains gapped, mirroring surface photon behavior in topological insulators.

ABSTRACT

We argue that the effective theory for electromagnetic fields near a meson domain wall in dense nuclear and quark matter is essentially the same as that at the interface between topological and trivial insulators in condensed matter systems: the axion electrodynamics. We show that one of the helicity states of photons has the nonrelativistic gapless dispersion relation $\omega \sim k^2$ at small momentum, while the other is gapped, around the meson domain wall or at the surface of topological insulator.

Motivation & Objective

• To establish a theoretical link between meson domain walls in dense nuclear and quark matter and the surface physics of topological insulators.
• To investigate whether electromagnetic modes near such domain walls obey axion electrodynamics, a hallmark of topological phase transitions.
• To determine the dispersion relations of photon modes near the domain wall and identify any nonrelativistic behavior.

Proposed method

• Adopt the effective field theory of axion electrodynamics to describe electromagnetic responses near the meson domain wall.
• Model the domain wall as a topological interface between trivial and nontrivial topological phases in the context of quantum chromodynamics.
• Analyze the photon dispersion relations by solving the modified Maxwell equations with an axion-like coupling term.
• Use symmetry and topological invariants to classify the surface modes and predict their gap structure.
• Compare the resulting photon spectrum to that of surface states in condensed matter topological insulators.
• Derive the low-momentum dispersion relation ω ∼ k² for one helicity state, indicating nonrelativistic behavior.

Experimental results

Research questions

• RQ1 Does the effective electromagnetic theory near a meson domain wall in dense quark matter resemble axion electrodynamics found in topological insulators?
• RQ2 What is the dispersion relation of photons near the meson domain wall, and does it exhibit nonrelativistic behavior?
• RQ3 Are there distinct gapped and gapless photon modes, and how do they relate to helicity states?
• RQ4 How does the topological nature of the domain wall influence the electromagnetic response?
• RQ5 Can the surface modes be described by a nonrelativistic dispersion relation ω ∼ k²?

Key findings

• One photon helicity state near the meson domain wall exhibits a nonrelativistic, gapless dispersion relation ω ∼ k² at low momentum.
• The other photon helicity state remains gapped, with a gap size determined by the domain wall's energy scale.
• The effective theory for electromagnetic fields near the domain wall is equivalent to axion electrodynamics, as in topological insulator interfaces.
• The system supports topologically protected surface modes due to the nontrivial topology of the domain wall.
• The emergence of ω ∼ k² dispersion indicates a breakdown of Lorentz invariance at low energies, characteristic of nonrelativistic photon modes.
• The results establish a direct analogy between meson domain walls in dense quark matter and the surfaces of topological insulators in condensed matter physics.