[Paper Review] Two-body interaction induced axion-phason field in Weyl semimetals

D. Schmeltzer|arXiv (Cornell University)|Jun 1, 2022

Topological Materials and Phenomena30 references4 citations

TL;DR

This paper proposes a microscopic mechanism for axion-phason coupling in Weyl semimetals driven by two-body electron interactions, showing that a sliding charge density wave (CDW) phase induces a space- and time-dependent topological axion term θ(z,t) via phason fluctuations. The key result is that the phason field α(z,t) dynamically generates the axion term e²/(2πℏ) ∫θ(z,t)(E·B), explaining the experimentally observed axionic response in (TaSe₄)₂I under parallel E and B fields.

ABSTRACT

Following our results that the two-body interaction can induce a space and time dependent topological axion term $ \frac{e^2}{2\pi \hbar} heta(z,t)(\vec{E}\cdot\vec{B})$, we show that by applying this theory to a Weyl semimetal with two nodes in a magnetic field a one-dimensional sliding charge density wave (CDW) in agreement with the recent experimental finding of J. Gooth et al. [Nature, https://doi.org/10.1038/s41586-019-1630-4 (2019)]. We show that the theory is equivalent to a time and space dependent of the topological angle which represents the phason.

Motivation & Objective

• To establish a microscopic origin for the axion-phason field in Weyl semimetals without relying on phenomenological CDW models.
• To explain the recent experimental observation of axionic response in (TaSe₄)₂I under parallel E and B fields.
• To show that two-body electron interactions induce a time- and space-dependent topological angle θ(z,t) via phason fluctuations.
• To demonstrate that the phason field α(z,t) acts as the dynamical axion field, coupling to electromagnetic fields via E·B term.
• To derive the effective action and conductivity from a one-dimensional bosonized model of the Weyl semimetal in a magnetic field.

Proposed method

• Formulate a low-energy effective Hamiltonian for Weyl semimetals with two nodes, linearized around Weyl points and projected to the n=0 Landau level.
• Apply a two-body attractive interaction −U_eff n_R n_L and decouple it via Hubbard-Stratonovich transformation into a complex order parameter ∆(z) = |∆|e^{iα(z,t)}.
• Use one-dimensional bosonization to map fermionic operators to chiral bosonic fields θ(z,t) and ϕ(z,t), with α(z,t) identified as the phason field.
• Derive the effective action for the phason field by computing the triangle diagram involving γ5 and electromagnetic fields, regularizing divergences via ∆_Imag → ∆_Imag + ∂_zβ.
• Obtain the axion-phason action S_eff ∝ ∫dt∫dz (e²/h) β(z,t)(E·B), showing that β(z,t) = −½α(z,t) defines the dynamical axion field.
• Analyze the response to an electric field E_3(z,t) by deriving the equation of motion ∂_z(vc/K_c ∂_z α) = −eE_3, leading to σ = e²/h K_c.

Experimental results

Research questions

• RQ1 How can two-body electron interactions in a Weyl semimetal generate a dynamical axion field?
• RQ2 What is the microscopic origin of the sliding CDW phase observed in (TaSe₄)₂I under parallel E and B fields?
• RQ3 How does the phason field α(z,t) couple to the electromagnetic field to produce an effective E·B term?
• RQ4 What is the role of the chiral anomaly and axial anomaly in mediating the axion-phason coupling?
• RQ5 How does the Luttinger parameter K_c > 1 affect the stability of the gapless phase in the presence of interactions?

Key findings

• The two-body interaction induces a time- and space-dependent topological angle θ(z,t) through phason fluctuations α(z,t), leading to an effective axion term ∫θ(z,t)(E·B).
• The phason field α(z,t) is shown to play the role of the axion field, with δS ∝ ∫dt∫dz (e²/h) β(z,t)(E·B), where β(z,t) = −½α(z,t).
• The effective action derived from the triangle diagram yields a linearly divergent result, which is regularized by shifting ∆_Imag → ∆_Imag + ∂_zβ, leading to a finite axion coupling.
• The conductivity due to phason response is σ = e²/h K_c, with K_c = √(4π) > 1, indicating a stable gapless phase.
• The equation of motion for the phason is ∂_z(vc/K_c ∂_z α) = −eE_3, showing that the electric field drives the phason dynamics.
• The chiral transformation Ψ → e^{iγ5β(z)}Ψ shifts Q_3 → Q_3 + ∂_zβ, which directly generates the axion action, confirming the topological nature of the coupling.