[Paper Review] Universal transport and resonant current from chiral magnetic effect

Hiroyuki Fujita, Masaki Oshikawa|arXiv (Cornell University)|Feb 1, 2016

Topological Materials and Phenomena3 citations

TL;DR

This paper demonstrates that the chiral magnetic effect (CME) in Weyl semimetals leads to universal, material-independent capacitance even without an external magnetic field, and induces resonantly enhanced currents under time-varying fields due to electromagnetic standing wave formation. The interplay between CME and Maxwell's equations fundamentally alters transport responses beyond naive expectations.

ABSTRACT

For relativistic Weyl fermions in 3+1 dimensions, an electric current proportional to the external magnetic field is predicted. This remarkable phenomenon is called Chiral Magnetic Effect (CME). Here we show that actual transports in Weyl semimetals supporting CME cannot be discussed without proper consideration of the law of electromagnetism. First, even in the absence of an external magnetic field, CME leads to a material-independent, universal effective capacitance. Moreover, the induced current by a time-dependent external magnetic field can be resonantly enhanced reflecting a formation of electromagnetic standing waves.

Motivation & Objective

• To investigate how the chiral magnetic effect (CME) in Weyl semimetals is modified by the full laws of electromagnetism, including induction and Ampère’s law.
• To resolve the discrepancy between naive CME predictions and actual transport responses by solving the coupled Maxwell-Chern-Simons (MCS) equations.
• To identify novel transport phenomena arising from the interplay between CME and electromagnetic field dynamics in finite-sized systems.
• To determine whether CME can lead to observable, non-trivial responses such as universal capacitance or resonant current enhancement in realistic experimental setups.
• To establish that electromagnetism is not a passive backdrop but an essential component in predicting CME-driven transport in topological semimetals.

Proposed method

• Formulates the Maxwell-Chern-Simons (MCS) equations for a cylindrical Weyl semimetal sample inside an infinitely long solenoid, incorporating both ordinary conductivity σ and chiral magnetic conductivity σ_ch(ω).
• Applies Fourier transformation in time to derive frequency-dependent equations, assuming μσ ≫ ω/c² to simplify the system and focus on dominant terms.
• Introduces a dimensionless perturbation parameter δ = ωσ / (μσ_ch²) to perform a perturbative expansion in δ, valid for frequencies ω ∼ 100 kHz when Δ ∼ 100 meV.
• Imposes boundary conditions at the solenoid radius R_s to model surface currents, using Hankel functions to ensure causality and regularity in the complex ω-plane.
• Solves for electromagnetic fields in vacuum regions (inside and outside the solenoid) using Bessel functions J₀, J₁, Y₀, Y₁ and their combinations into Hankel functions H₀, H₁.
• Derives the total axial current I_z^tot through matching conditions at the sample boundary and analyzes its dependence on σ_ch, frequency ω, and sample radius r_s.

Experimental results

Research questions

• RQ1 How does the inclusion of full electromagnetism—specifically induction and Ampère’s law—alter the transport response predicted by the chiral magnetic effect?
• RQ2 Can a universal, material-independent effective capacitance emerge in Weyl semimetals due to CME even in the absence of an external magnetic field?
• RQ3 Under what conditions does the induced current from a time-varying magnetic field become resonantly enhanced in CME systems?
• RQ4 What is the role of electromagnetic standing wave formation in enhancing CME-driven currents in finite-sized Weyl semimetal samples?
• RQ5 To what extent does the observed conductance deviate from the naive prediction based solely on σ_ch(ω)?

Key findings

• Even without an external magnetic field, the chiral magnetic effect induces a material-independent, universal effective capacitance due to the interplay of CME and electromagnetism.
• The induced axial current I_z^tot exhibits resonant enhancement when the sample radius r_s matches specific values related to the zeros of Bessel functions, corresponding to the formation of electromagnetic standing waves.
• Resonances occur when r_s ≈ π(ℤ + 1/4)/ (μσ_ch) for ℤ ∈ ℕ, with the resonance condition tied to the frequency-dependent phase matching of electromagnetic modes.
• In the regime μσ_ch r_s ≪ 1, the total current decreases monotonically with increasing σ_ch, indicating a non-monotonic and non-universal response that contradicts naive CME expectations.
• The characteristic length scale for resonances is ℓ_CML = 1/(μσ_ch), which for Δ ∼ 100 meV yields resonances at r_s ≈ π(ℤ + 1/4) mm, making them potentially observable in realistic Weyl semimetal samples.
• The solution of the MCS equations reveals that the physically observed transport is not simply governed by σ_ch(ω), but is fundamentally shaped by the full electromagnetic response, including field feedback and wave interference.