[Paper Review] Amperean superconductivity cannot be induced by deep subwavelength cavities in a two-dimensional material

Gian Marcello Andolina, Antonella De Pasquale+4 more|arXiv (Cornell University)|Oct 19, 2022

Quantum and electron transport phenomena75 references4 citations

TL;DR

This paper demonstrates that deep sub-wavelength optical cavities cannot induce Amperean superconductivity in two-dimensional materials, despite theoretical proposals suggesting otherwise. The authors show that such cavities only mediate effective electron-electron interactions via density fluctuations, not the current-current interactions required for Amperean pairing, thus ruling out this mechanism in the deep sub-wavelength regime.

ABSTRACT

Amperean superconductivity is an exotic phenomenon stemming from attractive effective electron-electron interactions (EEEIs) mediated by a transverse gauge field. Originally introduced in the context of quantum spin liquids and high-Tc superconductors, Amperean superconductivity has been recently proposed to occur at temperatures on the order of 1-20 K in two-dimensional, parabolic-band, electron gases embedded inside deep sub-wavelength optical cavities. In this work, we first generalize the microscopic theory of cavity-induced Amperean superconductivity to the case of graphene and then argue that this superconducting state cannot be achieved in the deep sub-wavelength regime. In the latter regime, indeed, a cavity induces only EEEIs between density fluctuations rather than the current-current interactions which are responsible for Amperean pairing.

Motivation & Objective

• To investigate whether deep sub-wavelength optical cavities can induce Amperean superconductivity in two-dimensional electron systems.
• To clarify the nature of electron-electron interactions mediated by cavity photons in the deep sub-wavelength regime.
• To determine whether current-current interactions—essential for Amperean pairing—are generated in such cavities.
• To generalize the theory of cavity-induced Amperean superconductivity to graphene and other 2D materials.
• To rule out the feasibility of achieving high-temperature Amperean superconductivity via cavity coupling in the deep sub-wavelength limit.

Proposed method

• Theoretical analysis of the electromagnetic coupling between a 2D electron gas and a Fabry-Pérot cavity with deep sub-wavelength cavity length.
• Derivation of the effective electron-electron interaction Hamiltonian mediated by cavity photons using second-order perturbation theory.
• Identification of the dominant interaction channel as density-density, not current-current, due to the transverse nature of the cavity modes.
• Explicit calculation of the paramagnetic and diamagnetic current operators in momentum space to assess the form of the interaction.
• Use of the vector potential operator and light-matter coupling strength to estimate the magnitude of diamagnetic contributions.
• Generalization of the cavity-induced superconducting pairing mechanism to graphene, accounting for its Dirac cone band structure.

Experimental results

Research questions

• RQ1 Can deep sub-wavelength optical cavities mediate the current-current interactions necessary for Amperean superconductivity in 2D materials?
• RQ2 What type of effective electron-electron interaction is induced by cavity photons in the deep sub-wavelength regime?
• RQ3 Is the proposed mechanism of cavity-induced Amperean superconductivity in 2D parabolic-band systems applicable to graphene?
• RQ4 Does the dimensionless coupling constant in the deep sub-wavelength limit allow for a significant superconducting transition temperature?
• RQ5 Can the cavity-induced interaction be distinguished from density-density interactions in terms of symmetry and momentum dependence?

Key findings

• Deep sub-wavelength cavities mediate only density-density effective electron-electron interactions, not the current-current interactions required for Amperean pairing.
• The absence of current-current interactions in the deep sub-wavelength regime rules out the emergence of Amperean superconductivity in 2D materials.
• The effective interaction Hamiltonian derived from cavity photons is dominated by density fluctuations, not transverse current correlations.
• The light-matter coupling strength in the deep sub-wavelength limit is insufficient to generate the necessary attractive interaction for Amperean pairing.
• The theoretical proposal of high-temperature Amperean superconductivity in 2D electron gases via deep sub-wavelength cavities is not viable due to the incorrect form of the induced interaction.
• The analysis confirms that graphene, despite its unique Dirac band structure, cannot support cavity-induced Amperean superconductivity in the deep sub-wavelength regime.