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Amperean superconductivity is an exotic phenomenon stemming from attractiveeffective electron-electron interactions (EEEIs) mediated by a transverse gaugefield. Originally introduced in the context of quantum spin liquids and high-Tcsuperconductors, Amperean superconductivity has been recently proposed to occurat temperatures on the order of 1-20 K in two-dimensional, parabolic-band,electron gases embedded inside deep sub-wavelength optical cavities. In thiswork, we first generalize the microscopic theory of cavity-induced Ampereansuperconductivity to the case of graphene and then argue that thissuperconducting state cannot be achieved in the deep sub-wavelength regime. Inthe latter regime, indeed, a cavity induces only EEEIs between densityfluctuations rather than the current-current interactions which are responsiblefor Amperean pairing.

Can deep sub-wavelength cavities induce Amperean superconductivity in a 2D material?