Photocurrent Nanoscopy of Quantum Hall Bulk

Understanding nanoscale electronic and thermal transport of two-dimensional (2D) electron systems in the quantum Hall regime, particularly in the bulk insulating state, poses considerable challenges. One of the primary difficulties arises from the presence of chiral edge channels, whose transport behavior obscures the investigation of the insulating bulk. Using near-field optical and photocurrent nanoscopy, we probe real-space variations of the optical and thermal dynamics of graphene in the quantum Hall regime without relying on complex sample or electrode geometries. Near the charge-neutrality point, we detect strong optical and photothermal signals from resonant inter-Landau-level (LL) magnetoexciton excitations between the zeroth and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mo>±</a:mo><a:mn>1</a:mn></a:mrow></a:math> st LLs, which gradually weaken with increasing doping due to Pauli blocking. Interestingly, at higher doping levels and full-integer LL fillings, photothermal signals reappear across the entire sample over an approximately <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>10</c:mn><c:mtext>−</c:mtext><c:mrow><c:mi mathvariant="normal">μ</c:mi><c:mi mathvariant="normal">m</c:mi></c:mrow></c:mrow></c:math> scale, indicating unexpectedly long cooling lengths and nonlocal photothermal heating through the insulating bulk. This observation suggests that thermal conductivity persists for the localized states even as electronic transport is suppressed—a clear violation of the Wiedemann-Franz law. Our experiments provide novel insights into nanoscale thermal and electronic transport in incompressible 2D gases, highlighting the roles of magnetoexcitons and chiral edge states in the thermo-optoelectric dynamics of the Dirac quantum Hall state.