Absence of heat flow in {\nu} = 0 quantum Hall ferromagnet in bilayer graphene

The charge neutrality point of bilayer graphene, denoted as {\nu} = 0 state, manifests competing phases marked by spontaneously broken isospin (spin/valley/layer) symmetries under external magnetic and electric fields. However, due to their electrically insulating nature, identifying these phases through electrical conductance measurements remains challenging. A recent theoretical proposal introduces a novel approach, employing thermal transport measurements to detect these competing phases. Here, we experimentally explore the bulk thermal transport of the {\nu} = 0 state in bilayer graphene to investigate its ground states and collective excitations associated with isospin. While the theory anticipates a finite thermal conductance in the {\nu} = 0 state, our findings unveil an absence of detectable thermal conductance. Through variations in the external electric field and temperature-dependent measurements, our results suggest towards gapped collective excitations at {\nu} = 0 state. Our findings underscore the necessity for further investigations into the nature of {\nu} = 0.