Fig. 1: ν = 0 ground states of BLG, device schematic and measurement set-up.

a, ν = 0 QH phase of BLG with the four predicted ground states. b, The device and measurement set-up. The device was placed into the integer QH regime. The global BLG part (shown in blue and controlled by a graphite back gate, BG1) was placed into the ν = 4 state. The local BLG part (shown in green and controlled by a local graphite back gate BG2) was placed in the ν = 0 state. For simplicity, four edge channels are shown by a single line with an arrow. A d.c. current I_S was injected from contact A. This current moves in the anticlockwise direction set by the magnetic field. Chiral edge channels (red) at potential \({V}_\mathrm{M}=\frac{{I}_\mathrm{S}}{2}\times \frac{h}{\nu {e}^{2}}\) and temperature T_M leave the floating contact and terminate in two cold ground contacts (CG), where h and e are Planck constant and charge of an electron, respectively. The electron temperature T_M of the floating contact was determined by measuring the excess thermal noise at contact D at a frequency ≅725 kHz using an LCR-resonant circuit, which was followed by a cascade of amplifiers, and it was finally measured by a spectrum analyser (SA). The wiggly line emanating from the floating contact represents heat transport through Goldstone modes of the ν = 0 state. c, Same as b, but here both the global and local BLG parts are set to ν = 4. The hot spots in b and c at different corners are shown as red circles filled with a white flame.