Fig. 2. Correlation of graphene broken isospin states in macroscopic vs. microscopic measurements.

a Optical micrograph of the graphene quantum Hall device. The Hall bar edges are defined by a local graphite back gate, G1, underlying the area outlined in the red dashed line, and a global graphite back gate, G2, under the entire Hall bar device (see “Methods” for further details). The boundary between G1 and G2 defines the quantum Hall edge boundary along the red dashed line. The black circle shows the location for spatial maps across the boundary shown in Figs. 4–6. b, c Magnetotransport measurements of (b) the Hall resistance, R_XY, and (c) the longitudinal resistance R_XX. Filling factors $\nu$ are indicated in white numerals. In both measurements, broken-symmetry states in the zeroth Landau level are observed at $\nu =\pm 1$. d Schematic of the graphene Landau level density of states indicating the fourfold degeneracy due to valley and spin inside each main Landau level. e, f Microscopic atomic force spectroscopy measurements revealing the broken-symmetry states in (e) AFM frequency shift measurements and (f) simultaneously obtained oscillation amplitude signal with constant excitation of 520 mV as a function of sample bias and local gate at B = 15 T. A smooth background was subtracted from the data in (e) to enhance the contrast of the broken-symmetry states (see Supplementary Fig. 2 and “Methods”). The white line indicates the zero-contact potential difference (i.e., chemical potential) obtained from a parabolic fit to the frequency shift data vs. sample bias (Supplementary Fig. 3). The white numerals indicate the filling factor. All measurements were made at $T=10\mathrm{mK}$.