Extended Data Fig. 2: Spin- and valley- symmetry breaking.
From: Topological charge density waves at half-integer filling of a moiré superlattice
a, Metallic phases with broken flavour (spin and valley) degeneracies can be highlighted using quantity n* = (neff − n)/n0, where neff is the effective carrier density which was extracted here from Ryx measured at B = 1 T in device D2. n* corresponds to the filling of the superlattice at which the band that is being filled becomes completely empty (full) for n-type (p-type) Fermi surface. Thus, integer values of n* that are intermediate between 0 and 4 indicate interaction-induced symmetry breaking of the flavour degeneracies. b, Diagram of flavour symmetry broken phases corresponding to (a). The boundaries were determined using n* as well as measured Rxx and Ryx. The incompressible states at commensurate fillings are labeled with the Chern numbers observed for B > 0. The blue region around the ν=2 insulating state corresponds to a two-fold degenerate state, which we identify as spin-polarized phase because of the spin polarization of ν = 2 (see (c)) and the absence of the anomalous Hall effect [7]. Smaller red regions around ν=1 and 3 states correspond to phases with fully lifted spin-and valley- degeneracies, in which a single C = 2 band is being filled. States at ν = 3/2 and 7/2 emerge within these regions. c, In-plane magnetic field dependence of the gap at ν=2 determined from the thermal activation of Rxx in device D1 at D=0.443 V/nm. Linear fit yields g-factor of 1.59 ± 0.05 which indicates large spin polarization. The determined value is lower than g = 2 which is expected for fully spin-polarized state. The exact origin of this discrepancy is not fully understood and could include orbital effects of the in-plane magnetic field.
