Ferroelectric quantum Hall phase revealed by visualizing interference of Landau level wavefunctions*

Novel broken symmetry states can spontaneously form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. A powerful approach to distinguish among such states in two-dimensional systems is to visualize their wavefunctions with a scanning tunneling microscope (STM)¹. Here we investigate bismuth surface states, where strong spin-orbit coupling leads to six degenerate teardrop-shaped hole pockets. Our spectroscopic measurements reveal that this valley degeneracy is fully lifted at high magnetic field as a result of exchange interactions. We image the corresponding Landau level (LL) wavefunctions with a STM to address the nature of valley ordering for the case of a singly degenerate LL. The spatial patterns we observe around isolated defects contain unique signatures of interference between spin-textured valleys, which identifies the electronic ground state as a quantum Hall ferroelectric. Our observations confirm the recent prediction² that interactions in strongly anisotropic valley systems favor the occupation of a single valley, which gives rise to ferroelectricity in bismuth.
¹B. E. Feldman*, M. T. Randeria* et al., Science 354, 316 (2016)
²I. Sodemann et al., arxiv:1701.07836