Local probes for quantum Hall ferroelectrics and nematics

Two-dimensional multivalley electronic systems in which the dispersion of individual pockets has low symmetry give rise to quantum Hall ferroelectric and nematic states in the presence of strong quantizing magnetic fields. We investigate the local signatures of these states arising near impurities that can be probed via scanning tunneling microscopy (STM) spectroscopy. For quantum Hall ferroelectrics, we demonstrate a direct relation between the dipole moment measured at impurity bound states and the ideal bulk dipole moment obtained from the modern theory of polarization. We also study the many-body problem with a single impurity via exact diagonalization and find that near strong impurities a nontrivial excitonic state can form with specific features that can be easily identified via STM spectroscopy.