Quantum materials are a rich platform in which to explore novel phenomena that emerge due to interactions between electrons, giving rise to new phases of matter that cannot be explained by the properties of isolated, non-interacting electrons. Just like electrons have a spin degree of freedom, they can also be associated with a particular valley, which depends on the details of their momentum within the material system. In this work, we observe a new quantum Hall ferroelectric phase that develops on the surface of a bismuth crystal when the interacting electrons spontaneously occupy a single valley. This kind of quantum behavior typically occurs at very low temperatures, and our experiments are also performed in a high magnetic field to enhance interactions between electrons.
What is particularly exciting about our result is that we can image the electron’s wavefunction using a specialized scanning tunneling microscope. We use interference patterns around impurities to determine that the wavefunctions have an inherent in-plane electric field. When all the electrons pick the same valley, their collective dipole moments results in what is known as a ferroelectric phase with spontaneous electric polarization. Our wavefunction imaging provides insights at the atomic scale that would be impossible to obtain by most other global measurement techniques, which average over the entire sample. The ferroelectric phase we observe can respond to an external electric field, making it a possible candidate for potential applications in the field of valleytronics, an up and coming area of electronics research.