Graviton-like excitation observed with predicted chirality in fractional quantum Hall liquids

Fractional quantum Hall liquids are the prototypical topological states of matter, whose universal topological properties are well understood in most cases (with few exceptions that will be discussed later). However, as emphasized by Duncan Haldane, who shared the 2016 Nobel Prize for his contribution to topological physics in condensed matter, purely topological descriptions of fractional quantum Hall liquids are incomplete because they overlook a geometrical aspect of the physics. Based on this insight, Haldane and his Princeton associates1 argued that the long-wavelength collective excitations of fractional quantum Hall liquids correspond to oscillation of this geometry. In particular, the quantum of such oscillation carries spin angular momentum 2, very much like the gravitons in a putative quantum theory of gravity. For this reason, they use the same name (“graviton”) for these geometric excitations.

Such graviton-like excitations were clearly seen in a detailed numerical study.2 More importantly, this collaboration of Florida State University, Princeton, and California State University, Los Angeles,2 demonstrated that these “gravitons” carry a definitive chirality (or angular momentum) that is either −2 or +2, depending on whether the fractional quantum Hall liquid is electron-like (−2) or hole-like (+2) (Figure 1). It also provided a detailed recipe on how to reveal the chirality in a Raman scattering experiment using circularly polarized light.