Particle-Hole Symmetry in Descriptions of a Half-Filled Landau Level

August 21, 2017

Figure 1* [Reprinted under the Creative Commons Attribution 4.0 International license.]

Multiple descriptions of the half-filled Landau level, an exotic phase of matter seen in two-dimensional electron gases, have led to incompatible pictures that are widely believed to represent two distinct phases of matter. A new analysis in Physical Review X by Harvard Physics Junior Fellow Chong Wang, Prof. Bertrand Halperin, and colleagues from University of Cambridge and Weizmann Institute of Science suggests that this is not the case and that these descriptions are functionally equivalent.

One of the most fascinating phases of matter in modern quantum physics is the "composite Fermi-liquid" state in a half-filled Landau level—a metallic state formed by electrons in a strong magnetic field and confined to two dimensions. This state can be described in terms of an emergent particle called a "composite fermion," loosely understood as an electron attached to two quanta of magnetic flux. Composite fermions, in contrast to bare electrons, can move in straight lines despite the strong magnetic field, giving rise to the metallic behavior observed experimentally. In certain situations, it is possible to formulate a composite fermion theory in terms of holes—quasiparticles that represent the absence of electrons—but it creates a picture that appears to be at odds with the theory formulated in terms of electrons. A fundamental question is whether these different pictures actually represent distinct phases of matter. The new analysis suggests that there is a unique phase for which multiple theoretical descriptions are equivalent.

It has been widely believed, for two decades, that the two composite fermion theories—formulated in terms of electrons and holes, respectively—lead to qualitatively different physical predictions, implying that the different pictures describe different phases. However, by carefully evaluating certain key physically observable quantities, the authors show that the two pictures produce results that are surprisingly identical. This is true even when the symmetry relating these two pictures (known as particle-hole symmetry) is absent at the microscopic level.

The scientists expect that their results will motivate future research that will reveal deeper theoretical structures of the composite Fermi-liquid states and connect the theories to experimental observations.

*Read Chong Wang, Nigel R. Cooper, Bertrand I. Halperin, and Ady Stern, "Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level," Physical Review X 7, 031029 (2017) DOI: