Fractional quantum Hall states are topological quantum fluids observed in two-dimensional electron gases (2DEG) in strong magnetic fields. University of Illinois Physics researchers Gil Young Cho, Yizhi You, and Eduardo Fradkinhave shown that these electron gases can also harbor a quantum phase transition to an electronic nematic state inside the topological state.
Written by Celia Elliott
From left, researchers Gil Young Cho, Yizhi You, and Eduardo FradkinURBANA—Quantum Hall fluids are fascinating states of quantum matter observed in two-dimensional electron gases (2DEG) in high magnetic fields and at low temperatures. In a fractional quantum Hall state, the electron fluid is in a topological phase characterized by a fractional Hall conductivity (in units of e2/h), and its excitations are vortices that carry a fraction of the charge of an electron and fractional exchange statistics. Experiments have shown that electronic transport in tilted magnetic fields in these topological fluids becomes anisotropic at low temperatures and that the anisotropy has a pronounced temperature dependence. This effect suggests that the electron fluid inside this fractional quantum Hall phase may be close to a phase transition to a state in which the rotational invariance of the fluid is broken spontaneously, a state that is known as an electronic nematic phase. A nematic electronic fluid state has been found earlier in regimes in which the 2DEG is not topological, and in some cuprate and pnictide superconductors, but it had not been seen before in topological phases of matter.
In a paper published December 30 in Physical Review X (q.v. http://link.aps.org/doi/10.1103/PhysRevX.4.041050), researchers Gil Young Cho, Yizhi You, and Eduardo Fradkin at the Department of Physics and the Institute of Condensed Matter Theory at the University of Illinois have described this new state of matter by means of an effective field theory. This theory allows them to study the nematic transition and the nematic phase inside a fractional quantum Hall fluid. The researchers have shown that the quantum phase transition is triggered by effective attractive interactions in the quadrupolar channel that cause the lowest collective mode of the fractional quantum Hall fluid to condense.
The nematic quantum Hall fluid with a topological defect (called a disclination) and an excitation with fractional charge e/3The resulting nematic state is characterized by an order parameter that represents these quadrupolar fluctuations, which play the role of fluctuations of the local geometry of the quantum fluid. In other words, the nematic fluctuations behave as a fluctuating metric for the electrons in the fluid. The result is that they mimic a gravitational interaction among these degrees of freedom. An interesting feature of the nematic phase is that it has topological defects known as disclinations that act as local center of spatial curvature for the electronic degrees of freedom. The effective field theory provides a full description of the response of the quantum fluid to external electromagnetic probes and to local deformations of the underlying crystal.
Although the theory is specific for fractional quantum Hall states, these ideas and mechanisms are of general interest to understanding the behavior of geometric fluctuations in other topological phases in condensed matter.
This material is based upon work supported by the National Science Foundation under Grant No. 1408713. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.