Two dimensional electrons subjected to a strong magnetic field form highly degenerate Landau levels, whose flat dispersion makes them highly susceptible to interaction driven instabilities.  Among the most spectacular of such ground states are those leading to fractional quantum Hall effects–‘topologically ordered’ collective electron ground states where the elementary excitations of the system carry fractional charge, and follow fractional quantum statistics.

Driven by a string of technical advances in the field of two dimensional layered materials [1-2], including most recently in our group [3], graphene heterostructures are now among the best material platforms for studying these effects, combining pristine sample quality with highly controllable spin, valley, and orbital degeneracies. The Figure to the left shows data from our lab probing the density of states of a graphene bilayer, as the charge density and interlayer potential are varied.  Each thin vertical line is an incompressible fractional quantum Hall liquid, and the interlayer potential drives phase transitions between correlated states with differing layer occupation. (see [3] for details).

Ongoing projects include using these devices to experimentally detect nonabelian statistics using both interferometric and thermodynamic probes, and engineering nonabelian defect states in abelian fractional quantum Hall and ‘fractional Chern insulator’ phases.

[1] Dean et al., Nature Nanotechnology, 5:722-726 (2010).
[2] Wang et al., Science, 342:614-617 (2013).
[3] Zibrov et al., arXiv:1607.06461 (2016).



Understanding the nature of electronic states requires access to a variety of fundamental observables. Some can be extracted directly from a well designed sample–resistance and density of states, e.g.–but others require specialized tools.  We are building a nanoSQUID [4] microscope that will allow nanoscale mapping of magnetic [4] and thermal [5] properties, based on a superconducting quantum interference device fabricated at the tip of a quartz pipette. The image at right shows an electron micrograph of one such sensor, as well as an optical image of the pipette attached to a quartz tuning fork, used to implement topographic feedback. We anticipate best spatial resolution of ~40 nm, with sub-single spin sensitivity and high thermal sensitivity in the cryogenic temperature range; these features make nSOTs unique among scanning probes.  The first microscope, currently under construction, will operate at 4K and in magnetic fields of several tesla, allowing studies of magnetic materials and thermal transport in nanoscale systems, and a 50 millikelvin is being designed.

Unlike conventional planar scanned SQUIDs, nSOTs work in large magnetic fields (as shown in the response curve image).  Our immediatescientific projects include vortex dynamics in 2D superconductors, magnetism in low dimensional materials and heterostructures, and thermal transport properties in mesoscopic systems.

[4] Vasyukov et al., Nature Nanotechnology 8:639-644 (2013).
[5] Halbertal et al., Nature 539:407–410 (2016)


The condition of equilibrium puts constraints on what types of matter can exist, and on their quantitative characteristics.  It has been proposed that strong electromagnetic drive can induce new phases not available as ground states, or quantitatively favor one or more competing ground states under a set of similar equilibrium conditions (temperature, magnetic field, etc.).  Accessing such phases with electrical measurements, however, is limited by the short timescales during which electromagnetic drive can be applied, itself limited both by the availability of pulsed laser sources and limits on power dissipation within the sample itself.   We are developing a THz-on-a-chip technique to measure transport on picosecond timescales, allowing us to probe the nonequilibrium properties of strongly correlated and two dimensional materials. Photons for this project are provided by our collaborators, Rick Averitt (UCSD) and David Hsieh (Caltech).