Liam A. Cohen, PhD

My first love in condensed matter physics was the Quantum Hall effect (QHE); it is a beautiful, universal, consequence of electrons that are confined in two-dimensions when subjected to high magnetic fields.  While the QHE manifests in many two-dimensional systems, such as GaAs/AlGaAs quantum wells or ZnO, graphene based van der Waals heterostructures boast a number of advantages which make them a favorable platform for interrogating the more exotic properties of QH states, such as anyonic statistics, edge tunneling exponents, and fractional charge.  These advantages include, electronic density tunability via field-effect gating, large energy gaps (in comparison to competing platforms) of QH and fractional QH states, and thin dielectrics (typically h-BN with a thickness between 10nm and 60nm) which enable sharp confinement potentials that reduce deleterious charging effects.  

However, utilizing these advantages to perform experiments that are sensitive to the exotic properties found in QH and fractional QH states is challenging.  This requires engineering electrostatic potentials that can steer gapless edge-modes and trap quasiparticles on the scale of the magnetic length (~10nm) without introducing unwanted disorder potentials on the same length scale.  The bulk of my Ph.D. was dedicated to developing the techniques needed to solve this problem.  We achieved this primarily by pre-patterning graphite gates at the nano-scale using AFM based local anodic oxidation lithography and directly integrating the patterned gates into a van der Waals heterostructure while leaving the critical gate regions untouched by traditional nano-fab.  Doing this, we were able to observe a myriad of remarkable properties of fractional QH states, such as anyonic statistics, the slow-motion of quasiparticles, and the bizarre consequences of fractional charge transmutation.  

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During my post-doctoral appointment, my hope is to extend the work I did during my Ph.D along two separate paths.  The first is to take the techniques developed during my Ph.D. to create clean nanoscale potentials in a van der Waals heterostructure and fabricate devices which may be used to interrogate physics at zero-magnetic field.  Primarily, I would like to study novel superconducting interfaces made by gate-defined junctions in spin-orbit proximitized Bernal bilayer graphene or in pure rhombohedral few-layer graphite.  However, various gate-defined structures may also be able to shed light on other zero-magnetic field states such as magnetic or inter-valley coherent phases, as well as the newly discovered fractional Chern insulators.  The second is to integrate measurement techniques beyond low-frequency electrical transport, such as microwave dispersive readout and circuit QED, into the study of van der Waals mesoscopic devices at both zero- and high magnetic fields.  Without requiring superconducting resonators, even just a well impedance matched copper inductor can provide quality factors in the few thousands at cryogenic temperatures.  This would already enable the study of quasiparticle dynamics at time scales many orders of magnitude faster than traditional electronic transport, and may ultimately be a necessary technique for assessing the behavior of non-abelian QH states where quasiparticle fluctuations may cause rapid decoherence.  Utilizing superconducting resonators, and other circuit QED techniques, in combination with gate-defined van der Waals superconducting junctions will, in addition to fast high fidelity readout, allow for the direct study of the spectrum of Andreev-bound states.  Such measurements will provide new insights, inaccessible to other techniques, into both the superconducting phases of matter as well as any phase which is used as the intermediary part of the junction.