Fluctuating electron liquids in ultra-high mobility rhombohedral graphene nanoelectronics

Strong electron-electron interactions govern the low-temperature physics of rhombohedral multilayer graphene (RMG), leading to many different magnetic and superconducting phases. Fundamentally, all these phases emerge from magnetic and electronic correlations at elevated temperatures associated with excess magnetic entropy and short electron-electron correlation lengths. To study this regime, a clear hierarchy of interaction length, sample size and momentum relaxation length needs to be achieved, each separated by at least an order of magnitude. To this end, I introduce cryogenic shock exfoliation that produces the metastable RMG stock on a large scale, as well as new fabrication methods in order to reliably fabricate RMG nanoelectronics that satisfy mobility and size requirements.
In these improved devices, I uncover a fluctuating moment regime with excess entropy of ΔS ≈ k_B per carrier above the ordering temperatures – a signature of local moments entirely unexpected in an itinerant metal such as RMG. At first-order phase boundaries between competing isospin-polarized states, this entropy drives an isospin Pomeranchuk effect – leading to order with increasing temperature. Scanning nanoSQUID-on-tip magnetometry of current flow in RMG reveals that electrons at these temperatures behave like a liquid, and the charge transport is governed by the Gurzhi effect. This places RMG into the semi-quantum liquid regime where strong electron hydrodynamics appears at the scale of the Fermi wavelength equal to the isospin correlation length. Lastly, by increasing the device size, I demonstrate a crossover from Poiseuille to porous electron flow where the liquid is effectively no longer constrained by the sample boundaries.