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Résumé |
Ultra-clean materials now routinely access regimes where electron flow is neither purely Ohmic nor purely hydrodynamic, and where boundaries and device geometry are part of the physics rather than a complication. Toward quantitatively modelling the realities of electronic transport and correlated quantum systems more broadly, in this talk I develop geometry-aware transport models from two complementary viewpoints, kinetic theory and nonlinear continuum mechanics, before discussing how to combine them. I begin with a kinetic description of linear response transport across the ballistic–hydrodynamic crossover in 2D devices. Using an angular-harmonic expansion of the Boltzmann equation with a relaxation-time (BGK-like) collision model, the approach retains long-lived modes responsible for nonlocal and tomographic response while recovering viscous hydrodynamics in appropriate limits. Applied to complex geometries, it produces phase diagrams in momentum-conserving and momentum-relaxing scattering times and makes quantitative, space-resolved predictions for flow patterns and nonlocal voltages accessible to scanning-probe and multi-terminal measurements. In particular, I propose simple device geometries that delineate ballistic, hydrodynamic, and diffusive transport even without sophisticated local imaging. I then switch to a fluid-mechanical viewpoint, where the hydrodynamic limit provides analytic control over even nonlinear electronic flow. When driven toward the electronic sound speed, electron liquids should exhibit genuinely fluid-mechanical compressible flow phenomena such as choking and shock-like transitions that lie beyond Ohmic and purely ballistic descriptions. As one concrete example, I discuss bilayer graphene de Laval nozzle devices, where transport and local potential signatures are consistent with a viscous shock front, illustrating how compressibility opens a largely unexplored regime for electron fluids. Finally, I combine these threads by showing how the hydrodynamic limit constrains nonlinear kinetic theory across the crossover, where long-lived ballistic modes, boundaries, and dissipation compete in time-dependent and unstable dynamics. I use the 1D Dyakonov–Shur instability as a laboratory to discuss what becomes of nonlinear hydrodynamics as electron flow evolves from viscous to ballistic behaviour. |
