This is part of a seminar series for students and researchers interested in theoretical physics and applied mathematics. Listen to Nitay Ben-Shachar from Caltech give a seminar titled "Tomographic electron flows in confined geometries".
Abstract: Hydrodynamic-like electron flows are typically modeled using the Stokes-Ohm equation or a kinetic description that is based on a dual-relaxation time approximation. Such models assume a short intrinsic mean free path l_e due to momentum-conserving electronic scattering and a large extrinsic mean free path l_{MR} due to momentum-relaxing impurity scattering. This assumption, however, is overly simplistic and falls short at low temperatures, where it is known from exact diagonalization studies of the electronic collision integral that another large electronic mean free path l_o emerges, which describes long-lived odd electron modes––this is sometimes known as the tomographic effect. Here, using a matched asymptotic expansion of the underlying Fermi liquid kinetic equation that includes different electron relaxation times, we derive a general asymptotic theory for tomographic flows in arbitrary smooth boundary geometries. We find that the tomographic effect strongly modifies previous hydrodynamic theories: In particular, we find that (i) an equilibrium is established in the bulk, where the flow is governed by Stokes-Ohm like equations with significant finite-wavelength corrections, (ii) the velocity slip condition at the boundary is strongly modified and not accounted for by the widely-used hydrodynamic slip-length condition, (iii) a large kinetic layer of width \sim\sqrt{l_e l_o} arises near boundaries, which is much larger than in conventional near-hydrodynamic theories, and (iv) all these effects are strongly suppressed by an external magnetic field. We illustrate our findings for electron flow in a channel. The equations derived here represent the fundamental governing equations for hydrodynamic-like tomographic flows.
Participate on campus or via Zoom.
On campus: PJ Lecture Hall
Zoom link: https://gu-se.zoom.us/j/64681043702