Electron hydrodynamics

    In the vast majority of metals and semiconductors, electron flow is fully ohmic, and parameters such as the electrical resistance are determined purely by the properties of the material through which the electrons are flowing. Such ohmic behavior can be successfully modeled by using Boltzmann transport theory in the so-called relaxation time approximation. It has been known for decades, however, that in exceptionally pure materials the relaxation time approximation might not be adequate, and that including higher order terms in the transport theory could signal entry to an exotic regime in which the viscosity of the electron fluid plays a significant role in determining the resistance. In fact, a significant viscous contribution can even lead to completely non-ohmic effects such as backflow and ‘negative resistance’.

    Our groups have performed foundational work on electron hydrodynamics in two-dimensional electron gases in semiconductor heterostructures [1,2] and PdCoO2 [3], but these experiments are only the beginning. In this project, we aim to explore a host of new possibilities in these and other systems (e.g., materials with spin-momentum locking, notably Dirac and Weyl materials), particularly given the ability to design tailored devices using semiconductor technology or focused ion beam sculpting from single crystals. A further possibility is that hydrodynamic effects might exist in materials near the ‘quantum chaotic’ limit in which all internal scattering is extremely strong [4]. If this were so, it would be a natural link between experiment and adventurous modern theories linking the properties of general relativity and black holes with those of quantum field theories.

    Successful candidates will register for PhD study at the University of Würzburg, where Max Planck Fellow Laurens W. Molenkamp is based, and carry out research between Dresden and Würzburg as dictated by scientific priorities as the research unfolds. Willingness to travel between the two locations is therefore a prerequisite. Some of the experiments being envisioned would involve high-frequency technology at low temperatures. Experience in this domain would be advantageous but not required.

    [1] L.W. Molenkamp and M.J.M. de Jong, Phys. Rev. B 49, 5038 (1994)
    [2] M.J.M. de Jong and L.W. Molenkamp, Phys. Rev. B 51, 13389 (1995)
    [3] P.J.W. Moll, P. Kushwaha, N. Nandi, B. Schmidt, A.P. Mackenzie,
         Science 351, 1061 (2016)
    [4] J. A. N. Bruin, H. Sakai, R.S. Perry, A.P. Mackenzie, Science 339, 804 (2013)

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