Quantum corrections to conduction in “bad” metals

How should we think about quantum interference in metals where our established models don’t seem to work? Professor Douglas Natelson explains his recent paper in Journal of Physics: Condensed Matter.
Condensed matter physicists have their own “standard model” for metals, Landau’s Fermi Liquid theory. FL theory says that the low-energy excitations of a conventional metal are long-lived quasiparticles, with charge –e (for an electron conductor) and spin ½ (weak spin-orbit effects), and that these quasiparticles “live” a long time. If the mean free path for scattering is ℓ, and the Fermi wavevector for such excitations is kF, then in a “good” metal, kFℓ >> 1 – the quasiparticles propagate many times their own wavelength between scattering events.

When we teach conduction to undergrads, we often leverage this to treat the electrons in a metal like a classical gas (the Drude model) rather than a quantum system.  That is, we neglect quantum interference effects involving the quasiparticles, because inelastic interactions between those quasiparticles and other dynamical degrees of freedom (other electrons; magnetic impurities; lattice vibrations) cause decoherence on comparatively short time and length scales.  In the 1970s and 80s, theorists developed a nice treatment of quantum corrections to classical conduction, perturbative in 1/(kFℓ), and predicted the appearance of “mesoscopic” quantum interference effects at low temperatures and on short distance scales where quantum decoherence is not yet complete.   These mesoscopic corrections are often seen in the magnetoresistance, and include weak localization and universal conductance fluctuations.  Studies in the 1980s and 90s established that real systems’ response generally agrees very well with the theoretical expectations.

However, the story isn’t complete.  There are “bad” metals where, based on simple interpretation of their electronic transport properties, kFℓ < 1.  While this most often happens at very high temperatures, there are some systems where this seems to be true at cryogenic temperatures as well, with no obvious signs of strong localization.   What do quantum corrections to semiclassical conduction look like in such systems?

In our latest paper, we consider one such system, HxVO2.  Vanadium dioxide is a long-studied correlated material with a phase transition between a correlated high temperature metallic state and a low temperature insulating phase.  The intercalation of atomic hydrogen suppresses that transition, and is one way to stabilize an unusual metallic state down to low temperatures.  In epitaxial films, single-crystal nanowires, and single-crystal flakes of HxVO2, we find phenomena that strongly resemble weak localization and universal conductance fluctuations.  This suggests that despite the resistivity implying kFℓ < 1, quantum coherence effects over longer length scales become important at low temperatures in this system.   However, at present there is no self-consistent quantitative model to treat these effects in this “bad metal” regime.   We hope that this work helps motivate theoretical considerations of quantum transport in bad metals and other systems that appear to deviate from the Fermi Liquid regime.

A “bad” metal, HxVO2. (a) Resistivity of a VO2 film before (black, showing the metal-insulator transition) and after (red) 30 s exposure to atomic hydrogen. The resistivity afterward is high (1000x higher than that of Au, for example), but shows no obvious signs of true insulating behavior at low temperatures. (b) In this weird system, the magnetoresistance grows and develops features as temperature is lowered. These features resemble quantum interference effects seen in conventional metals, but the theoretical model for that situation is inconsistent with the observed high resistivity. New ways of thinking about these mesoscopic phenomena in such “bad” metals need to be developed. Figure taken from J. Phys. Cond. Mat. 185601 © IOP Publishing 2017.


About the Authors

Will Hardy and Panpan Zhou are graduate students in Professor Douglas Natelson’s group at Rice University, as was Dr Heng Ji.  The Natelson group applies nanoscale techniques to address condensed matter physics questions, including the study of correlated materials.  Dr Hanjong Paik is a postdoctoral researcher in the Professor Darrell Schlom’s  research group at Cornell University.  The Schlom group excels at the epitaxial engineering and growth of novel crystalline materials, particularly correlated oxides.


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