SciPost Phys. 13, 004 (2022) ·
published 21 July 2022
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· pdf
Understanding electrical transport in strange metals, including the seeming
universality of Planckian $T$-linear resistivity, remains a longstanding
challenge in condensed matter physics. We propose that local imaging
techniques, such as nitrogen vacancy center magnetometry, can locally identify
signatures of quantum critical response which are invisible in measurements of
a bulk electrical resistivity. As an illustrative example, we use a minimal
holographic model for a strange metal in two spatial dimensions to predict how
electrical current will flow in regimes dominated by quantum critical dynamics
on the Planckian length scale. We describe the crossover between quantum
critical transport and hydrodynamic transport (including Ohmic regimes), both
in charge neutral and finite density systems. We compare our holographic
predictions to experiments on charge neutral graphene, finding quantitative
agreement with available data; we suggest further experiments which may
determine the relevance of our framework to transport on Planckian scales in
this material. More broadly, we propose that locally imaged transport be used
to test the universality (or lack thereof) of microscopic dynamics in the
diverse set of quantum materials exhibiting $T$-linear resistivity.
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