# Synopsis: Dirac connection

Ballistic electron transport through a clean superconductor with d-wave symmetry has features in common with graphene.

In response to a voltage, the electrical current in a pure sheet of graphene diminishes as $1/L$, where $L$ is the length over which the current is transmitted. This form of scaling, called pseudodiffusive because of its similarity to diffusion in a random potential, occurs when $L$ is less than the width of the sheet and the mean free path.

In graphene, pseudodiffusion occurs because the electrons behave like massless Dirac fermions. Now, in a paper appearing in Physical Review B, János Asbóth and collaborators at Leiden University in the Netherlands calculate the transmission of electrons and holes between two normal-metal electrodes, separated over a distance $L$ by a clean d-wave superconductor. Asbóth et al. find that the transmitted electrical and thermal currents both have the pseudodiffusive $1/L$ scaling characteristic of massless Dirac fermions—regardless of the presence of tunnel barriers at the metal-superconductor interfaces—as long as $L$ is larger than the superconducting coherence length and smaller than the width of the superconductor and the mean free path. This occurs because the d-wave superconductor forms ballistic conduction channels for coupled electron-hole excitations that are described by an anisotropic two-dimensional Dirac equation analogous to that of graphene. This finding is likely to spur experimental efforts to search for pseudodiffusive transmission in clean single crystals of high-$T{}_{c}$ cuprates. – Sarma Kancharla

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