# Transport across junctions of pseudospin-one fermions

## TL;DR

This paper investigates transport phenomena in junctions of pseudospin-one fermion materials, revealing perfect collimation effects and symmetries in conductance, with implications for experimental tests of such quantum systems.

## Contribution

It introduces the unique boundary conditions and transport properties of pseudospin-one fermion junctions, including perfect collimation at specific barrier potentials and a novel conductance symmetry.

## Key findings

- NBN junctions act as perfect collimators at specific barrier potentials.
- Conductance invariance under a specific barrier potential transformation.
- Subgap tunneling conductance is affected by collimation effects.

## Abstract

We study transport across ballistic junctions of materials which host pseudospin-one fermions as emergent low-energy quasiparticles. The effective low-energy Hamiltonians of such fermions are described by integer spin Weyl models. We show that current conservation in such integer spin-$s$ Weyl systems requires continuity across a boundary of only $2s$ (out of $2s+1$) components of the wave function. Using the current conservation conditions, we study the transport between normal metal-barrier-normal metal (NBN) and normal metal-barrier-superconductor (NBS) junctions of such systems in the presence of an applied voltage $eV$. We show that for a specific value of the barrier potential $U_0$, such NBN junctions act as perfect collimators; any quasiparticle which is incident on the barrier with a non-zero angle of incidence is reflected back with unit probability for any barrier width $d$. We discover an interesting symmetry of this system, namely, the conductance is invariant under $U_0 \to 2(\mu_L \pm eV)-U_0$, where $\mu_L$ is the chemical potential and the +(-) sign corresponds to particle (hole) mediated transport. For NBS junctions with a proximity-induced $s$-wave pairing potential, which also display such a collimation, we chart out the properties of the subgap tunneling conductance $G$ as a function of the barrier strength and applied voltage. We point out the effect of the collimation on the subgap tunneling conductance of these NBS junctions and discuss experiments which can test our theory.