  Nanoelectronic quantum dot devices exploiting the charge-Kondo paradigm have
been established as versatile and accurate analog quantum simulators of
fundamental quantum impurity models. In particular, hybrid metal-semiconductor
dots connected to two metallic leads realize the two-channel Kondo (2CK) model,
in which Kondo screening of the dot charge pseudospin is frustrated. Here, we
consider theoretically a two-channel charge-Kondo device made instead from
graphene components, realizing a pseudogapped version of the 2CK model. We
solve the model using Wilson's Numerical Renormalization Group method, and
uncover a rich phase diagram as a function of dot-lead coupling strength,
channel asymmetry, and potential scattering. The complex physics of this system
is explored through its thermodynamic properties, scattering T-matrix, and
experimentally measurable conductance. We find that the strong coupling
pseudogap Kondo phase persists in the channel-asymmetric two-channel context,
while in the channel-symmetric case frustration results in a novel quantum
phase transition. Remarkably, despite the vanishing density of states in the
graphene leads at low energies, we find a finite linear conductance at zero
temperature at the frustrated critical point, which is of non-Fermi liquid
type. Our results suggest that the graphene charge-Kondo platform offers a
unique possibility to access multichannel pseudogap Kondo physics.
