  Thermoelectric devices that operate on quantum principles have been under
extensive investigation in the past decades. These devices are at the
fundamental limits of miniaturized heat engines and refrigerators, advancing
the field of quantum thermodynamics. Most research in this area concerns the
use of conduction electrons and holes as charge and heat carriers, and only
very recently have superconductors been considered as thermal engines and
thermoelectric devices. Here, we investigate the thermoelectric response of an
Abrikosov vortex in type-II superconductors in the deep quantum limit. We
consider two thermoelectric geometries, a type-II SIN junction and a local
Scanning Tunneling Microscope (STM)-tip normal metal probe over the
superconductor. We exploit the strong breaking of particle-hole symmetry in
bound states at sub-gap energies within the superconducting vortex to realize a
giant thermoelectric response in the presence of fluxons. We predict a
thermovoltage of a few mV/K at sub-Kelvin temperatures using both semi-analytic
and numerical self-consistent solutions of the Bogoliubov-de Gennes equations.
Relevant thermoelectric coefficients and figures of merit are found within our
model, both in linear and nonlinear regimes. The ZT of the SIN junction is
around 1, rising to above 3 for the STM junction centered at the vortex core.
We also discuss how this system can be used as a sensitive thermocouple, diode,
or localized bolometer to detect low-energy single photons.
