  Thermoelectric measurements have the potential to uncover the density of
states of low-dimensional materials. Here, we present the anomalous
thermoelectric behaviour of mono-layer graphene-nanowire (NW) heterostructures,
showing large oscillations as a function of doping concentration. Our devices
consist of InAs NW and graphene vertical heterostructures, which are
electrically isolated by thin ($\sim$ 10nm) hexagonal boron nitride (hBN)
layers. In contrast to conventional thermoelectric measurements, where a heater
is placed on one side of a sample, we use the InAs NW (diameter $\sim 50$ nm)
as a local heater placed in the middle of the graphene channel. We measure the
thermoelectric voltage induced in graphene due to Joule heating in the NW as a
function of temperature (1.5K - 50K) and carrier concentration. The
thermoelectric voltage in bilayer graphene (BLG)- NW heterostructures shows
sign change around the Dirac point, as predicted by Mott's formula. In
contrast, the thermoelectric voltage measured across monolayer graphene
(MLG)-NW heterostructures shows anomalous large-amplitude oscillations around
the Dirac point, not seen in the Mott response derived from the electrical
conductivity measured on the same device. The anomalous oscillations are a
signature of the modified density of states in MLG by the electrostatic
potential of the NW, which is much weaker in the NW-BLG devices. Thermal
calculations of the heterostructure stack show that the temperature gradient is
dominant in the graphene region underneath the NW, and thus sensitive to the
modified density of states resulting in anomalous oscillations in the
thermoelectric voltage. Furthermore, with the application of a magnetic field,
we detect modifications in the density of states due to the formation of Landau
levels in both MLG and BLG.
