  We report on the observation of nanoscale conduction at ferroelectric domain
walls in hexagonal HoMnO3 protected by the topology of multiferroic vortices
using in situ conductive atomic force microscopy, piezoresponse force
microscopy, and kelvin-probe force microscopy at low temperatures. In addition
to previously observed Schottky-like rectification at low bias [Phys. Rev.
Lett., 104, 217601 (2010)], conductance spectra reveal that negatively charged
tail-to-tail walls exhibit enhanced conduction at high forward bias, while
positively charged head-to-head walls exhibit suppressed conduction at high
reverse bias. Our results pave the way for understanding the semiconducting
properties of the domains and domain walls in small-gap ferroelectrics.
