  As a secondary structure of DNA, DNA tetrahedra exhibit intriguing charge
transport phenomena and provide a promising platform for wide applications like
biosensors, as shown in recent electrochemical experiments. Here, we study
charge transport in a multi-terminal DNA tetrahedron, finding that its charge
transport properties strongly depend upon the interplay among contact position,
on-site energy disorder, and base-pair mismatch. Our results indicate that the
charge transport efficiency is nearly independent of contact position in the
weak disorder regime, and is dramatically declined by the occurrence of a
single base-pair mismatch between the source and the drain, in accordance with
experimental results [J. Am. Chem. Soc. {\bf 134}, 13148 (2012); Chem. Sci.
{\bf 9}, 979 (2018)]. By contrast, the charge transport efficiency could be
enhanced monotonically by shifting the source toward the drain in the strong
disorder regime, and be increased when the base-pair mismatch takes place
exactly at the contact position. In particular, when the source moves
successively from the top vertex to the drain, the charge transport through the
tetrahedral DNA device can be separated into three regimes, ranging from
disorder-induced linear decrement of charge transport to disorder-insensitive
charge transport, and to disorder-enhanced charge transport. Finally, we
predict that the DNA tetrahedron functions as a more efficient spin filter
compared to double-stranded DNA and opposite spin polarization could be
observed at different drains, which may be used to separate spin-unpolarized
electrons into spin-up ones and spin-down ones. These results could be readily
checked by electrochemical measurements and may help for designing novel DNA
tetrahedron-based molecular nanodevices.
