Singlet–triplet transition induced by Zeeman energy in weakly coupled vertical double quantum dots

We use Pauli-spin blockade (P-SB) in a vertical double quantum dot to study the interplay between the nuclear spin effect and exchange interaction. We observe a specific P-SB lifting, reflecting coexistence of singlet–triplet admixing due to fluctuating nuclear spin field and singlet–triplet transition induced by the Zeeman effect when the exchange energy and the fluctuating nuclear field energy are comparable. From measurement of the Zeeman-induced P-SB lifting, we derive the exchange energy as a function of inter-dot level detuning. We confirm enhancement of exchange energy by resonance, and use Hubbard model calculation to account for it.