We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely,the Heitler-London(HL) and the Hund-Mulliken(HM) approximations, which use linear combinat...We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely,the Heitler-London(HL) and the Hund-Mulliken(HM) approximations, which use linear combinations of Fock-Darwin states to approximate the two-electron states under the double-well confinement potential. We compared these results to a case in which the solution to a one-dimensional Schr ¨odinger equation was exactly known and found that typical microscopic calculations based on Fock-Darwin states substantially underestimate the value of the exchange interaction, which is the key parameter that controls the quantum dot spin qubits. This underestimation originates from the lack of tunneling of Fock-Darwin states, which is accurate only in the case with a single potential well. Our results suggest that the accuracies of the current two-dimensional molecularorbit-theoretical calculations based on Fock-Darwin states should be revisited since underestimation could only deteriorate in dimensions that are higher than one.展开更多
基金supported by the Research Grants Council of the Hong Kong Special Administrative Region of China(Grant No.City U 21300116)the National Natural Science Foundation of China(Grant No.11604277)the Guangdong Innovative and Entrepreneurial Research Team Program(Grant No.2016ZT06D348)
文摘We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely,the Heitler-London(HL) and the Hund-Mulliken(HM) approximations, which use linear combinations of Fock-Darwin states to approximate the two-electron states under the double-well confinement potential. We compared these results to a case in which the solution to a one-dimensional Schr ¨odinger equation was exactly known and found that typical microscopic calculations based on Fock-Darwin states substantially underestimate the value of the exchange interaction, which is the key parameter that controls the quantum dot spin qubits. This underestimation originates from the lack of tunneling of Fock-Darwin states, which is accurate only in the case with a single potential well. Our results suggest that the accuracies of the current two-dimensional molecularorbit-theoretical calculations based on Fock-Darwin states should be revisited since underestimation could only deteriorate in dimensions that are higher than one.
