Calculation of tunnel couplings in open gate-defined disordered quantum dot systems

Quantum computation based on semiconductor electron-spin qubits requires high control of tunnel couplings between the quantum dots and the electron reservoirs. Potential disorder and the increasing complexity of the two-dimensional gate-defined quantum computing devices set high demands on the gate design and the voltage tuning of the tunnel barriers. We present a Green's formalism approach for the calculation of tunnel couplings between a quantum dot and a reservoir. Our method takes into account in full detail the two-dimensional electrostatic potential of the quantum dot, the tunnel barrier, and the reservoir. A wideband limit is employed only far away from the tunnel barrier region where the density of states is sufficiently large. We calculate the tunnel coupling including potential disorder effects, which become increasingly important for large-scale silicon-based spin-qubit devices. Studying the tunnel couplings of a single-electron transistor in Si/SiGe as a showcase, we find that charged defects are the dominant source of disorder leading to variations in the tunnel coupling of four orders of magnitude