Abstract
We study the transmission phase shift across a Kondo correlated quantum dot in a GaAs heterostructure at temperatures below the Kondo temperature , where the phase shift is expected to show a plateau at for an ideal Kondo singlet ground state. Our device is tuned such that the ratio of level width to charging energy is quite large ( rather than ). This situation is commonly used in GaAs quantum dots to ensure Kondo temperatures large enough ( mK here) to be experimentally accessible; however, it also implies that charge fluctuations are more pronounced than typically assumed in theoretical studies focusing on the regime needed to ensure a well-defined local moment. Our measured phase evolves monotonically by across the two Coulomb peaks, but without being locked at in the Kondo valley for , due to a significant influence of large . Only when is reduced sufficiently does the phase start to be locked around and develops into a plateau at . Our observations are consistent with numerical renormalization group calculations, and can be understood as a direct consequence of the Friedel sum rule that relates the transmission phase shift to the local occupancy of the dot, and thermal average of a transmission coefficient through a resonance level near the Fermi energy.
- Received 10 April 2016
- Revised 20 June 2016
DOI:https://doi.org/10.1103/PhysRevB.94.081303
©2016 American Physical Society