Takada, S.; Yamamoto, M.; Bäuerle, C.; Alex, A.; Delft, J. von; Ludwig, A.; Wieck, A. D.; Tarucha, S.
(2016):
Lowtemperature behavior of transmission phase shift across a Kondo correlated quantum dot.
In: Physical Review B, Vol. 94, No. 8, 81303

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Abstract
We study the transmission phase shift across a Kondo correlated quantum dot in a GaAs heterostructure at temperatures below the Kondo temperature (T < TK), where the phase shift is expected to show a plateau at pi/2 for an ideal Kondo singlet ground state. Our device is tuned such that the ratio Gamma/U of level width Gamma to charging energy U is quite large (less than or similar to 0.5 rather than << 1). This situation is commonly used in GaAs quantum dots to ensure Kondo temperatures large enough (similar or equal to 100 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 Gamma/U << 1 needed to ensure a welldefined local moment. Our measured phase evolves monotonically by pi across the two Coulomb peaks, but without being locked at pi/2 in the Kondo valley for T << TK, due to a significant influence of large Gamma/U. Only when Gamma/U is reduced sufficiently does the phase start to be locked around pi/2 and develops into a plateau at pi/2. 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.