Low-temperature behavior of transmission phase shift across a Kondo correlated quantum dot

Abstract

We study the transmission phase shift across a Kondo correlated quantum dot in a GaAs heterostructure at temperatures below the Kondo temperature ($T<T_{\mathrm{K}}$), 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 ($\lesssim 0.5$ rather than $\ll 1$). This situation is commonly used in GaAs quantum dots to ensure Kondo temperatures large enough ($\simeq 100$ 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 $\Gamma /U\ll 1$ needed to ensure a well-defined 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 $T\ll T_{\mathrm{K}}$, 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.

5 pages, 4 figures

References in corpus (3)

• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Electrical control of a solid-state flying qubit
• Transmission phase of a singly occupied quantum dot in the Kondo regime

Cited by in corpus (4)

• Three-body correlations in nonlinear response of correlated quantum liquid
• Fano-Kondo resonance versus Kondo plateau in an Aharonov-Bohm ring with an embedded quantum dot
• Mesoscopic phase behavior in a quantum dot around crossover between single-level and multilevel transport regimes
• Time-dependent wave packet simulations of transport through Aharanov-Bohm rings with an embedded quantum dot