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The Transmission Phase Shift
of a Quantum Dot with Kondo Correlations

Jan von Delft^{a}, Ulrich Gerland^{a},
Theo Costi^{b}, and Yuval Oreg^{c}

^{a} Institut fuer Theoretische Festkoerperphysik,
Universitaet Karlsruhe, D-76128 Karlsruhe, Germany

^{b} Theoretische Physik III, Universitaet Augsburg,
86135 Augsburg, Germany

^{c}Lyman Laboratory of Physics, Harvard University,
Cambridge MA 02198, USA

vondelft@tfp-physik.uni-karlsruhe.de
The Kondo effect, which occurs in metals containing magnetic
impurities, has been studied for more than thirty years, yet one of
its most fundamental properties has so far eluded direct experimental
verification: at sufficiently low temperatures, a conduction electron
scattering off a spin-1/2 impurity is predicted [1,2,3] to experience
a resonance phase shift of pi/2, without any phase randomization. A
direct observation of this phase shift, not possible in bulk systems,
has now become feasible using quantum dots, due to two recent
experimental breakthroughs: Kondo-type correlations were observed in
dots strongly coupled to leads [4-8], and the transmission phase shift
of a dot was measured by Aharanov-Bohm interferometry [9,10]. By
combining these two experiments, it should be possible to directly
measure the transmission phase shift of a Kondo-correlated dot -- this
would elucidate phase-coherent transport of electrons traversing a
strongly-interacting environment (the dot-lead system) that is tunable
from being uncorrelated at high temperatures through a
strongly-correlated crossover regime to a Fermi liquid at sufficiently
low temperatures. I give a detailed introduction to the
two types of experiments, and explain what could be expected to happen
if they were combined, including how the
pi/2 phase shift would manifest itself.

**References**

[1] J. Friedel, Can. J. Phys. 34, 1190 (1956).

[2] D. C. Langreth, Phys. Rev. 150, 516 (1966).

[3] P. Nozieres, J. Low Temp. Phys. 17}, 31 (1974).

[4] D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magdaer,
U. Meirav, and M. A. Kastner, Nature 391, 156 (1998).

[5] S. M. Cronenwett, T. H. Oosterkamp, and L. Kouwenhoven,
Science 281, 540 (1998).

[6] D. Goldhaber-Gordon, J. Goeres, M. A. Kastner, H. Shtrikman,
D. Mahalu, and U. Meirav, Phys. Rev. Lett. 81, 5225 (1998).

[7] J. Schmid, J. Weis, K. Eberl, and K. von Klitzing,
Physica B 256-258, 182 (1998).

[8] F. Simmel, R. H. Blick, J. Kotthaus, W. Wegscheider,
and M. Bichler,
submitted to Phys. Rev. Lett. \noindent [cond-mat/9812153].

[9] R. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, and
H. Shtrikman, Nature 385, 417 (1997).

[10] A. Yacoby, R. Schuster, and M. Heilblum,
Phys. Rev. B, 53, 9583 (1996).