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The Aharonov-Bohm (AB) [1] effect induces a persistent current in
mesoscopic rings whose circumference is smaller than the phase
coherence length. This persistent current is a marker of quantum
coherence phenomena on the mesoscopic scale. We report on
two such mesoscopic systems.
In the first, the ring is coupled via tunnelling to another mesoscopic
structure: a side-branch quantum dot in the Kondo regime. We
obtain exact results for two variants of this set-up [2,3] using the
finite-size Bethe ansatz method [4,5]. Our findings suggest
a generic behaviour also found in other Bethe ansatz integrable
models [6,7].
The second mesoscopic system we report on, models a
ring-shaped metallic wire with a weak junction. We infer the
charge stiffness or Drude weight from the persistent current
induced by an Aharonov-Bohm flux through the ring. Using a
combination of exact Bethe ansatz calculations and numerical
results from the density renormalization group and quantum
Monte Carlo methods, we find that the stiffness scales to zero,
indicating a conductorinsulator transition, in the bulk limit as
soon as there is a weak junction [8].
[1] Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959). [2] H.-P. Eckle, H. Johannesson and C. A. Stafford, Phys. Rev. Lett. 87, 016602 (2001). [3] J. Nilsson, H.-P. Eckle, and H. Johannesson, Phys. Rev. B 76, 073408 (2007). [4] F. Woynarovich and H.-P. Eckle, J. Phys. A 20, L97 (1987); L443 (1987). [5] H.-P. Eckle and C. J. Hamer, J. Phys. A 24, 191 (1991). [6] H.-P. Eckle, A. Punnoose and R. A. Römer, Europhys. Lett. 39, 293 (1997). [7] H.-P. Eckle, Rep. Math. Phys. 61 (2008), 221. [8] T. M. R. Byrnes, R. J. Bursill, H.-P. Eckle, C. J. Hamer and A. Sandvik, Phys. Rev. B 66, 195313 (2002). |
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