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Magnetization of Disordered Ballistic Quantum Billards

Daniel Braun·Yuval Gefen·Gilles Montambaux
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Abstract

We study the magnetic response of mesoscopic quantum dots in the ballistic regime where the mean free path $l_e$ is larger that the size $L$ of the sample, yet smaller than $L (k_F L)^{d-1}$. In this regime, disorder plays an important role. Employing a semiclassical picture we calculate the contribution of long trajectories which are strongly affected by static disorder and which differ sharply from those of clean systems. In the case of a magnetic field, they give rise to a large linear paramagnetic susceptibility (which is disorder independent), whose magnitude is in agreement with recent experimental results. In the case of a Aharonov-Bohm flux, the susceptibility is disorder dependent and is proportional to the mean free path as in the diffusive regime. We also discuss the corresponding non--linear susceptibilities.

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Daniel Braun, Yuval Gefen, Gilles Montambaux. 1994-05-09. Magnetization of Disordered Ballistic Quantum Billards. https://doi.org/10.1002/andp.19945060605

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