Universität zu Köln

Saha, Arijit, Gefen, Yuval, Burmistrov, Igor, Shnirman, Alexander ORCID: 0000-0003-4937-8189 and Altland, Alexander (2012). A quantum dot close to Stoner instability: The role of the Berry phase. Ann. Phys., 327 (10). S. 2543 - 2560. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 0003-4916

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Abstract

The physics of a quantum dot with electron-electron interactions is well captured by the so called Universal Hamiltonian if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close to the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [IS. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179]. (C) 2012 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Saha, Arijit UNSPECIFIED UNSPECIFIED UNSPECIFIED Gefen, Yuval UNSPECIFIED UNSPECIFIED UNSPECIFIED Burmistrov, Igor UNSPECIFIED UNSPECIFIED UNSPECIFIED Shnirman, Alexander UNSPECIFIED orcid.org/0000-0003-4937-8189 UNSPECIFIED Altland, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-482088
DOI:	10.1016/j.aop.2012.07.013
Journal or Publication Title:	Ann. Phys.
Volume:	327
Number:	10
Page Range:	S. 2543 - 2560
Date:	2012
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	0003-4916
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language COULOMB-BLOCKADE; METALLIC GRAINS; FERROMAGNETISM; SYSTEMS; FIELD; SPIN Multiple languages Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/48208