Geometric phase for a dimerized disordered continuum: Topological shot noise

P. Pradhan; N. Kumar

doi:doi:10.1209/epl/i1998-00446-x

DOI: 10.1209/epl/i1998-00446-x

Europhys. Lett, 44 (2), pp. 131-136 (1998)

Geometric phase for a dimerized disordered continuum:
Topological shot noise

P. Pradhan ¹ and N. Kumar ²

¹ Jawaharlal Nehru Centre for Advanced Scientific Research
Jakkur, Bangalore, 560 064, India
and Department of Physics, Indian Institute of Science
Bangalore, 560 012, India
² Raman Research Institute - Bangalore, 560 080, India

(received 27 March 1998; accepted in final form 25 August 1998)

PACS. 03.65Bz - Foundations, theory of measurement, miscellaneous theories (including Aharonov Bohm effect, Bell inequalities, Berry's phase).
PACS. 73.23 ${\rm -b}$ - Mesoscopic systems.
PACS. 72.15 ${\rm -v}$ - Electronic conduction in metals and alloys.

Abstract:

Geometric phase shift associated with an electron propagating through a dimerized disordered continuum is shown to be 0, or $\pm \pi$ (modulo $2\pi$ ), according to whether the associated circuit traversed in the two-dimensional parameter space excludes, or encircles a certain singularity. This phase shift is a topological invariant. Its discontinuous dependence on the electron energy and disorder implies a statistical spectral and conductance fluctuation in a corresponding mesoscopic system. Inasmuch as the fluctuation derives from the discreteness of the phase shift, it may aptly be called a topological shot noise.

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