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 - Mesoscopic systems.
PACS. 72.15 - Electronic conduction in metals and alloys.
Geometric phase shift associated with an electron propagating through a dimerized disordered continuum is shown to be 0, or (modulo ), 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.