Geometric phase for a dimerized disordered continuum: Topological shot noise
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
Accepted: 15 August 1998
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.
PACS: 03.65.Bz – Foundations, theory of measurement, miscellaneous theories (including Aha ronov Bohm effect, Bell inequalities, Berry's phase) / 73.23.-b – Mesoscopic systems / 72.15.-v – Electronic conduction in metals and alloys
© EDP Sciences, 1998