Berry’s phase

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

Potential fluid dynamics, molecular systems, modulus-phase formalism, quantum mechanics and, 265—266 Pragmatic models, Renner-Teller effect, triatomic molecules, 618-621 Probability densities, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 705-711 Projection operators, geometric phase theory, eigenvector evolution, 16-17 Projective Hilbert space, Berry s phase, 209-210... 

Novoselov KS, McCann E, Morozov SV et al (2006) Unconventional quantum Hall effect and Berry s phase of 2pi in bilayer graphene. Nat Phys 2 177-180... 

Spontaneous polarisation, that is polarisation in the absence of an electric field, has been calculated using both a Wannier function approach and a Berry s phase approach. Berry s phase involves an adiabatic change around a closed loop which results in a change of phase without change in energy. A recent paper by Ferretti et alP used the PAW method with ultrasoft pseudopotentials and Wannier functions to calculate the spontaneous polarisation of AIN in its wurtzite phase. 

It is important to mention that the relation between the phases of the D-matrix and Berry s phase of each of the electronic adiabatic states is discussed by R. Baer [23]. In particular, for a real electronic basis set where the two phases are shown to be identical. 

B. Simon, Holonomy, the quantum adiabatic theorem, and Berry s phase, Phys. Rev. Lett. 51 2167 (1983). 

Key words Geometric phase effect - Conical intersection - Molecular Aharonov-Bohm effect -Berry s phase... 

Zhang YB, Tan YW, Stormer HL, Kim P. Experimental observation of the quantum Hall effect and Berry s phase in graphene. Nature. 2005 438 201. 

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