Dipole moment and Berry Phase¶

By default, Band computes (and prints to the output) only the components of the dipole moment orthogonal to the periodic direction(s).

Since the position operator is ill-defined in periodic systems, computing the longitudinal components of the dipole moment (i.e. the components along periodic directions) is not completely trivial. To obtain the longitudinal components of the dipole moment, you can perform a Berry Phase calculation:

BerryPhase Yes/No

BerryPhase

Type:	Bool
Default value:	No
Description:	Boolean that determines whether the dipole as determined through the Berry phase approach should be calculated.

In the graphical user interface (AMSinput) you can find the Berry Phase checkbox in the Details → Expert BAND panel.

In a Berry phase calculation, the dipole moment of a unit cell is calculated with the help of the geometric phase within the unit cell. The theoretical framework of the calculations originates from the ‘Modern theory of polarization’ that was come up with in the early 1990s by King-Smith, Vanderbilt and Resta. [1] [2] The implementation in BAND is a generalization of the one-dimensional Berry phase approach for quantum chemistry codes with local basis sets devised by Kudin and Car. [3]

An option that can be useful when validating the Berry Phase calculation is ShiftCoordinates in the AMS System block:

System header
   ShiftCoordinates float_list
End

System

ShiftCoordinates

Type:	Float List
Unit:	Bohr
Description:	Translate the atoms by the specified shift (three numbers).

References