[Pw_forum] Question about induced dipole moment

Nicola Marzari marzari at MIT.EDU
Wed Sep 19 14:40:11 CEST 2007

lan haiping wrote:
> Dear Stefano,
> i notice such problem, but in Prof Marzari's work on cnt, the transverse 
> polarizabilities of metallic nanotubes are given.  My confusion may be 
> due to this example.
> Thank you
> Regards
> Hai-Ping

Dear Hai-Ping,

1) the transverse polarizabilities are finite for both metallic
and insulating nanotubes. It's the longitudinal one that is
infinite in metallic tubes. Note that 3n,0 tubes at small diameters
are semiconducting with small gaps.

2) as mentioned, we did calculate them in real space from the integral
of the charge density. This is an appropriate operation for a finite,
isolated system - in the transverse direction this is what they are.

3) re. electric enthalpy - not sure what the status of that is.
I'll try to discuss it when Paolo Umari visits later in October.

4) you could use WFs - both for truly semiconducting nanotubes,
and even for the worse case scenario of (n,n) armchair (metallic)
ones. Treat the system as insulating, and you should
find a solution with WFs that corresponds to covalent bonds,
and 1 p_z-like WF every 2  carbons. The center displacement as a
function of field gives you the polarizaton.



Prof Nicola Marzari   Department of Materials Science and Engineering
13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu

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