From bahramy at riken.jp Tue Feb 1 18:24:48 2011 From: bahramy at riken.jp (Saeed Bahramy) Date: Wed, 2 Feb 2011 02:24:48 +0900 Subject: [Wannier] How to calculate current operator Message-ID: Dear Wannier90 developers and users, I'm trying to calculate the current operator Jx using Wannier90 code. By definition, I consider Jx to be the first derivative of H(k) with respect to kx. Having the real space Wannier hamiltonian H(R), then It should be possible to calculate Jx analytically by, Jx(k)=SUM_R[ i Rx H(R) exp(ik.R)] were SUM_R indicates the summation over all real space R-vectors. My procedure to calculate Jx is as follows, 1) I read the components of R-vectors (irvec) and H(R) from the Wannier90 output file seedname_hr.dat. 2) I build the R-vector as R=irvec(1,j)*A1+irvec(2,j)*A2+irvec(3,j)A3. Here, A1, A2 and A3 are my HEXAGONAL lattice vectors and j is the index for the jth R-vector. Having R, I then take its x-component as Rx, namely Rx=R(1). 3) I construct a fine k-mesh, and finally calculate Jx at each k using the above equation. While this procedure seems to be very straightforward, it doesn't appear to be giving me correct Jx results. For example, If construct H(R) from a 10x10x10 ab-initio k-mesh the calculated Jx would somehow differ from that obtained form another H(R) made from 16x16x16 k-mesh (note that this k-mesh differs from what I described in step 3). Moreover, due to the hexagonal symmetry of my structure, I expect that the Jx should be invariant under 60 deg rotation, but it doesn't seems so. I suspect that the problem should be somehow related to the way I calculate Rx. The reason is simply because I can properly construct H(k) and by that reproduce the ab-intio band dispersions without any problem. I was wondering if somebody in this forum could let me know If I'm missing something. I would greatly appreciate your comments and suggestions. Sincerely, Saeed ----------------------------------------------------------- Saeed Bahramy Correlated Electron Research Group Advanced Science Institute, RIKEN Saitama 351-0198 JAPAN ----------------------------------------------------------- From jonathan.yates at materials.ox.ac.uk Wed Feb 2 00:58:58 2011 From: jonathan.yates at materials.ox.ac.uk (Jonathan Yates) Date: Tue, 1 Feb 2011 23:58:58 +0000 Subject: [Wannier] How to calculate current operator In-Reply-To: References: Message-ID: <293387F9-FB5A-4B5E-928C-154073FADE2A@materials.ox.ac.uk> On 1 Feb 2011, at 17:24, Saeed Bahramy wrote: > Dear Wannier90 developers and users, > > I'm trying to calculate the current operator Jx using Wannier90 code. > By definition, I consider Jx to be the first derivative of H(k) with > respect to kx. Having the real space Wannier hamiltonian H(R), then It > should be possible to calculate Jx analytically by, > > Jx(k)=SUM_R[ i Rx H(R) exp(ik.R)] > > were SUM_R indicates the summation over all real space R-vectors. My > procedure to calculate Jx is as follows, > > 1) I read the components of R-vectors (irvec) and H(R) from the > Wannier90 output file seedname_hr.dat. > > 2) I build the R-vector as R=irvec(1,j)*A1+irvec(2,j)*A2+irvec(3,j)A3. > Here, A1, A2 and A3 are my HEXAGONAL lattice vectors and j is the > index for the jth R-vector. Having R, I then take its x-component as > Rx, namely Rx=R(1). > > 3) I construct a fine k-mesh, and finally calculate Jx at each k using > the above equation. > > While this procedure seems to be very straightforward, it doesn't > appear to be giving me correct Jx results. Saeed, Maybe you already know this - but the formalism is contained in Physical Review B 75, 195121 (2007). The formula you have quoted for J (or velocity to keep with the notion of that paper) is not in the basis of eigenstates - so it needs to be rotated into this basis. This will give you the elements of velocity diagonal in the band index. There are additional terms for the interband contributions. As the diagonal elements of v are simply the band gradients you could use this to test your implementation (ie compare against numerical differentiation of the wannier interpolated bands along some path in the BZ) Jonathan -- Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, UK tel: +44 (0)1865 612797 http://users.ox.ac.uk/~oums0549/ From no-reply at dropboxmail.com Fri Feb 4 13:21:04 2011 From: no-reply at dropboxmail.com (Dropbox) Date: Fri, 04 Feb 2011 12:21:04 +0000 Subject: [Wannier] Mohammad Saghayezhian invited you to Dropbox Message-ID: <20110204122105.01A713F57B0@mailman-2.dropboxmail.com> Mohammad Saghayezhian wants you to use Dropbox to sync and share files online and across computers. 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