gipaw&–&linear&response&& inthe& presenceof magnec &ﬁelds& ·...

GIPAW – Linear response in the presence of magne7c fields

Uwe Gerstmann University of Paderborn, Germany

Trieste, January 18 – 21, 2016

QE developers’ mee7ng Linear Response

Davide Ceresoli Emine Kucukbenli Ari Parvo Seitsonen

Originally aimed to calculate NMR chemical shiBs, later also the EPR electronic g-‐tensor, ...

Standard version: qe-gipaw-5.3.tar @ qe-‐forge

Uwe Gerstmann University of Paderborn, Germany



Davide Ceresoli Emine Kucukbenli Ari Parvo Seitsonen

Originally aimed to calculate NMR chemical shiBs, later also the EPR electronic g-‐tensor, ...

Standard version: qe-gipaw-5.3.tar @ qe-‐forge

GIPAW – Linear Magne7c Response



Originally aimed to calculate NMR chemical shiBs, later also the EPR electronic g-‐tensor,...

GIPAW rouOnes/pseudopoten7als are also used for

-‐ X-‐ray spectra (Xspectra): XANES, (XMCD)

-‐ orbital magneOzaOon, converse NMR-‐approach

-‐ SOC including two component noncolinear scheme using scalar-‐relaOvisOc GIPAW pseudos

GIPAW – Linear Magne7c Response

QE Developers’ MeeOng, Trieste, January 18 – 21, 2016

EssenOal: B-‐field brings the phase of the wfc into play (to insure translaOonal invariance within PBC) The PAW augmentaOon scheme has to be extended in a Gauge Including way: à GIPAW

GIPAW-‐ Linear Magne7c Response

Basic quan7ty for NMR (EPR): (spin) currents induced by the B-‐field

à Green‘s funcOon required

spin-‐currents

EPR:

GIPAW-‐ Linear Magne7c Response QE Developers’ MeeOng, Trieste, January 18 – 21, 2016

Basic quan7ty for NMR (EPR): (spin) currents induced by the B-‐field

à Green‘s funcOon required

spin-‐currents

EPR:

NMR: Bind(r‘) = ... ... |r‘-‐ r|3


r‘-‐ r

Central rou7ne: greenfunction.f90


Green‘s funcOon@k+q to be applied on a modified version of the unperturbed wfc: Gk+q |psi > = Gk+q { Vk+q,k|evc>}; q = {0, ± Δq ei with i=x,y,z} Similar to solve_linter.f90 in PH, it calls cgsolve_all.f90 iteraOve solver of linear systems cg_psi.f90 for (simple) precondiOoning (via diagonals of H), ch_psi_all.f90 for applicaOon of H-‐eS+P_cv orthogonalize.f90 for compuOng P_cv

( h_psi_q.f90 for BAND parallelzaOon only; otherwize: h_psi, calbec, s_psi )



Green‘s funcOon@k+q to be applied on a modified version of the unperturbed wfc: Gk+q |psi > = Gk+q { Vk+q,k|evc>}; q = {0, ± Δq ei with i=x,y,z} Similar to solve_linter.f90 in PH, it calls cgsolve_all.f90 iteraOve solver of linear systems cg_psi.f90 for (simple) precondiOoning (via diagonals of H), ch_psi_all.f90 for applicaOon of H-‐eS+P_cv orthogonalize.f90 for compuOng P_cv

( h_psi_q.f90 for BAND parallelzaOon only; instead: h_psi, calbec, s_psi )



Gk+q |psi > = Gk+q { Vk+q,k|evc>}; q = {0, ± Δq ei with i=x,y,z} in addiOon: apply_operators.f90 , e.g. apply Vk+q,k to rhs compute_u_kq.f90 prepares unperturbed wfc@k+q

NEW: Speed-‐up for small Δq: resuse Gk+q |psi > from previous q, ch_psi.f90 only for q=0. Includes all things for precondiOoning, e.g. also small parts from phq_init.f90: eprec = 1.35*zdotc(evq,work)



Gk+q |psi > = Gk+q { Vk+q,k|evc>}; q = {0, ± Δq ei with i=x,y,z}

in addiOon: apply_operators.f90 , e.g. apply Vk+q,k to rhs

compute_u_kq.f90 prepares unperturbed wfc@k+q

Specific topics:

-‐ quanOOes at k and k+q must have the same G-‐vector ordering; we call gk_sort only for k, not for k+q.

-‐ symmetry operaOons that do not map cartesian axes might be – in principle – removed (as done in 5.3.0), but: NEW: it works also with full symmetry, if symmetrizaOon is applied at the very end (onto the full tensors) excusively.

LR related rou7nes (as a general observa6on):

LR in GIPAW has very few dependencies, can be easily decoupled from the code, and can be „librarized“ away (into LR_Modules). As my present personal opinion: greenfunction.f90 (or something like that) should be either kept GIPAW-‐specific or solve_linter.f90 should be reorganized, split-‐up into less PH-specific logical subrouOnes, may be all of them kept within the same file.

interface between GIPAW/LR_Modules can be changed accordingly.


Open Ques7on (loosely related to LR):


-‐  Zero-‐Field Spliqng (ZFS) of EPR, both DS-‐S and DSO! -‐  NMR/EPR for hybrid funcOonals -‐  NMR with spin-‐orbit coupling, colinear & non-‐colinear based on relaOvisOc & scalar relaOvisOc (GI)PAW pseudos -‐  Circular Dichroism of X-‐ray AdsorpOon (XMCD) (Mateo Calandra, UG)

Work in progress, perspec7ves:

-‐  Where to put the Berry-‐phase rouOnes applicable onto NMR/EPR, GIPAW-‐tree or (parOally) PW-‐core? -‐  orbital magneOzaOon as a more general quanOty (MTM analogue to MTM, suggesOng PW), but to compute accurate du/dk: greenfunction.f90

Proposal: keep it close to “NMR/EPR“, should be found in GIPAW, e.g.:

Thanks for your aZen7on!

QE Developers’ MeeOng, Trieste, January 18 – 21, 2016

GIPAW-‐ Linear Magne7c Response

2nd method: beyond perturba7on theory Orbita

l magne

7za7

on

EPR

htp://www.quantum-‐espresso.org

Both methods are now applicable also on metallic systems, e.g. electrons trapped by the conducOon band minimum in Si bulk:

Strongly delocalized states: conducOon band electrons in Si: gexp = 1.9995 cc unit cell (2 atoms), (24 × 24 × 24) MP k-‐point set: gDFT 1 = 1.9991 (Berry phase)

gDFT 2 = 1.9990 (non-‐eq. GIPAW)

Young et al., PRB 55, 16245 (1997)

Calcula7ng the g-‐tensor – two different methods

Efficient relativistic DFT calculations

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scalar-rel.

scalar-‐rela/vis/c pseudopoten/als: -‐ RelaOvisOc kineOc energy -‐ spin-‐orbit (SO) coupling neglected

Bi(111) bilayer


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scalar-rel.

scalar-‐rela/vis/c pseudopoten/als: -‐ RelaOvisOc kineOc energy -‐ spin-‐orbit (SO) coupling neglected full-‐rela7vis7c approach: large SO coupling effects, but: factor-‐of-‐40 more computaOonal costs

Bi(111) bilayer


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Pauliscalar-rel.

scalar-‐rela/vis/c pseudopoten/als: -‐ RelaOvisOc kineOc energy -‐ spin-‐orbit (SO) coupling neglected alterna7ve rela7vis7c approach: PAW-‐reconstruc7on of SO coupling

Bi(111) bilayer


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M ! K M

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Pauliscalar-rel.


ZORA:

Bi(111) bilayer


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Pauliscalar-rel.

iden7cal results !

Bi(111) bilayer

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efficient „reconstruc6on-‐only“ approach:

No -‐k à k scatering @ impurity site

rela7vis7c calcula7ons for large systems (500 atoms) possible:


gipaw&–&linear&response&& inthe& presenceof magnec &ﬁelds& ·...

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