Tight-binding Hamiltonians from Solids to Molecules

D.A. Papaconstantopoulos Department of Computational and Data Sciences

George Mason University, Fairfax

CollaboratorsM.J. Mehl, NRL

A. Shabaev, GMUM. Johannes, NRLN. Bernstein, NRLX. Sha, GMU

E. N . Economou, FORTH

Grant Support from DoE and ONR“Wavepro” Crete, Greece

June 10, 2011

PHYSICAL REVIEW B

o N b

e Nb3Go

I Nb:Sn

+ Nb35b

I Nb3f lL

o N b 3 5 L

e Nb30e

0 2 D t 0 a t 0 r mR E S I S T I V I T Y

FIG. 9. Calculated London

ra rao t80 160 80( p Q c m )

penetration depth at

locToBER 1982

o vJGo

o V3Sn

+ vssi-

o VsGe

o ?0 r0 m E0 100 tm !0 160 ltr aoR t S I S T I V t T Y ( p 0 c n l

0 K in A as a function of residual resistivity p0.

VOLUME 26. NUMBER 7

Effects of disorder on properties of 115 materials

C. M. SoukoulisCorporate Research Science Laboratories, Exxon Research and En$ineeilng Company,

Linden, New Jersey 07036

D. A. PapaconstantopoulosNaual Research Laboratory, Washington, D.C. 20375

(Received 4 May 1982)

We have calculated the effects of disorder on the density of states, Fermi velocity, andDrude plasma frequency for V and its,4 15 compounds VjX, with X:Al, Ga, Ge, Si, andSn, and for Nb and its ll5 compounds Nb3X, with X:Al, Ga, Ge, Si, Sn, and Sb usingthe electron-lifetime model and the results of band-structure calculations. [n most cases thedensity of states and the superconducting transition temperature T. are found to decreasewith increasing disorder, in qualitative agreement with experiment. Exceptions are Nb3Sband Nb3Si, for which we have found a small increase in ?'". We are also presenting calcula-tions of the effects of disorder on the mean free path, BCS coherence length, Londonpenetration depth, Ginzburg-Landau ,(, and the temperature dependence of the upper criti-cal field for the above materials. Comparison with the exisiting experimental data is made.

R E S I S T I v I T Y ( p 0 c m )

FIG 8. Ginzburg-Landau r near?"" as a function of residual resistivity po

z

io

!

z

z

o

z

z

z

z

2o

J

3

I

I

fl

E

3'

t 0 a m t m l a r 0R E S I S T I v I T Y ( p 0 c n )

NRL Tight-Binding Method Fit to DFT bands and total energies as a function of volume for

high-symmetry structures. Calculate quantities accessible to standard DFT not fitted

above, i.e., elastic constants, phonon spectra, and surface energies.

Perform large scale simulations not practical via DFT, such as static calculations for the energetics of systems containing up to 10,000 atoms, or calculations for a very large number of k-points as needed for mapping Fermi surfaces and evaluating susceptibilities.

Perform molecular dynamics simulations using up to 1,000 atoms and 5,000 MD time-steps, an impossible task for standard DFT codes.

NRL Tight-Binding Method: ApplicationsWe have applied the NRL-TB to the following materials: All transition metals (including the ferromagnets) Alkali, alkaline earth, and simple metals (Al-Pb) Semiconductors: C, Si, Ge Binary compounds:

NiH, PdH, FeAl, CoAl, NiAl, NbC, VN, Cu3Au, SiC, MgB2, FeNi, MgO

Ternary compounds: NaxCoO2, Sr2RuO4, SrRuO3, PbTiO3

Molecules: C-H-O

An improved Harrison-TB approach, inspired by the NRL-TB, was developed: Phys. Rev. B 70, 205101 (2004)

Vibrations in Amorphous Silicon using TB

Use NRL-TB to relax structure, compute phononsGet vibrational DOS, zero point motion

• zero-point motion is significant (even for relatively heavy Si)• asymmetry in 1st neighbor peak (influences analysis of coordination, defect concentration)

with zero-point motion

staticstructure

Feldman, Bernstein, Papa, Mehl, Phys. Rev. B 70, 165201 (2004); J. Phys.: Cond. Matter. 16, S5165 (2004).

radial distribution

Palladium vacancy formation energy

Single vacancy: 1.27 eV (experiment: 1.85 eV)

Double vacancies

2.52 eV 2.65 eV

2.67 eV 2.81 eV

40 50 60 70 80 90 100 110 120 130 140 150 160

-0.05

0.00

0.05

0.10

0.15

PdH (CsCl) -TBPdH (CsCl) -LAPWPdH2 (Fluorite) - TBPdH2 (Fluorite) - LAPWPd4H3 - TBPd4H3 - LAPWPd3H - TBPd3H - LAPW

Pd (fcc) - TBPd (fcc) - LAPWPd (bcc) - TBPd (bcc) - LAPWPd (sc) - TBPd (sc) - LAPWPdH (NaCl) - TBPdH (NaCl) - LAPW

Form

atio

n en

ergy

(Ry)

Volume (a.u.)

-2

0

2

4

Ene

rgy

(eV

)

40 60 80 100 1201.8

2.0

2.2

2.4

2.6

Dis

tanc

e (Å

)

Number of H atoms

PdH

0.4

0.45

0.5

0.55

0.6

0.65

0.7

! " X Y M # ! $ Z

En

erg

y (

Ry)

FeAsO: TB /LAPW Band comparison (13 bands fit)

TBLAPW

TBandLAPWmatchwell,eveninorbitalcharacter

Ques?on:Whydoesactualpseudogapoccurwithlowercomplexcontainingthreestatesanduppercomplexcontainingtwostates?(i.e.oppositeofexpectedligandfieldconfigura?on)

Localsymmetryistetrahedral

t2g

eg

(3)

(2)

Expect:lowerdoublet,uppertriplet23

Calcula?onshows:lowertriplet,upperdoublet

Elimina?ngallbutnearestneighborFe‐AshoppinginTBmodel:

!"

!#""

!$""

!%""

!&""

!'""

!(""

!)""

!"*&' !"*' !"*'' !"*( !"*(' !"*) !"*)' !"*+

!!""!,-./.01234250667

88!90!:1!;<.0=/>.?@<!A!B/1?1!=@./.0C!&'!C0D=001

"9

90!E=F?./61G@./6

HIJIKKH

K$!H

$

I$

23

Ligandfiledconfigura?onisregained(asexpected)