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#YMR
- DFT is now used also in industry, arrived?
- Solvable system with analytica solutions: available on wikipedia, little number. We need a portable system.
- BTAH attaches to surfaces and can inhibit corrosion. Questions are:
- position of molecules
- size system.
- presence of stacking, VdW interaction (important to detect some configuration)
- calculation of adsorption energy with different geom and different functionals.
- prediction of spectra: DFT basede
- PAW, substituted with a PAW with a core hole
- XCH excited core hole: atom is constrained in an excited stte
- XAS spectra are obtained by a Fermi golden rule
- Techniques are probes of molecular disposition.
Codes are VASP and QE.
- Hitchcock posters
- computers less efficient to keep up with Moore's law.
- Thermoelectrics, minimize phonon heat conductivity. very little conductibility Modelling requires
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Phonon frequencies, group velocities ( 2nd order
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Anharmonic III order with respect to displacement ( L. paulatto et al. Phys. Rev. B 87, 214303) with DF(P)T
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BTE = C_v \nabla (\part n_v \ \part T) = \part n_v / \part t
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use of the Fermi golden rules with isotopes effects.
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Umklaup scattering reduce the momentum,
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Cite M. Omini and a. sparavigna , il nuovo cimento D 19, 1537 (1997) Graphene: first hypotesis was to ignore phonon out of the plane (z), but they are actually about 50% of the total k.
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G. Fugallo et al. Nanoletters 14(11) 6109-6114-2015
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Callaway model: developed in 1964 for germanium 2D.
- similar to 3D low temperature. 2D system at room temperature behaves like the 3D. Is similar to the single mode.
- too small for any practical applications.
- you can solve it in a adiabatic fashion
Q/A
- Lorenzo: maximum is always wrong. But also at larger temperature, so
#Jarvist Disorder in semicondctor for photovoltaics.
- ternary and uaternary compounds, hve lot more entropy. Even 0K, even for "perfect" crystals.
- sombrero potential. Solution are known, the probability can be derived. Then we can impose the bose distribution.
- Sturm sequencies.
- VASP+PBE sp + BoltzTrap
- Ni3Sn2S2: metallic, non magnetic, no d-states below fermi level.
#Carla Verdi frolich e-ph coupling. Different effects are related to real part or imaginary part of self energy.
- Electron linewidtsh and lifetimes. tau= htagliato/2 Im self energy
Photoluminescence PL in function of T - Laura herz
- simple model Linewidth = zero + gamma Lo
- Wright, Verdi et al. Nat commuic 7, 11755 (2016)
modern trends in quantum magnetism *Giant magnetoresistance: in the MR there is a bias magnet that ensure the perpendicularly of spins
- racetrack memory
- topological domain walls. If you have two voundaries and you twist the two spin vectors, the relative rotation is important. It is a topological properties.
- Skyrmions: are stable magnetic structures. you can not remove them just by applying a transformation.
- The energy depends on the SO of the system F = ... + Sum D_ij (MixMj)
- if you put a magnetic field , you create "fields" of strange objects. Landau-lifshitz-gilbert equation :magnetization does notchange in magnutude delta t M = Beff x M Free energy is constante \delta F[M} = 0
How does Magnetic interact with QM? -Coloumb interaction is charge charge -pauli exclusion principle
- H = T + W
- there is a critical density at when the exchange energy is more important than the kinetic one.
- Ruderman-Kittel-Kasuya-Yosida:
- interaction of spin mediated by eectron gas, similar to friedel oscillation.
The fermi sphere is actualy peanut like frmi surfcace, at the side of sphere there is up and down.
Spin spiral wave in gamma-iron. advances in physics 47(1), 91, 1998
-introduce spin coupling. E x p spin orbital interaction.
- Breit hamiltonian, is the electron -electron equivalent. Work with Gross
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usually treated semiclassical with llg approx.
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model to thread them: Short distance exchange dominates, long distance dipole dipole, higher order term in 1/c expansion QED hamiltonian Itoh 1965
#Lorenzo Spectroscopy and elecronic excitation Is DFT good enough to describe excitation. We need to include screenening and polarizability
- 1 particle exxcitation is a fermion that move in space-time
- we need a propagator that describes the IPS or fotoemision
- The propagation of a particle change the system, that change the propagation that change the propagation etc: Dyson equation G = G_H+G_H\SigmaG_H + G_H\SigmaG_H\SigmaG_H Dyson equation G=G_H + G_h \SigmaG
G0W0 with static hamiltonian i find a delta peak with many body G I can observe: broadening of peak + satellites peaks.. G0W) correct the band gap rpoblem of DFT, but it is not a rigid shift. Works well for poorly correlated
2particles neutralexcitation neutral excitation, the charge of the sstem doesnt change: electron CB, hole VB. RPA = you neglet the exchange correlation
RPA self consistent description of electron-hole that speak each other with some interaction bare dipole dipole Static GW-BetherSalpeter, you create a bound state (Exciton)
- If you calculate SrTiO3 with RPA, you have an underextimated band gap and the energy is wrong. So you need to do a quasiparticle correction. But now you overextimate., so you need to move to BSE, that rearrange te transitions weights.
*H_BSE\PSI_lamba = E_Lambda\Psy_Lambda
- you can represent the excition.
DFT + QED = quantised light. Linear TDDDFT, extended to electron-phonotn system. *Linear dynamic vs non dynamic
#Brian Cunningham CCCP5 quasiparticle Self consistent GW QSGW
- description of fotodescription, inverse photoemission, absorption.
- DFT problems, not excited states, too many XC potential, KS eigenvalues phsyical meaning, spectroscopic quantities not well represented.
Hedin's GWA \Sigma contains exchabge and correlations. Ekn, = E_LDA + Z (phi|sigma - E_XC|phi>
- improvement over LDA, PRL96(2006) Schilfgaarde
problems: depends on LDA, systematically underextimate, approximation as RPA, introduces self-consistency.
- The starting point are from the KS hamiltonian, that is used to calcolate Sigma(omega)
- inclusion of SelfConsistency. but more importantily QSGW does not depends on DFT
- Full potential LMTO DFT Code
- smoothed hankel, convolution of regular hankel with a gausian.
- muffin tin
- MBPT = self energy replaces V_XC
- W = (1- V PI)^-1 V
- PI Calculated at the RPA level, ned to go beyond this for proper description of polarisation PI_BSE = (1- PI K)-1 PI K = \delta Sigma / Delta G 4 point object
BSE = E_Abs = E_add +E_Rem +E_eh
- how to correct GW shifted spectra.
#Walter Tarantino Lucia reining - Lsi politechnique france. MBPT : G(r1,t1;r2,t2) Path integral Feynman 1948, berezin 1966 way to visualize scattering
- functional-differential Schwinger 1951, less tudid, but used to derive formaly GW Only approachable thing is perturbation theory
- G = G0 +G0vG0+g0vG0vG0+/... this is probably only asymptotically cnverging, few terms improve, too many diverge, than converge again?
- solution is to introduce dyson equation, with the self energym and then eprturbate it.
- instead of taylor expansion, we use a functional expansion, so G= 1/ G0^-1 - (vG0+vG0G0vG0) ,this object converges even if the series doesnt.
*formaly G=G0+g0S[g]g formal way legengre transform of free energy wrt G pratical way perturbation theory, skeleton series, luttinger and ward 1960
- Fara says it convergs, but probably to wrong number. kozik ferrer, georges, prl 114 156402 2015
Many body calculations Idea is to reproduce spectral function, without passing by Self energy which is nn local and imaginary So the introduce an effective potential which is real and local, and is selfstanding.
Cluser very small. LSPR.
2D + nanoparticles. Plasmonic field enhancement. nanoparticle experience a nanoparticle field.