Physics, Modeling, and Simulation of the Optical Response of Layers of Semiconductor Nano-Objects. O. Voskoboynikov
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- Suzan Morrison
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1 hyscs Modlg ad Sulato of th Optcal Rspos of Lays of Scoducto Nao-Objcts O. Vosoboyov Dpatt of lctocs gg ad Isttut of lctocs Natoal Chao Tug Uvsty Hschu Tawa Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
2 Outl Itoducto. Why do w sulat th optcs of systs of scoducto ao-objcts? Scoductos th ao-scal. Scoducto ao-objcts Mtaatals ad scoducto ao-objcts Quatu foato ad scoducto ao-objcts Sulato statgy Scoducto ao-objcts. Idvdual ad collctv sposs Mult-Scal Hybd Appoach Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos ffctv Haltoa ad daagtc spos Mappg thod Optcal spos fo systs of scoducto ao-objcts Ba ad dssd polazablty of scoducto ao-objcts lctoagtc tacto btw scoducto ao-objcts Mast quato Ipltato of th statgy Gal flow daga of th appoach pltato Lays of bddd quatu gs Lays of bddd quatu dot olculs. Magto-llpsoty Th dsoal aays of scoducto ao-objcts Coclusv Ras Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
3 Itoducto Moo's Law: Th ub of tasstos o a chp doubls about vy two yas wda.og A hoto/aul Saua Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
4 Itoducto Th ao - scal s a qualtatvly w scal wh atals popts dpd o sz ad shap as wll as coposto ad dff sgfcatly fo th sa popts th bul Nao-scc ss to udstad ths w popts. Nao-tchology ss to dvlop systs ad stuctus that xhbt ovl popts ad fuctos du to th ao-scal sz Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 4
5 Itoducto Nao-aadg: NANO MANS QUANTUM tyg to fd a coput sulato of physcs ss to to b a xcllt poga to follow out ad I ot happy wth all th aalyss that go wth just th classcal thoy bcaus NATUR ISN T CLASSICAL dat ad f you wat to a a sulato of atu you d btt MAK IT QUANTUM MCHANICAL ad golly t s a wodful pobl bcaus t dos t loo so asy. Rchad Fya Itatoal Joual of Thotcal hyscs Vol. p Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 5
6 Itoducto Scoductos th ao-scal. Scoducto ao-objcts Rlvat lgths scal - Ma f path th quatu Hall g - Ma f path hgh oblty scoductos at T< 4 K - - d Bogl wavlgth scoductos. - d Bogl wavlgth tals dstac btw atos Coft of th lcto oto at last o spatal dso affcts th gy lvls ad th dsty of stats Dt Bbg. Scoducto Naostuctus. Spg 8 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 6
7 Itoducto Scoductos th ao-scal. Scoducto ao-objcts Th-dsoal STM ag of a ucovd IAs quatu dot gow o GaAs. STM ctu Gally lcto Spctoscopy Goup Ftz-Hab-Isttut Bl Atoc soluto STM ag of a stac of slf assbld quatu dots 5x5.. M. Koaad t al. hysca 7 56 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 7
8 Itoducto Scoductos th ao-scal. Scoducto ao-objcts Advacs th fabcato of scoducto ao-stuctus hav allowd us to costuct ao-scal systs wth a wd ag of gots ~5 Slf assbld latal IAs/GaAs Quatu Dot Molcul G. Mũoz-Matutao t al. RB Slf assbld IAs/GaS Quatu Rgs J.M. Gasa at al. 997 Slf assbld vtcal Quatu Dot Molcul M. Bay t al. Scc 9 45 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 8
9 Itoducto Mtaatals ad scoducto ao-objcts Atos Bul Mtaatal ad fo bddd SNOs Bul covtoal atal SNO Quatu wll Quatu w Quatu Dots Quatu Dot Molculs Quatu Dot osts Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa Quatu Rgs tc. Doubl Quatu Rgs 9
10 Itoducto Mtaatals ad scoducto ao-objcts ffctv Mda Dscpto aft V. Vslago966 ablty I A R I A R Mtals < > = No Tassso I A R Covtoal > > = + I A T R ttvty T NRIM < < = - Fts > < = No Tassso Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
11 Itoducto Mtaatals ad scoducto ao-objcts Ngatv factg th Sll s low: Wh < aft V. Vslago 968- ad J.B. dy : hyscs Covtoal Appoxato xact Sll s law Doppl ffct Chov ffct s s s s f ad Fsl Foulas z s cos cos cos cos s z z cos z cos z cos cos O could a w typs of tassso ls flts ad coupls tc. Ad - tly w possblts thos w ca t cogz today Rflcto coffct fo oal cdc o a tfac No flcto codto Bwst law cos ta cos z z z z z z z cos z z ta z cos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
12 Th sufac plaso soac at th sufac fo lctc ad agtc copots lads to a aplfcato of th vasct wavs: ; ; a taatal tfac c c c c y x y x z y x y x z z z Th wavlgth stcto o soluto fo wavs J. B. dy RL a atal - a a taatal - a Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa Itoducto Mtaatals ad scoducto ao-objcts
13 Itoducto Mtaatals ad scoducto ao-objcts fct Ls J. dy Souc NRIM = =- Iag a << Lght Cloa J.B. dy Cotpoay hyscs : J.B.dy D. Schug ad D. R. Sth Scc Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa NRIM Objct
14 Itoducto Mtaatals ad scoducto ao-objcts Most popula ad dct way s to aag a du whch xhbt th lctc Dud ad agtc Lotz dspso latos p ; pm pm I I M R R Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 4
15 Itoducto Mtaatals ad scoducto ao-objcts Fst pltatos Sth D. R. t al. hys. Rv. Ltt R. A. Shlby Scc 9 77 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 5
16 Itoducto Mtaatals ad scoducto ao-objcts Uaxal Mtaatal bult fo IAs/GaAs ao-gs. Ut cll dso: al <<. s-polazd lght / ; 5 5 xx ε yy ; zz xx μ yy ; zz ffctv pttvty ad pablty of th syst. Ral pats of xx ad xx O. Vosoboyov t al. Mcolctocs Joual xx xx yy yy zz zz M M Hz Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 6
17 Itoducto Mtaatals ad scoducto ao-objcts D photoc-taatal stuctus C. M. Sououls ad M. Wg Natu photocs 5 5 Doubl-fsht wth sval lays Mtaatal fabcatd though stacd lctoba lthogaphy Mtaatal ad usg dct-las wtg ad lctoplatg Hypbolc taatalad by lctoplatg hxagoal-hol-aay tplats Mtal dlctc layd taatal Mtaatal fabcatd usg ba pojcto lthogaphy Vsbl gatv-dx taatal basd o a coaxal dsg Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa Mtaatal stuctu aabl to dct las wtg Mtaatal ad usg lag-aa slfassbly All-dlctc gatvdx taatal coposd of two sts of hgh-factv-dx dlctc sphs aagd o a splcubc lattc 7
18 8 zz yy xx zz yy xx ; ε Th Maxwll wav quato fo th lctc fld -copot xp [t-] o-sotopc da Fsl s quato fo th oal ods ε c y z zz y z x z z y z x xx x y z x y x z y xx c c c Uaxal Mda: Hypbolc taatals. Idft dx taatals Itoducto Mtaatals ad scoducto ao-objcts Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
19 Itoducto Mtaatals ad scoducto ao-objcts Fsl s quato fo th oal ods x zz y z xx c xx c oday od OM xx c xtaoday od OM x zz y z xx c xx zz xx zz llpsodal Hypbolc Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 9
20 Itoducto Mtaatals ad scoducto ao-objcts Th optcal so-fqucy sufacs = fo xtaoday ods: z z z x y x y x y llpsodal Mtaatal: xx zz > Typ Hypbolc Mtatatal zz < ; xx > Typ Hypbolc Mtatatal zz > ; xx < Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
21 Itoducto Mtaatals ad scoducto ao-objcts hotoc dsty of stats DOS d dv z d d z d z y x llpsodal Mtaatal x y x y dv c xx zz d Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa Hypbolc Mtatatal :Optcal Topologcal Tasto dv ax ~ ax d DOS
22 Itoducto. Mtaatals ad scoducto ao-objcts Hypbolc taatals o of th ost uusual classs of lctoagtc taatals. Thy dsplay hypbolc o dft dspso whch ogats fo o of th pcpal copots of th lctc o agtc ffctv tso havg th oppost sg to th oth two pcpal copots. Such asotopc stuctud atals xhbt dstctv popts cludg stog hact of spotaous sso dvgg dsty of stats gatv facto ad hacd suplsg ffcts. A. odduby I. Iosh. Blov ad Y. Kvsha Natu photocs Sup dcay volvg hgh- stats of quatu tts wh placd o a typ HMM substat: x d x c 8 a N. S. Hash t al. Scc 6 5 a xx zz d c x y ; d Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
23 Itoducto Mtaatals ad scoducto ao-objcts p xx xx I z z p x z z ; c xx xx zz zz N. S. Hash t al. Scc 6 5 xx Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
24 Itoducto Mtaatals ad scoducto ao-objcts xx zz Mtaatal stuctu cosstg of altatg lays of slv 9 ad ttau doxd TO cospodg to a 9% fll facto of slv Th tasto fo llptcal to hypbolc dspso occus at 6 N. S. Hash t al. Scc 6 5 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 4
25 Itoducto Mtaatals ad scoducto ao-objcts T-solvd photoluscc data fo QDs dpostd o th taatal cotol sapl ad glass substat at 65 6 ad 65 Lft of th QDs as a fucto of wavlgth o taatal cotol sapl ad glass substat N. S. Hash t al. Scc 6 5 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 5
26 - Qubts: -lvl quatu systs - Quatu as: Supposto: taglt Bll's bass: - Qubts a xtly dlcat ;. 6 Itoducto Quatu foato ad scoducto ao-objcts Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
27 σ S ; ; z y x s xp cos - lcto sp s a atual qubt 7 Bloch Sph Itoducto Quatu foato ad scoducto ao-objcts Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
28 Itoducto. Quatu foato ad scoducto ao-objcts - Iso-sp s a atual qubt: Doubl Dot syst Quatu Dot Molcul UD U LD L Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 8
29 9 V dv S y x B l D B C B B z y x B Sgl Quatu Dot Itoducto Quatu foato ad scoducto ao-objcts Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
30 Itoducto. Quatu foato ad scoducto ao-objcts Vtcal Quatu Dot Molcul Sytcal Asytcal B Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
31 Itoducto Quatu foato ad scoducto ao-objcts Vtcal IAs/GaAs Quatu Dot Molcul L = 5 U = 9.5 h L = h U = 4 d = O. Vosoboyov RB 78 8 Two lowst lctoc stats l s Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
32 s l s l f N s l s l s l f B M B M Magtzato agtc ot of th syst wh Magtc suscptblty Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa Itoducto Quatu foato ad scoducto ao-objcts
33 Itoducto Quatu foato ad scoducto ao-objcts Daagtc Qubt Vtcal Quatu Dot Molcul O. Vosoboyov ad C. M. J. Wjs JCTN 7 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
34 4 Quatu Gat cotol Vtcal Quatu Dot Molcul z y x Z Y X Ĥ Η Η X X Itoducto Quatu foato ad scoducto ao-objcts Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
35 Itoducto Quatu foato ad scoducto ao-objcts Th potac of scalablty: Factog of a 4-bt tg ub a asoabl t w d 8 9 physcal qubts Massvly paalll opato ca b achvd by a optcal dsg Quatu dots a plaa optcal cocavty fo th bass of th QuDOS hadwa platfo N. Cody Jos RX 7 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 5
36 Sulato statgy Scoducto ao-objcts. Idvdual ad collctv sposs Statc Idvdual Rspos: polazato la appoxato d SNO d α B SNO α B B Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 6
37 Absopto sso Sulato statgy Scoducto ao-objcts. Idvdual ad collctv sposs Dyac Idvdual Rspos: lght absopto - sso out xctos LD Lass lastc scattg No-pola hotoc Cystals Dyac polazato Actv Mataatals Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 7
38 Sulato statgy Scoducto ao-objcts. Idvdual ad collctv sposs Collctv lctoagtc Rspos I R p s = ta T llpsoty : ost sstv la optcal tchqu Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 8
39 Sulato statgy Mult-Scal Hybd Appoach ASY ffctv Mda Mthod Bud cotuous Lays NOT SO ASY MS Hybd Mthod Bud Lays of SNOs a Taspat Matx Cotus Mda Dsct SNO Cotus Mdu Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 9
40 Sulato statgy Mult-Scal Hybd Appoach To buld up fo th botto fo >> a > d systs Nao Scal Dsct Maco Scal Hybd Maco Scal Cotus Quatu Mchacs of SNO: lcto s gy vlop Fuctos F olazablty of SNO: Dyac α ad Statc α S Itacto quatos: Lays of Dsct Dpols of Stgth d bddd to Cotus Dlctc Matx Rot Flds: R. Optcs Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 4
41 Quatu thoy of D scoducto ao-objcts Mdu ffctv xta pottal V xta SNO Π V cystal g σb Π σv V = Π A B 4 c B A B cystal xta - Boh agto ; Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 4
42 Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos H p p p thod th bul 4 c V p σ V cystal = cystal ; Bloch typ soluto Ψ = xp u Bloch typ p Schödg quato H H u = u H π π 4 c σ V cystal ; Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 4
43 Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Th fst Bllou zo fo a FCC ad zc bld stuctu lctos Hols Bad Stuctu bul GaAs Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 4
44 44 No-dgat ptubato thoy to th p quato fo a solatd bad a = ; u u : u u u u ' ' ' π π Zcbld ad daod cystals = ad o sp-obt tacto: Oly two bads c ad v lctoc ffctv ass : j j j j j j p p ; ; v c g v c p j g p j u p u Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
45 Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Oly two bads c ad v Lght hol ffctv ass : lh j p g j p ~ V g ~ 5 V lh Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 45
46 Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Th stadad stat odg fo zcbld ad daod g g Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 46
47 Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Mo accuat dscpto o bad paats to b cludd: u C u u Obtal j j Syty u /;+/ S u /;-/ S u /;+/ X Y - g g u 4 /; +/ Z X Y - g u 5 /;-/ Z X Y - g u 6 /;-/ X Y - g u 7 /;/ - g - Z u 8 /; -/ Z X Y - g X Y Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 47
48 48 g z g z g g z g z g z z z C C C H No zo atx lts: x y Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
49 49 Ka s soluto: ffctv asss fo th solutos xpaso a = : ; g g g g g SO g lh hh g g 4 4 Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
50 Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Bac to -hoogous stuctus ad flds Mdu ffctv xta pottal V xta SNO Π V cystal g σb Π σv V = Π A B 4 c B A cystal xta ; Most coo choc - vlop fucto appoxato to pst wav fuctos ts of th Bloch fuctos u = F u Ψ Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 5
51 5 bul bul a V H H vlop fucto quato th bul a F u F a u xp xp vlop fucto appoxato Ad Lt a vcty of = So: bul a u H xp b bul F u F b u b a u H xp F u F V u Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
52 Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos vlop fucto quato fo lctos a solatd bad b b b * * V F F Mo gal j=xyz j j j V F F V F F Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 5
53 T 8p p p 8 8 F... F F F;F F H cof a S K 8 8 V H H H H H S R S Q U V Q S R S V U S Q Q S R V U R S S Q R V S R R Q S V Q S R S Q U V U V V V U V U U V V A A H * * * * * * * * * * * * * * * * K Ktc pat aul pat Sta pat = =c v y x z y x z y x y x z y x z y x v z y x c A D D D V D U D D D S D D D D R D D D Q D D D D D D 6 A C. yo RB ; plus agtc fld zo pat 5 ght-bad appoxato Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
54 s s q u v q s s v u s q q p s v u s s q p v s q p s v q s s q p u v u v v v u v u u v v v * v * * * * * * * * * * * * * c * * c S a a a a H σ J σ H BB. 4 4 ; sp fo atx sp sp fo atx sp J σ j j j j zz yy xx y x z yz xz xy yy xx yy xx zz w w w D v D u d s d b b q p 6 a v Dvatvs of th local dsplacts statg fo th tfacs th tfac at d d d d yz xz xy xyxy zz xx zz xx yy xx xxyy zz yy xx xxxx a a a a a a wth C C C d F ; δf ; : zo - fld V p z y x 4 xy zx yz 54 ght-bad appoxato. Sta zo ad aul Quatu thoy of D scoducto ao-objcts K thod ad vlop fuctos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
55 If w focus o th cas of th lctos hols w ca obta a ffctv Haltoa fo o copot vlop fucto Mult-bad Schödg quato ojcto oto lcto hol subspac Fouldy-Wouthuys tasfoato ffctv Haltoa fo lctoc vlop fucto wth sp-obt tacto W H H W V H H Ψ Ψ Ψ Ψ h h h h V H H. Ĥ Ĥ A B A Π Π Π σ B σ Π Π g V V V BIA B pzo sta cof d Aada Slva t al. 997 Schäps t al. 998 Vosoboyov t al. s s Π σ Π Π σ Π Sp dpdt bouday codtos 55 Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
56 aats of th thoy fo lctos. g sta cof g sta cof g sta cof g sta cof g sta cof V V g V V V V V V V V 56 Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
57 Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos ffctv Haltoa fo lctoc vlop fucto two bad sp splt Ka Haltoa L. M. Thu ad O. Vosoboyov RB Π A Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 57
58 58 ffctv Haltoa fo hol vlop fuctos fou-bad Luttg-Koh Haltoa { } - st of th Luttg paats * * * * I H h h V R S R S S R S R. hz h h hz h S R hy hx h hy hx h h A Π Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
59 Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos lctoc stats two copot spo vlop fucto F F F S S Ĥ F F F F Hol stats fou copot spo vlop fucto Chalty: = Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 59
60 Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos xctoc ffcts xctoc Haltoa Th G s fucto of th osso quato xctoc vlop wav fucto xctoc tasto gs Coffcts xctoc pstato dt G h g h g x j Gj a j j x [ G ] h a [ h h ] x j j Wh: G j J z J ' z F [ l V F J z ; J ' h; h' ' l' z ' V ] J z ; J ' h; h' F z J h ' z d F J ' h' z ' *COMSOL Multphyscs FM solvs Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 6
61 6 z B B Magtc fld dpdt ts th Haltoa: B y x B g S S L L B S L ; ; 8 H Magtc fld as a ptubato lads to: y x B g g B B 8 ' ' ' S L B S L B paaagtc daagtc O: j j B V V g q q S B A p A p H Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
62 Gaug-og dpdt dfto: Π Π H h h h h h V A Π h h q B A B A * d h h h Gaug-og dpdt daagtc coffct B z: 8 B h h h h ρ ρ y x ρ B A 6 Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
63 Quatu thoy of D scoducto ao-objcts ffctv Haltoa ad daagtc spos Quatu Dot Atfcal ato Idal so-scal g O-dsoal loop >5 yas of th Ahaoov-Boh ffct Quatu Rg B B B B l C B Dl B l ; l B l F S B Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa h Sgatu of th AB ffct ~ S B h ;
64 Quatu thoy of D scoducto ao-objcts Mappg thod Flow daga of th appg pocdu Fo a ao-objct of coplx goty paats to ap V ; g ; ; ; ; C j;l 4 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 64
65 Quatu thoy of D scoducto ao-objcts Mappg thod hoto sso lcto Mcoscopy M Coss-sctoal tassso lcto coscopy XTM Atoc Foc Mcoscopy AFM Klv ob Foc Mcoscopy KFM Coss-sctoal scag tul Mcoscopy XSTM xapl: IAs/GaAs ao-g XSTM. Offas t al. AL Nao objct s goty pofl h x y ffctv lctoc hol s coft pottal x hxy y Vff [ x y z h x y] V ax outsd Vff V sd V V lctoc C ax bad offst Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 65
66 66 Cappd wobbld IxGa x As/GaAs x slf-assbld quatu g. xapl of th hght pofl - hxy. ; R y x R y x h y x y x h h y x h R y x R y x R y x R R h y x y x h h y x h M M Quatu thoy of D scoducto ao-objcts Mappg thod Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
67 osto dpdt coductg bad offst: 4 Δ a y x h z T a z s T V h h Tx = tahx h = hout h 67 Utlss appg fucto V M Mappd paats... ; ; ; ; ; ; M M M M M M V M V M M M M M M M V out out out g out g h out out out g g g aats of th thoy... ; ; ; ; ; ; h h h g g V Quatu thoy of D scoducto ao-objcts Mappg thod Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
68 Quatu thoy of D scoducto ao-objcts Mappg thod Stad IAs sd gias =.84 V Δ IAs =.9 V IAs =.44 ₀ hias =.74 g hias =. ad IAs = 5. GaAs atx outsd ggaas =.5 V Δ GaAs =.4 V GaAs =.67 ₀ hgaas =.5 g hgaas =.6 ad = GaAs =. ojctos of th lcto V ad hol V h coft pottals o th xrz pla wth th actual gy gap btw O. Vosoboyov t al. RB Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 68
69 Quatu thoy of D scoducto ao-objcts Mappg thod C. Ka t al. AL V V x z Vtcal IAs/GaAs Quatu Dot Molcul ojctos of th lcto V coft pottals o th xz pla Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 69
70 Optcal spos fo systs of scoducto ao-objcts Ba ad dssd polazablty of scoducto ao-objcts Mda d SNO Icog lght ba: Th dpol stgth Dsct Dpol Appoxato d V SNO d th la thoy fo th spos fuctos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 7
71 Optcal spos fo systs of scoducto ao-objcts Ba ad dssd polazablty of scoducto ao-objcts α Dsct Dpol Appoxato >> a > d fo SNOs Vosoboyov t al. RB 5-9 olazablty Tso B ω Statc pat = α Mda SNO S B + α D Dyac pat ω Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa d Dpol stgth Bul optcal atx lt Ba xcss bddd polazablty B f d α B A Appld lctc fld vlop fucto Ovlap tgal * T x h h x Fqucy dpdt facto f x 7
72 Optcal spos fo systs of scoducto ao-objcts Ba ad dssd polazablty of scoducto ao-objcts d α B A Actual Local fld Spatal avag SNO calculatd th thoy d α D L xtal ot fld asud xpts Ba polazablty A = L + td bdd Dssd polazablty Local fld x th cas of a sgl SNO lctoagtc tasf tso dpolazato Accodg to th dftos: α α B D t Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 7
73 Optcal spos fo systs of scoducto ao-objcts lctoagtc tacto btw scoducto ao-objcts Syst of bddd SNOs th la DDA Th local fld at th posto of th th dpol = fjd j L X + Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 7
74 Optcal spos fo systs of scoducto ao-objcts lctoagtc tacto btw scoducto ao-objcts d D ε so ε T j ε j f j G xp Δ Itcllula tasf tso Dyadc G Fucto Δ T j T I I j j j j 4 Δ j Δ j j j ; j ; j c I a statc ag: >>a > >d I fa wav ag >> >>a >d I T xp Δ G j T j j G I j ; 4 Δ 4 Δ T j j j Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 74
75 Optcal spos fo systs of scoducto ao-objcts lctoagtc tacto btw scoducto ao-objcts. Mast quato Th syst s Mast quato T R R T G T X T G T d R Th syst s collctv spos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa d d j t T wh T j t Dj j d O Xj j f j d f t s j 6 c Xj j t α B j I Bj α D Dso: N Lotz adato dapg 75
76 Optcal spos fo systs of scoducto ao-objcts lctoagtc tacto btw scoducto ao-objcts. Mast quato Rflcto ad tassso R = F d wh z T = F d wh z X T Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 76
77 Optcal spos fo systs of scoducto ao-objcts lctoagtc tacto btw scoducto ao-objcts. Mast quato Fo a sgl bddd SNO solv: Spatal avag calculatd SNO Fo th bouday codtos Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 77
78 Optcal spos fo systs of scoducto ao-objcts lctoagtc tacto btw scoducto ao-objcts. Mast quato Two-dsoal squa lattc a lay of SNOs of th lattc paat a L : th Vlg s soluto J. Vlg hysca th Vlg s ot tplaa tasf tso z z Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 78
79 Optcal spos fo systs of scoducto ao-objcts lctoagtc tacto btw scoducto ao-objcts. Mast quato Th flcto sp ad tassso t sp coffcts flctac R sp tasttac T sp ad absobac A sp of th lay R A s p s p s p ; R T T s p s p p s = ta Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 79
80 Ipltato of th statgy Gal flow daga of th appoach pltato Scal of a Idvdual Nao-Objct Scal of Maco-Systs of Nao-Objcts Laplac quato Statc xcss olazablts S α S D α B Slf Itacto Tso S t Shödg quato H h F h h F h Tasto gs ad Ovlap Itgals x Ψ Ψ Φ l h l Ovall bddd Ba olazablty α S B Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa Mult-Dpol Itacto quato Mast quato C R T abs j T j d G j G Optcs :.g. Fsl's X Absopto 4 d l * l coffcts coss d } d N l d scto Id d l X α Dl * 8 d * l
81 Ipltato of th statgy Lays of bddd quatu gs Tasto gs of th IAs/GaAs dots ad gs R = O. Vosoboyov t al. RB ; C. M. J. Wjs t al. RB ; pssc 78 6 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 8
82 Ipltato of th statgy Lays of bddd quatu gs llpsoty fo =6 ad = 5 V o bddd a L =8 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 8
83 Ipltato of th statgy Lays of bddd quatu gs llpsoty fo =6 = 5 V ad a L = 8 ; Dashd- o bddd Sold -bddd Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 8
84 Ipltato of th statgy Lays of bddd quatu dot olculs. Magto-llpsoty Ka t al. AL p lays of IAs QD's flctos ŝ ΔR 6 5 xpt ΔR Th Mthod Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 84
85 Ipltato of th statgy Lays of bddd quatu dot olculs. Magto-llpsoty B B Lag Dot lctoc bad Sall Dot Hol bad B B B C B B Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 85
86 Ipltato of th statgy Lays of bddd quatu dot olculs. Magto-llpsoty Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa L. M. Thu ad O. Vosoboyov RB ; hysca
87 Ipltato of th statgy Lays of bddd quatu dot olculs. Magto-llpsoty B * T x h h f Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 87
88 Ipltato of th statgy Lays of bddd quatu dot olculs. Magto-llpsoty Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 88
89 8 - dg 8 - dg dg dg Ipltato of th statgy Lays of bddd quatu dot olculs. Magto-llpsoty Icdc of = 6º = V ttdot dstac - ; N = c - B z Bz Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 89
90 Ipltato of th statgy Lays of bddd quatu dot olculs. Magto-llpsoty Icdc of = 6º = V ttdot dstac - ; N = c - B z Bz Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 9
91 Ipltato of th statgy Lays of bddd quatu dot olculs. Magto-llpsoty Icdc of = 6º ttdot dstac - ; N = c - Ap BT V BT V = V = 5 V Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 9
92 Ipltato of th statgy Th dsoal aays of scoducto ao-objcts Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
93 Ipltato of th statgy Th dsoal aays of scoducto ao-objcts opagato Matx Appoach Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa ad tatvly apply to + lays 9
94 Ipltato of th statgy Th dsoal aays of scoducto ao-objcts Rflctac of quatu dot ultlayd stuctus ad 5 lays as fucto o th optcal tasto gy ad agl of cdc d dstac btw lays L. M. Thu ad O. Vosoboyov JCS 45 7 Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa
95 Ipltato of th statgy Th dsoal aays of scoducto ao-objcts Scal of a Idvdual Nao-Objct Scal of Maco-Systs of Nao-Objcts Laplac quato Shödg quato H F h h h F h ffctv Clausus-Mossott suscptblty I D Statc xcss Tasto gs ad olazablts Ovlap Itgals S l Fh F α S l D α ffctv pttvty B χ QDM N α N α D Slf Itacto Tso S t Ovall bddd Ba olazablty α S B ε I χ QDM Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa L. M. Thu ad O. Vosoboyov AI Cof. oc
96 R xx / I xx / Ipltato of th statgy Th dsoal aays of scoducto ao-objcts Itdot dstac - ; N =.6 6 c - ; B z xx yy zz Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 96
97 R xx / I xx / Ipltato of th statgy Th dsoal aays of scoducto ao-objcts Itdot dstac - ; N =.6 6 c - ; B z Itatoal Woshop o Modlg ad Sulato of Scoducto Naostuctus ad gy Nao-Dvcs 4/7/5 Tohou Uvsty Sda Japa 97
98 Coclusv Ras Mult-scal hybd thod s a w labl ad posg appoach to sulatos of optcal popts of scoducto ao-stuctud taatals Th thod cobs dsct ad cotuu dscptos th ao ad aco scals Th thod allows us to oto coht apulatos of lctoc quatu stats scoducto ao-objcts by th covtoal optcal tchqus Ou calculato sults claly suggst asuabl valus fo chags of th ffctv pttvty of D aays of SNOs. 98
99 Tha You! 99
Today s topics. How did we solve the H atom problem? CMF Office Hours
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Ch. 22: Classical Theory of Harmonic Crystal
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D. Bertsekas and R. Gallager, "Data networks." Q: What are the labels for the x-axis and y-axis of Fig. 4.2?
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Aotomorphic Functions And Fermat s Last Theorem(4)
otomorphc Fuctos d Frmat s Last Thorm(4) Chu-Xua Jag P. O. Box 94 Bg 00854 P. R. Cha agchuxua@sohu.com bsract 67 Frmat wrot: It s mpossbl to sparat a cub to two cubs or a bquadrat to two bquadrats or gral