Estudo de reconstrução (2x6) em GaSb (001)
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(27) ¯±Ë. v|YhyPSZìe~_¼XNcR_ stZWPZ ZìPSNQxc_hV lmnPmyq}rg_7eaà øìNcbúù#Z ë L¯ûÃfhf [aý ÜxQ_hVlonPSy {UX_¾ZìstZWPonYUPX_ b_¼XNcR_ XN ë YNhNQP#û ~_¼XNQRU_c ý ÜN@ÿ¹yN#_hL´NcXNQxcN@_b¾_¼XNcR_4XN@xc_hVnZhNcböXN@NcRUõnPm_hVl â kYUlmnZìXN-n_hs´_ â. v|YhyPSZ5o ~_¼XNcR_ stZWPZ ZìPSNQxc_hV lmnPmyq}rg_7eaà øìNcbúù#Z ë L¯ûÃfhf [aý ÜxQ_hVlonPSy {UX_¾ZìstZWPonYUPX_ b_¼XNcR_ XN ë YUNWNcP xQ_hböxcZWPSQVxcYUZ X N-X_hYUlNcRUõnPm_hVl VtZìxcõQRUyRUZìeaà øû ~_¼XNQRU_. ý ÜtZ4ÿ¹ytZWR3NQlmn X NcRUYbYnpZWXZ s´NcRUZWl RUYVétZWl s´_hVnYRUétZgXtZWlcܼ`¼YUlmnZìXN-n_hs´_ â.
(28) ¯Ì. : Í. = ñ !4ð>ó %. ñ. ó. òÎ1!$=-ðÂ:ð®!$#&Ï ´. =Á' ô. ñ. j NQlSXN@_ lSy PhYbNQV¹nS_4XtZìb¾Ncx}TgVYUxcZJÿ¹ytTWVnYx}Z4`WPSYUZWlnSNcVnpZgnSY`gZWlnSNcb lSYUX _ Ý NcYnZWl V_ YV¹nSyYnS_ k XNXNQlSxcPmNQ`WNcPêlSYlmnSNcbZWl:bJyRnSYUNcRNQnSPhVYxc_hlQÜ]NcVnPmNQnZWVn_¢lm_hRUyq NQl|ZgVtZWRU{nYx}ZWlXtZMNcÿ¹ytZWqcrW_kX N ë xpéPÐg XYV hNQP-lS÷lrW_sO_WlSlS{`hNQYUl@stZWPSZlmYUlonNcbZWl@b4yYn_lmYUb¾sRUNQl-N¾lm_hRUy q ¼Ncl@V¹ybõQPSYx}ZWl@Nà ZgnZWl@sO_¼XNQb lmNcPNcVxQ_hVnPSZWXtZWlZWs´NcVtZglsZWPZ-yb s´Ncÿ¹yNQV_JlV ¤b¾NcPm_@X« N gn_hb¾_hlêN b¾_hRUõQxcyRUZWl â á:_WPYlSlm_#X NclSX N_ VtZglSxcYbNQVn_#XtZ#b¾NcxcTWVYx}Z-ÿ¹ytTWVnYx}ZJZËnõÕé_ËåmNZ#L ylSxcZ2s´_hPNclSÿ¹yNQbdZglÿ¹yNsONQPSb¾YnpZgb NcV xc_hVnPSZWP PmNclSy RnpZgX_hl NÌàZËn_hl nSNcböb¾_WnSY`gZWX_2_ìlSyP hYUb¾NcVn_ìX Nk` WPSYUZWlnNQ_hPSYUZWlN@ZgsPS_}àYUbZWq ¼Nclÿ¹yN-`YlSNQb Ý ZWxQYURYnpZgPJNclonpZHL ylSxcZ â KbZ X NclmnZWldõ0Z*ZgsPS_}àYUbZWq}rg_*XN~ß_hPmV ss´NcYVéNQYUb¾NcP N ÿ¼y N~`hNQb XNQlSxQPSYnZìlSN WyYUP â y nSPZWl ZgsPS_}àYUbZWq¼NclstZWPSZìZ4PSNclm_hRUy q}rW_4XZ4Ncÿ¹ytZWqcrW_ XN ë xpéPÐX YUVhNQP stZWPSZ4lSYlmnNQbdZgl b4yR nSYUNcRNQnSP0hVYxc_hl NQlmnpTg_XNQlSxQPSYnS_hlÕV_ YnSNcbúe â e4N@V_hlÕx}Zgs{nSyRU_hloÜi N â ÑcÒÓ. Ô. Õ¼Ö8×[Ø«ÙwÚ Û. ÕqÜ0ݼØ. ÞßáàÃØ¼×ãâzä1åæÖ8Ößâ*çßJÚ Û. ß0×. í XNQlSxQPSYUqcrW_X_NclmnZWX_ Ý yVXtZgbNQV¹nZWR¢XN<yb tX ZWX_lSYlmnSNcbZ Ý {lSYxc_lSNåSZNQRUNb¾_hRUõQxcyRUZWlcÜ gnS_hb¾_hl_hylm÷hRUYX_hl lmN-X Z sZWPmnSYUPXZ NQÿ¹ytZWq}rg_XN ë xpé PмXYUV2hNcP YVXNcs´NcV XNcVnN@X_ìnSNcb¾sO_ìstZgPZ {_hVl N@NcRõQnPm_hVl xQ_hb_¾ZWs PSNclmNcVnpZgXtZZgLtZWYà_ â û e â [aý. ˆ r, R) ~ = (Tˆe + Tˆi + Vˆe−e + Vˆe−i + Vˆi−i )Ψ(~r, R) ~ = EΨ(~r, R) ~ HΨ(~. ^ ZNQÿ¼yZWq}rW_~ZWxQYUbZ Ü ˆ õ¾__hs´NcPSZWX_hP-éZWbYRnS_hVY ZgV_dX_lSYlmnSNcbZ Ü ~ õ¾Z Ý y Vq}rW_XN H Ψ(~r, R) _hV XtZdn_WnZWR|X _lmYUlonNcbZ7NcV`W_hR`WNcVX_~YUV Ý _WPSbZWq¼NclMnpZWVn_X _hl-NcRõQnPm_hVl-xQ_hb_X _hl-{U_hV l¢N ã õì_ ZWyn_]`gZWRU_hPXN@NcVNQP hYUZ X _¾lmYUlonNcbZ â lÕXNcbZWYlnNQPSb¾_hlÕlrW_ XNQlSxcPmYnS_hlMZ lmNhy YUPc P h ¯ ∇ Tˆe = i − 2mi ≡ 2. 2. P h ¯ ∇ Tˆi = j − 2mj ≡ 2. 2. _hs´NcPSZWX_hPÕNQVNcPhY Z4xQYUVõnYUxcZìX_hlÕNcRè NnPS_WVl _hs´NcPSZWX_hP NQVNcPhY ZìxQYUVõnYUxcZìX_hlÕ{U_hV l. P e2 Vˆe−e = 12 |~r−~ ≡ r 0|. _hs´NcPSZWX_hP NQVNcPhY Zìs´_WnNQVxcYUZWR3XN`YX_u YVnNcPSZWq}rg_¾NQRUõnPS_WV NQRUõnPS_WV −.
(29) ¯±é P Vˆe−i = − j. Zj e2 ~j| |~ri −R. P Vˆi−i = − 21 j6=i. ≡. e2 Zj Zi ~ i −R ~j| |R. _hsONQPZWX _hP NcVNQPhYUZìsO_WnSNcVxQY ZWR·XNQ`¼YUX _duìYUVnSNcPZgq}rW_ NcRõQnSPS_hV {U_WV −. ≡. _hs´NcPSZWX_hP NQVNcPhY Zìs´_WnNQVxcYUZWR3XN`¼YUX_¾u YUVnNQPZWqcrW_ {U_hV {U_WV −. ªá _hPSõQb~Ü ZJlS_hRyq}rg_4XNclonpZìNcÿ¹ytZgq}rW_ìXN¢ZWy n_]`gZWR_hPSNQlõ¢XNQbdZglSY ZgXtZWb¾NcVnNxc_hb¾sRUYx}ZWXZ Ü s´_hPmÿ¼y N NQR Z0xQ_hVnõcbzybêhPZWV XN7Vl¤b¾NcPS_X NstZWPmnS{UxQyR ZWl2YUVnNQPZWNcVnNQlcÜxc_hb bZWlSlSZWl4b4yYn_DX Y Ý NcPmNcVnN â ë y P hNNcVnrW_(Z<VNcxQNclmlSYUXZWXN0X N~ZgsPS_}àYUbZWq ¼Ncl ÿ¹yN Ý ZWxcYRUYnNcb lSyZ lm_hRUyqcrW_ â KMbdZ<sPSYbNQYUPSZ ZWs PS_}àYUbZWq}rW_~Ü·xQ_hVéNQxcYUXZ7xc_hb¾_ í s PS_}àYUbZWq}rW_XN ß_hPmV ss´NcV éNcYbNQPcÜ´xc_hVlmYUlonN4NQb xc_WVlSYX NQPZWPmb_hlÿ¼y N-_hl {U_hV l NclonprW_ìsPSZgnYx}ZWb¾NcVnSNkþ à_hl Ncb ybZ4xc_hV þ hyPZgq}rW_ stZWPonYxcyRUZWPcܼlS_hLZ ZWqcrW_ XNìy b x}Zgbs´_bõQXYU_dxcPSYUZWX_s´NcR_7b_]`¼YUb¾NcVnS_X_hl-NcRõQnSPS_hVl-ÿ¹yNìs´_hP-s´_hlSlmyYUPmNcb ybdZbdZWlmlZ b4y Yn_bNQV_hP X _-ÿ¼y NÕZ¢bdZWlmlZ¢X_Wl {U_hV lcÜWnSNcPrg_-ybdZk`WNcR_xQYUXtZWX Nb4yYn_¢bZWY_hP:NlSN PSNcZWPSPSZWVËåSZWPSrW_ ÿ¹ytZWlmN@ÿ¼y N#YVlmnZWVnpZWV N}ZWb¾NcVnN#Zìx}ZgXtZìxc_hV þ hyPZgq}rW_ Y WVYUxcZûÃZWsPm_}à YbdZgq}rW_ìZgXY ZWL gnYx}Z ý â jkNQlmnpZ Ý _hPmbdZÜ3Z Ý yVqcrW_XNì_hVXZNQRUNnP WVYUxcZdõìxc_hV lSYUX NcPZgXtZxc_hb¾_XNcs´NcV XNcVnN¾XtZ7xQ_hV þ hy PZWqcrW_X_hl {_hVlXNMybdZ Ý _hPmbdZ-b4yYn_#lSytZ}`WNWÜ NQVÿ¹ytZWVn_4Z Ý yV q}rW_2XN_WVXtZ2X _hl{_hVlVtrW_2XNQ`WNcP JXNcs´NcV XNcP XtZglêxc_¼_hPSXNQVtZWXtZglNQRUNnP WVYUxcZWlêN sO_¼XNÌlSN Ý ZWîQNcPêybZ-lSNQstZWPZgq}rW_@XN `gZWPSY }`hNcYlêVtZ Ý yVqcrW_@XNÕ_hVXtZ nS_WnpZWR·X_ lSYUlonNQbdZ Ü _¾ÿ¹yN#PSNQlSyRnpZWP ìNcb. ~ = λ(R)Φ(~ ~ ~ Ψ(~r, R) r , R). û e âe ý. VXN ~ PmNcsPmNclmNcVnpZZWlsO_hlmYUq NQlkX_hlk{U_hVlMN PmNcsPmNclSNQVnpZZWl R = (R~1 , ..., R~k ) ~r = (~ ri , ..., r~n ) s´_hlSYq¼NclìX_WlNQRUõQnSPS_hV l âí étZWb¾YURnS_hVYUZWVtZ~X _*lmYUlmnSNcbZsO_¼XNZh_hPSZDlSNQPXNQlSxQPSYnZ XZ lmNhyYVnN bZWVNQYUPZÜ ûÃe â o ý ˆ ˆ ˆ H = He + Hi. xQ_hb ˆ e = Tˆe + Vˆe−e + Vˆe−i H. ûÃe â i ý. N ˆ i = Tˆi + Vˆi−i H. ûÃe â hý. ^ZWl:NQÿ¹ytZWq¼Ncl|ZWxcYbdZ ˆ xcZWPSPmNZZWsONQVtZWl¯_hl¯nNQPSb¾_hl¯PSNcRUZgnY`h_hlªZW_WlªNQRUõnPS_WVlcÜgstZWPZÕybZ XtZWXtZ He xQ_hV þhy PZWqcrW_2V¹yxQRUNcZWPcܹNcV ÿ¼yZWVn_ ˆ xcZWPSPmNZ#ZWs´NcVtZWl_hlnNQPSb¾_hlêPSNQR ZgnSY`W_hlZW_hl{U_WVl â:í sRYUx}ZgVX_ Hi Ý â t V Z y. V } q W r ¾ _ X @ N h _ V t X ¾ Z e J e n Q N S P c N ¾ b _hl ˆ. He.
(30) ¯±ë. ˆ e [λ(R)Φ(~ ~ ~ = λ(R) ~ H ˆ e Φ(~r, R) ~ H r , R)]. û e âø ý. jk_¾lSN hyVX _¾nSNcPSb¾_ XNclonpZ Ncÿ¹ytZWqcrW_¾sO_¼XNcb¾_hl xpéN ZWPMZW_ lSN hyYV¹nSN@PSNclmyRnZWX_. ~ Tˆe + Vˆe−i + Vˆe−e ]Φ(~r, R) ~ = λ(R)ε ~ e (R)Φ(~ ~ ~ λ(R)[ r , R). _hV XN. εe. û e â jhý. xc_hPmPSNclmsO_WVXN2ZW_hlÕZWy nS_]`WZgRU_hPmNcl X_¾sPS_WLRUNQbdZ4NQRUNQnSPhV YUxc_ â. ÕNcs´NQnSYUVX_. _ sPm_xQNcXYbNQV¹nS_¾ZWxcYbdZ4stZgPZ. ˆi H. nSNcPmNcb¾_hl. ˆ i [λ(R)Φ(~ ~ ~ ∼ ~ H ˆ i λ(R) ~ H r , R)] = Φ(~r, R). û e â ý. ÿ¹yN#PSNQlSyRnpZWP4Ncb. _hV XN. εi. ~ Tˆi + Vˆi−i ]λ(R) ~ = Φ(~r, R)ε ~ i λ(R) ~ Φ(~r, R)[ xQ_hPSPmNclmsO_hV XNJZg_hlÕZWy nS_a`gZWR_hPSNQl Yh V YUxc_Wl â. û e â \ý. _hb¾_7s´_X Ncb¾_hlk_hL lSNcPo`gZWPcÜO_7nNcPmb_X_R ZgX_dXYPSNQYn_XtZdNQÿ¼yZWq}rW_ ûÃe â jhý V_Wl¢sONQPSb¾YnSN2xQ_hV éNQxcNQP-_~Zgy n_]`gZWRU_WPkXNìNQVNcPhY Z7NQRUNQnSPhV YUxc_dstZWPZybZdstZgPmn{xcyRUZdL´Ncb xQ_hb¾_Z Ý y Vq}rW_X Nì_hVXtZ NQRUNQnSP hV YUx}ZÜ´N2XNclonpZdbZWVNQYUPSZ¾n_¼XtZWlZWl_hLlSNQPm` }`hNQYUl¢X_dlSYUlonNQbdZ¾sO_¼XNcb lmNcP¢NQVxc_hVnSPZWXtZgl â áª_hP _hynPS_ìRUZWX_ ZìNcÿ¹ytZgq}rW_0û e â \ý V _hlÕsONQPSb¾YnNkxc_hVé NcxcNQPÕ_Zgy n_]`gZWRU_WP XN@NcVNQP hYUZ4Y hV YUxc_JLONQb xc_hb¾_ Z Ý yVq}rg_7XN4_hV XtZY hVYUxcZX_lSYlmnNQbdZ â¢ë NJlSyLlonYny{PSb¾_hlNQlmnZWl¢XytZglkNcÿ¹ytZgq ¼NclcÜêû e â jhý Nû e â \ý Ü VtZìNQÿ¼yZWq}rW_0û e â o ý Üxpé N ZWPSNQb_WlZg_¾lmN hy YUVnN@PSNQlSyRnpZWX _. ~ H ˆ i λ(R) ~ + λ(R) ~ H ˆ e Φ(~r, R)] ~ = ET λ(R)Φ(~ ~ ~ [Φ(~r, R) r , R). _hV XN _hb¾_ bZWVNQYUPZ. ET. ûÃe â [ f ý. xc_hPmPSNclmsO_WVXN#ZW_¾ZWy nS_a`gZWR_hP XN#NcV NcPWY ZJn_gnpZWR3X _lmYUlmnSNcbZ. ˆ e Φ(~r, R) ~ H. õYhytZWR. ~ ~ εe (R)Φ(~ r , R). ZNcÿ¹ytZWqcrW_DZWxQYUbZ7sO_¼XNìlmNcP#NclSxQPSYnpZXtZlmNhy YUVnN. ~ H ˆ i λ(R) ~ + λ(R)ε ~ e (R)Φ(~ ~ ~ = ET λ(R)Φ(~ ~ ~ [Φ(~r, R) r , R)] r , R). ûÃe â [h[aý.
(31) °/ì. ã RUYbYVtZWVX _ ~ NcbzZWb4L´_hl2_hl4R ZgX_hlJNdxc_hR_xcZWVX_ Φ(~r, R) ÿ¹yNQPSX_¾XtZìNcÿ¹ytZWqcrW_7ZgxcYUbZJNQVxc_hVnSPZË lSN@þtVtZWRbNQV¹nSN. ~ λ(R). Ncb NQ`¼YUX cVxQY ZDV_DRUZWX_DNQlo. ~ ~ = ET λ(R) ~ [Tˆi + Vˆi + εe (R)]λ( R). ûÃe â [ e ý. _hb¾_ks´_¼XNlmNcP:_hLlSNQPm`gZWX_ksONQR ZNQÿ¹ytZWq}rg_-ZWxcYbdZ ~ XNclmNcb¾sONQVétZ¢_stZWs´NcR¼XNyb s´_WnNQV εe (R) xQY ZWRb¾õcX YU_-stZWPSZ#_WlVl¤xQRUNQ_hlcܼNÕõÕnZWb4L´õcb xQ_hVéNQxcYX_2xQ_hb¾_#lmys´NcP Ý {xcYN XNÕNcVNQPhYUZ#s´_WnNQVxcYUZWR âªí hPSZWVXNåm_ ZWXtZìXtZ ZWsPm_}à YbdZgq}rW_ìXN#ß_WPSV ss´NcV éNcYbNQP õ#_ XNQlSX_WLPZWb¾NcVnS_XtZ Ncÿ¹ytZgq}rW_¾XN ZWyn_]`gZWRU_hPmNcl|nS_WnpZgRNcb y bdZ¢NQÿ¼yZWq}rW_#XNMZWy nS_]`WZgRU_hPmNcl NQRUNQnSP hV YUx}Z¢NÕybZ¢Ncÿ¹ytZgq}rW_#XNMZWy nS_a`gZWR_hPSNQl YhVYUxcZ~ZglSlSYb~ܪXNdZWxc_hPmX_DxQ_hb Z~VNQxcNclmlSYXtZWXNs´_X NlmNPmNclm_hR`WNcPìZWs´NcVZWlJybZ~X NcR Zgl7û _x WRxcyR_hl XN2NclonPSynyPSZ7NcRUNnP hVYUxcZ ý _hyZWl¢X ytZWl û NclmnSyX_hlkXN4b¾_hRUõQxcyRUZWl ý âkã lmnZ7ZWsPm_}à YbdZgq}rW_¾n_hPmV_hy lSN X+ N hPSZWVXN¾YUb¾sO_WPmnpTgVxcYUZdlSNåSZ~stZWPSZ0Zÿ¹y{Ub¾YUxcZ_WyHstZWPSZ~Z Ý {UlmYUxcZ ܯlSNcV X_Ds´_hPmnZWVn_ylZWXZ~xc_Wb hPSZWVXN-lmyxcNQlSlm_Zgnõ-_WlMX Y ZWl XN@é_aåmN â ÑcÒ Ñ. í£ßî3ßâcïØqð±ïÚÛ. ßâ.ñ9ØáÞ8ÕîóòbßJØ×[ÚÕîÊÕôzä2ÚâÚ±ñ9Ú Ø. Õ¼ØÎðØqâ8õØ¡ÞØqî. ÕqâØqî. ^ NclmnZ0lSNQq}rW_DZWsPSNQlSNQV¹nZWPSNQb_Wl4yb LPmNQ`hNdéYUlon÷hPmYUxc_X_DX NclSNQV`h_hR`YbNQVn_DXtZgl2nNQ_hPSYUZWl@y nY M RYUî}ZgXtZWl-NcbÔxWRUxQyRU_hl#ZWL¼YUV YnY_ZW_RU_hVW_~X_WlJZWV _hlcÜ ûüNcbÔyb xWRUxQyRU_~ZWL YUVYnY_7VtrW_~lSNdynYURYUîcZ XtZgX_hl-Nàs´NcPmYUb¾NcVnpZWYlcÜ3`gZWRNcVX_ËlSN4ZWsONQVtZWl@XN ZWR hybZWl-ZWs PS_}àYUbZWq¼NclknSõc_hPmYUxcZWl ý âJí sPSYbNQYUPSZ N4nZWb4L´õcb ybdZ7XZWl-bdZgYUlky lZWXtZgl2ZgsPS_}àYUbZWq ¼NclkstZWPZZ Ý y Vq}rW_XNì_WVXtZlSNìXN`hN¾8 Z pkZWPonPmNcN jN ÿ¹yNdV_0ZWV_~XN [}\ e lS y hNQPSYy(ÿ¹yN7Z Ý yVq}rg_0XN¾_hVXtZstZWPSZ~ybÔlSYlmnSNcbZb4y RnY NQRUNQnSP hV YUxc_ Ý _hlmlSN#NclmxcPSYnpZìxc_Wb_ yb s PS_¼Xy n_ XN Ý yV q ¼NclÕXN@stZWPon{UxQyR 5 Z ¤ VYUxcZ Ü. Ψ(r~1 , r~2 , ...r~n ). Ψ(r~1 , r~2 , ..) = Ψ1 (r~1 )Ψ2 (r~2 )...Ψn (r~n ). ûÃe â [ o ý. _hV XN x}ZWXZ@y bdZ¢XtZgl Ý yVq¼Ncl lZgnSYUl Ý ZgîcNcb Z-Ncÿ¹ytZWqcrW_@XN ë xpéPÐXYVhNQPêXN yb NQRUõQnSPS_hV·Ü Ψi (~ ri ) Qx _hb y b s´_WnNQVxcYUZWRªxc_hyR_hb4LYUZWV_PSNclmyRnZWVnN4X _x}ZWb¾sO_dbõQXYU_xcPSYUZWX_7s´NcR_hlkX NcbZWYUlNcRUõnPm_hVl X _ lmYUlmnSNcbZ âã lmnZ¾NQÿ¼yZWq}rW_¾õ#ZìlSNWyYUVnN ". #. h ¯ 2 ∇ + Vext + φi Ψi (~r) = εi Ψi (~r) − 2m. ^MNclmnZ2NQÿ¼yZWq}rW_J_Js´_WnNQVxcYUZWRtxc_hy RU_hb4L Y ZWV_. φi. ûÃe â [ i ý. õMXtZWX _Js´NcR Z@Ncÿ¹ytZgq}rW_2XN¢áª_hYUlmlS_hV3ܼNM_Js´_WnNQV.
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