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Estudo de reconstrução (2x6) em GaSb (001)

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(29) ¯±é P Vˆe−i = − j. Zj e2 ~j| |~ri −R. P Vˆi−i = − 21 j6=i. ≡. e2 Zj Zi ~ i −R ~j| |R. _hsONQP‡ZWX _hP NcVNQPhYUZìsO_WnSNcVxQY ZWR·XNQ`¼YUX _duìYUVnSNcP‡Zgq}rW_ NcRõQnSPS_hV {U_WV −. ≡. _hs´NcPSZWX_hP NQVNcPhY Zìs´_Wn‡NQVxcYUZWR3XNŸ`¼YUX_¾u YUVn‡NQP‡ZWqcrW_ {U_hV {U_WV −. ªá _hPSõQb~Ü ZJlS_hRyq}rg_4XNclonpZìNcÿ¹ytZgq}rW_ìXN¢ZWy n‡_]`gZWR_hPSNQlƒõ¢XNQbdZglSY ZgXtZWb¾NcVn‡Nxc_hb¾sRUYx}ZWXZ Ü s´_hPmÿ¼y N NQR Z0xQ_hVn‡õcbzybêhP‡ZWV XN7Vl¤b¾NcPS_X N–stZWPmnS{UxQyR ZWl2YUVn‡NQP‡ZWNcVn‡NQlcÜxc_hb bœZWlSlSZWl4b4yY€n‡_DX Y Ý NcPmNcVn‡N â ë y P hN‚NcVn‡rW_(Z<VNcxQNclmlSYUXZWXN0X N~ZgsPS_}àYUbœZWq ¼Ncl ÿ¹yN Ý ZWxcYRUY€n‡Ncb lSyZ lm_hRUyqcrW_ â KMbdZ<sPSYbœNQYUPSZ ZWs PS_}àYUbœZWq}rW_~Ü·xQ_hVéNQxcYUXZ7xc_hb¾_ í s PS_}àYUbœZWq}rW_œXN ߃_hPmV„ Ž ss´NcV éNcYbœNQPcÜ´xc_hVlmYUlon‡N4NQb xc_WVlSYX„ NQP‡ZWPmbœ_hlƒÿ¼y N-_hl {U_hV l NclonprW_ìsPSZgn‡Yx}ZWb¾NcVnSNkþ à_hl Ncb ybœZ4xc_hV þ hyP‡Zgq}rW_ stZWPon‡YxcyRUZWPcܼlS_hL‚Z ZWqcrW_ XNìy b x}Zgbœs´_–bœõQXYU_dxcPSYUZWX_–s´NcR_7bœ_]`¼YUb¾NcVnS_–X_hl-NcRõQnSPS_hVl-ÿ¹yNìs´_hP-s´_hlSlmyYUPmNcb ybdZœbdZWlml‡Z b4y Yn‡_bœNQV_hP X _-ÿ¼y NÕZ¢bdZWlml‡Z¢X_Wl {U_hV lcÜWnSNcP‡rg_-ybdZk`WNcR_xQYUXtZWX Nƒb4yY€n‡_¢bœZWY_hP:NƒlSN PSNcZWPSPSZWVËåSZWPSrW_ ÿ¹ytZWlmN@ÿ¼y N#YVlmn‡ZWVnpZWV N}ZWb¾NcVn‡N#Zìx}ZgXtZìxc_hV þ hyP‡Zgq}rW_ Y WVYUxcZ‚ûÃZWsPm_}à YbdZgq}rW_ìZgXY ZWL gn‡Yx}Z ý â jkNQlmnpZ Ý _hPmbdZÜ3Z Ý yVqcrW_‚XNì_hVXZ‚NQRUNŸn‡P WVYUxcZdõìxc_hV lSYUX NcP‡ZgXtZ–xc_hb¾_–XNcs´NcV XNcVn‡N¾XtZ7xQ_hV þ hy P‡ZWqcrW_‚X_hl {_hVlXNMybdZ Ý _hPmbdZ-b4yY€n‡_#lSytZ}`WNWÜ NQVÿ¹ytZWVn‡_4Z Ý yV q}rW_2XN_WVXtZ2X _hl{_hVlVtrW_2XNQ`WNcP JXNcs´NcV XNcP XtZglêxc_¼_hPSXNQVtZWXtZglNQRUNŸn‡P WVYUxcZWlêN sO_¼XN̄lSN Ý ZWîQNcPêybœZ-lSNQstZWP‡Zgq}rW_@XN `gZWPSY }`hNcYlêVtZ Ý yVqcrW_@XNÕ_hVXtZ nS_WnpZWR·X_ lSYUlon‡NQbdZ Ü _¾ÿ¹yN#PSNQlSyR€npZWP ìNcb. ~ = λ(R)Φ(~ ~ ~ Ψ(~r, R) r , R). û e âe ý. Ž VXN ~ PmNcsPmNclmNcVnpZ‚ZWlsO_hlmYUq NQlkX_hlk{U_hVlMN PmNcsPmNclSNQVnpZ‚ZWl R = (R~1 , ..., R~k ) ~r = (~ ri , ..., r~n ) s´_hlSYq¼NclìX_WlœNQRUõQnSPS_hV l âí étZWb¾YURnS_hVYUZWVtZ~X _*lmYUlmnSNcbœZsO_¼XN‹Zh_hPSZDlSNQPœXNQlSxQPSYn‡Z XZ lmNhyYVn‡N bœZWVNQYUP‡ZÜ 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 ⠂hý. ^ZWl:NQÿ¹ytZWq¼Ncl|ZWxcYbdZ ˆ xcZWPSPmNZZWsONQVtZWl¯_hl¯n‡NQPSb¾_hl¯PSNcRUZgn‡Y€`h_hlªZW_WlªNQRUõŸn‡PS_WVlcÜgstZWP‡ZÕybœZ XtZWXtZ He xQ_hV þhy P‡ZWqcrW_2V¹yxQRUNcZWPcܹNcV ÿ¼yZWVn‡_ ˆ xcZWPSPmNZ#ZWs´NcVtZWl_hln‡NQPSb¾_hlêPSNQR ZgnSY`W_hlZW_hl{U_WVl â:í sRYUx}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 hyYV¹nSN@PSNclmyRn‡ZWX_. ~ 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_xQNcXYbœNQV¹nS_¾ZWxcYbdZ4stZgP‡Z. 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#PSNQlSyR€npZWP4Ncb. _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. Œ _hb¾_7s´_X Ncb¾_hlk_hL lSNcPo`gZWPcÜO_7n‡NcPmbœ_œX_–R ZgX_dXYPSNQYn‡_œXtZdNQÿ¼yZWq}rW_ ûÃe â jhý V_Wl¢sONQPSb¾YnSN2xQ_hV„ éNQxcNQP-_~Zgy n‡_]`gZWRU_WPkXNìNQVNcPhY Z7NQRUNQnSPhV YUxc_dstZWP‡Z–ybœZdstZgPmn‡{xcyRUZdL´Ncb xQ_hb¾_‚Z Ý y Vq}rW_–X Nì_hVXtZ NQRUNQnSP hV YUx}ZÜ´N2XNclonpZdbœZWVNQYUPSZ¾n‡_¼XtZWlZWl_hLlSNQPm` }`hNQYUl¢X_dlSYUlon‡NQbdZ¾sO_¼XNcb lmNcP¢NQVxc_hVnSP‡ZWXtZgl â áª_hP _hyn‡PS_ìRUZWX_ ZìNcÿ¹ytZgq}rW_0û e â \ý V _hlÕsONQPSb¾Yn‡Nkxc_hVé NcxcNQPÕ_œZgy n‡_]`gZWRU_WP XN@NcVNQP hYUZ4Y hV YUxc_JLONQb xc_hb¾_ Z Ý yVq}rg_7XN4_hV XtZœY hVYUxcZœX_œlSYlmn‡NQbdZ â¢ë NJlSyLlon‡Y€n‡y{PSb¾_hlNQlmn‡ZWl¢XytZglkNcÿ¹ytZgq ¼NclcÜêû e â jhý N‚û e â \ý Ü VtZìNQÿ¼yZWq}rW_0û e â o ý Üxpé N ZWPSNQbœ_WlZg_¾lmN hy YUVn‡N@PSNQlSyR€npZWX _. ~ H ˆ i λ(R) ~ + λ(R) ~ H ˆ e Φ(~r, R)] ~ = ET λ(R)Φ(~ ~ ~ [Φ(~r, R) r , R). _hV XN Œ _hb¾_ bœZWVNQYUP‡Z. ET. ûÃe â [ f ý. xc_hPmPSNclmsO_WVXN#ZW_¾ZWy nS_a`gZWR_hP XN#NcV NcPWY ZJn‡_gnpZWR3X _œlmYUlmnSNcbœZ. ˆ e Φ(~r, R) ~ H. õœYhytZWR. ~ ~ εe (R)Φ(~ r , R). Z–Ncÿ¹ytZWqcrW_DZWxQYUbœZ7sO_¼XNìlmNcP#NclSxQPSY€npZ‚XtZ‹lmNhy YUVn‡N. ~ 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 RUYbœYVtZWVX _ ~ NcbzZWb4L´_hl2_hl4R ZgX_hlJNdxc_hR_xcZWVX_ Φ(~r, R) ÿ¹yNQPSX_¾XtZìNcÿ¹ytZWqcrW_7ZgxcYUbœZJNQVxc_hVnSP‡Z˄ lSN@þtVtZWRbœNQV¹nSN. ~ λ(R). Ncb NQ`¼YUX cVxQY ZDV_DRUZWX_DNQlo„. ~ ~ = ET λ(R) ~ [Tˆi + Vˆi + εe (R)]λ( R). ûÃe â [ e ý. Œ _hb¾_ks´_¼XNlmNcP:_hLlSNQPm`gZWX_ksONQR ZNQÿ¹ytZWq}rg_-ZWxcYbdZ ~ XNclmNcb¾sONQVétZ¢_stZWs´NcR¼XNƒyb s´_Wn‡NQV„ εe (R) xQY ZWRb¾õcX YU_-stZWPSZ#_WlVl¤xQRUNQ_hlcܼNÕõÕn‡ZWb4L´õcb xQ_hVéNQxcYX_2xQ_hb¾_#lmys´NcP Ý {xcYN XNÕNcVNQPhYUZ#s´_Wn‡NQVxcYUZWR âªí hPSZWVXNåm_ ZWXtZìXtZ ZWsPm_}à YbdZgq}rW_ìXN#߃_WPSV„ Ž ss´NcV éNcYbœNQP õ#_ XNQlSX_WLP‡ZWb¾NcVnS_œXtZ Ncÿ¹ytZgq}rW_¾XN ZWyn‡_]`gZWRU_hPmNcl|nS_WnpZgRNcb y bdZ¢NQÿ¼yZWq}rW_#XNMZWy nS_]`WZgRU_hPmNcl NQRUNQnSP hV YUx}Z¢NÕybœZ¢Ncÿ¹ytZgq}rW_#XNMZWy nS_a`gZWR_hPSNQl YhVYUxcZ~ZglSlSYb~ܪXNdZWxc_hPmX_DxQ_hb Z~VNQxcNclmlSYXtZWXN–s´_X NŸ„lmNœPmNclm_hR`WNcPìZWs´NcVZWlJybœZ~X NcR Zgl7û _x WRxcyR_hl XN2Nclon‡PSyn‡yPSZ7NcRUNŸn‡P hVYUxcZ ý _hyZWl¢X ytZWl û NclmnSyX_hlkXN4b¾_hRUõQxcyRUZWl ý âkã lmn‡Z7ZWsPm_}à YbdZgq}rW_¾n‡_hPmV_hy„ lSN X+ N hPSZWVXN¾YUb¾sO_WPmnpTgVxcYUZdlSNåSZ~stZWPSZ0Z‚ÿ¹y{Ub¾YUxcZ‚_WyHstZWPSZ~Z Ý {UlmYUxcZ ܯlSNcV X_Ds´_hPmn‡ZWVn‡_‹yl‡ZWXZ~xc_Wb hPSZWVXN-lmyxcNQlSlm_–Zgn‡õ-_WlMX Y ZWl XN@é_aåmN â ÑcÒ Ñ. í£ßî3ßâcïœØqð±ï—ÚÛ. ßâ.ñ9ØáÞ8ÕîóòbßJØ×[ÚÕîÊÕôzä2ÚâÚ±ñ9Ú Ø. Õ¼ØÎðØqâ8õØ¡ÞØqî. ÕqâØqî. ^ Nclmn‡Z0lSNQq}rW_DZWsPSNQlSNQV¹n‡ZWPSNQbœ_Wl4yb LPmNQ`hNdéYUlon‡÷hPmYUxc_‹X_DX NclSNQV`h_hR€`YbœNQVn‡_DXtZgl2n‡NQ_hPSYUZWl@y n‡Y „ M RYUî}ZgXtZWl-NcbÔxWRUxQyRU_hl#ZWL¼„YUV Yn‡Y_‚ZW_‹RU_hVW_~X_WlJZWV _hlcÜ ûüNcbÔyb xWRUxQyRU_~ZWL„ YUVY€n‡Y_7VtrW_~lSNdyn‡YURYUîcZ XtZgX_hl-NŸàs´NcPmYUb¾NcVnpZWYlcÜ3`gZWRNcVX_˄lSN4ZWsONQVtZWl@XN ZWR hybœZWl-ZWs PS_}àYUbœZWq¼NclknSõc_hPmYUxcZWl ý âJí sPSYbœNQYUPSZ N4n‡ZWb4L´õcb ybdZ7XZWl-bdZgYUlky l‡ZWXtZgl2ZgsPS_}àYUbœZWq ¼NclkstZWP‡Z–Z Ý y Vq}rW_‚XNì_WVXtZ–lSNìXNŸ`hN¾8 Z pkZWPon‡PmNcN  jN ÿ¹yNdV_0ZWV_~XN [}\ e  lS y hNQPSYy(ÿ¹yN7Z Ý yVq}rg_0XN¾_hVXtZ‹stZWPSZ~ybÔlSYlmnSNcbœZ‹b4y Rn‡Y „NQRUNQnSP hV YUxc_ Ý _hlmlSN#NclmxcPSY€npZìxc_Wbœ_ 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 l‡ZgnSYUl Ý ZgîcNcb Z-Ncÿ¹ytZWqcrW_@XN ë xpéPÐXYVhNQPêXN yb NQRUõQnSPS_hV·Ü Ψi (~ ri ) Qx _hb y b s´_Wn‡NQVxcYUZWRªxc_hyR_hb4LYUZWV_œPSNclmyRn‡ZWVn‡N4X _–x}ZWb¾sO_dbœõQXYU_œxcPSYUZWX_7s´NcR_hlkX NcbœZWYUlNcRUõŸn‡Pm_hVl X _ lmYUlmnSNcbœZ âã lmn‡Z¾NQÿ¼yZWq}rW_¾õ#ZìlSNWyYUVn‡N ". #. h ¯ 2 ∇ + Vext + φi Ψi (~r) = εi Ψi (~r) − 2m. ^MNclmn‡Z2NQÿ¼yZWq}rW_J_Js´_Wn‡NQVxcYUZWRtxc_hy RU_hb4L Y ZWV_. φi. ûÃe â [ i ý. õMXtZWX _Js´NcR Z@Ncÿ¹ytZgq}rW_2XN¢áª_hYUlmlS_hV3ܼNM_Js´_Wn‡NQV„.

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