lecture3-表面電子態(tài)(存儲版)
【正文】 z0 0sin zkk? ? 2 00 22 mWk ?Where: Phase shift 當前模型的局限 ? 沒有考慮電子間的交換關聯(lián)作用。 更精確的方法： DFTLDA Ves(r) Remarks ? The jellium model description of a metal surface neglects the details of the electronion interaction and emphasizes the nature of the smooth surface barrier. ? The nearly free electron model emphasizes the lattice aspects of the problem and simplifies the form of the surface barrier. 2. 近自由電子模型 ? The nearly free electron model, which is valid when the lattice potential is weak. Consequently, this potential is treated as a perturbation, the unperturbed states being free electron plane waves. This model can describe the electronic structure of normal metals and some narrowgap semiconductors. M. C. Desjonq249。 鏡像勢 Strongly correlated interaction En = eV/(n+a)2, n = 1,2,... 類似于氫原子的能級 金屬電子對表面外電荷的屏蔽效應 21() 14bv a cbeV z Ez?????Cu(100)和 Cu(111)表面的鏡像態(tài) Nonresonant Resonant 金屬 /絕緣體界面的鏡像態(tài) Progress in Surface Science 80 (2022) 49–91 兩個界面都有鏡像態(tài)！ 2PPE 測得的 Cu(100)表面的鏡像態(tài) Progress in Surface Science 80 (2022) 49–91 STM z(V) spectroscopy n=1 n=2 n=3 n=4 n=5 n=6 利用 STM探測表面的鏡像態(tài) 3 4 5 6 7 8 9 120 115 110 105 100 95 Cu(100) rel. Tip height (A) sample bias (V) 休息 15分鐘 實例 1：貴金屬表面態(tài) Ag(111)表面在費米面附近存在能隙，而其他表面不存在能隙 Ag各個表面的能帶結構 各種貴金屬的（ 111）面 Au(111) 表面態(tài)的測量 ARPES STM dI/dV spectroscopy Constant density of states (2D) 100 50 0 50 100012345 L0/(L0+ ?b) = L0?bE0= 67mVdI/dV (arb. u.)EEF (meV)自旋軌道耦合 表面駐波 Standing waves on Ag(111) surface / / / / //( ) ~ ~ c o si k x i k xk x e e k x? ??2 //( ) ~ ( ) ~ c o s 2kkx x k x?? 局域態(tài)密度： 表面態(tài)電子被臺階的散射 kx ky k1i k1s k2i k2s 0 臺階 等能面 E’ M. F. Crommie et al., Science 363, 524 (1993) 局域態(tài)密度： 表面態(tài)的能量色散 Y. Hasegawa and Ph. Avouris, Phys. Rev. Lett. 71, 1071 (1993) Quantum corrals Fe adatoms on Cu(111) 1993 IBM39。 gV g /0 ?? ?波函數(shù)在表面處的連續(xù)性 Vg0 Vg0 Shockley state E 1 2 3 The curvature of Ψk can match the decaying vacuum solution only for Vg0 近
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