Abstract
為了了解高溫超導體的物理性質與高溫超導機制, 我們研究了二維t-J 模型這個強關聯電子系統。由反鐵磁與超導長程序共存的平均場理論計算,我們得到了一個新的嘗試波函數。由我們所發展出的數值方法: Power-Lanczos Method, 加上這個新的嘗試波函數, 可以很有效地研究強關聯的電子系統。我們發現在反鐵磁背景中的一個空穴的色散關係可以由ResonatingValence Bond (RVB)理論加上反鐵磁關聯來解釋；當電洞的數目增加時, 反鐵磁長程序會很快的減小, 而在電洞密度約為百分之五時完全消失；在高電子密度的極限下, 當 J > 0.6t 時會發生相分離,系統分成一個沒有電洞的海森堡反鐵磁磁鐵以及一個含有電洞的區域；在實驗上的高溫超導的物理參數附近時, t-J 模型的超導長程序太弱而無法解釋實驗上的高溫超導現象。To understand the physical properties and mechanism of thehightemperature superconductors, a strongly correlatedelectronicsystem, the two-dimensional $t-J$ model, is studiednumerically.A new trial wave function with bothantiferromagnetic andsuperconducting long-range order is derivedfrom the mean-field theory.We develop a powerful numericalmethod, the power-Lanczos method,for studing the stronglycorrelated electron systems.We found that the dispersionrelation of one hole in antiferromagnetcan be explained by thetheory of d-RVB together with antiferromagnetism.As the numberof doped holes increases, the antiferromagnetic long-rangeorderdecreases rapidly and vanishes for doping density $x \sim5\%$.In the high density limit, phase separates into a hole-freeHeisenberg island and a hole-rich region at $J_c/t = 0.6 \pm0.1$.$J_c/t$ increases as the hole density increases. In thephysicalregion of high temperature superconductors, the signalofsuperconductivity of this model is too weak to explain thehigh$T_c$ of the high temperature superconductors.