Abstract
我們將R. Friedberg和李政道先生所提出的『超導體的玻色─費米子模型(boson-fermion model of superconductivity)』做了推廣，以求能符合最近實驗上所觀察到的高溫超導體具有d-wave形式能隙(energy gap)的現象。我們考慮一個密閉系統中同時存在有費米子，以及由費米子所結合、自旋為2的玻色子，發現這樣的系統確實具有d-wave形式─dx^2-y^2─的能隙。另外我們也導出能隙方程式(gap equation)和接近絕對零度時的比熱(heat capacity)，求得d-wave模型的一個重要特徵：T^2ln(T)形式的比熱。最後，我們亦求出了臨界磁場(critical field)；由此結果，我們可推出：當系統通過臨界溫度(critical tempereture, Tc)時，系統比熱之變化是無限大，而非有限的暴增(jump)。We extend the boson-fermion model of superconductivityproposed by Friedberg and Lee to incorporate the recentlyobserved d-wave gap in high temperature superconductors. Thespin of the boson field is generalized to be 2. By appropriatelychoosing coupling constants, a d-wave energy gap, dx^2-y^2, canbe reproduced. We further derive the gap equations and the heatcapacity near zero temperature. The heat capacity shows acharacteristic behavior of T^2ln(T) near T=0. We also calculatethe critical field; in particular, our result implies that whencrossing the critical temperature Tc, the change of the specificheat is not a finite jump, but is infinite.