第2章，我的同学章维益

　　章维益，是我的同学中的佼佼者，他是常州人，跟随父母亲下放到高淳，因此我们才有缘相识相知。
　　我们从初中开始就是同学，一直到高中毕业。他和我同年，个子也和我差不多，瘦瘦的，尖脸。
　　我们曾经坐过一桌，经常一起打篮球、学习、玩耍。但他的学习成绩比我好，他一直是班上的尖子，老师一直把他作为榜样。78年考取南京大学，他学的是物理专业，后又留学芬兰。因为女朋友在德国留学，他又到德国工作了几年，等到女朋友毕业后，90年又回到南京大学任教。回国时为博士后，到南京大学后为副教授。
　　章维益学习成绩一直是很优秀，在我们眼中他是'书呆子'──一心研究学问，对外界的事管得很少。穿著朴素，人很随和。
　　他从德国归来，我94年去拜访过他，那时他结婚不久，女儿才一岁，在他的宿舍里我们聊了很多，十几年没有见面了，非常亲切。我真是羡慕他，他给我看了他的一些论文，全是英文。最让我敬佩的是一本他的英文专著上的一行中文字：谨以此书献给我的父亲--章宇清。我翻开那书，他告诉我是他的论文专集（见后），专业的东西我是不大能看懂的。
　　我们交谈时，有时用高淳话，有时用普通话。他和学生时又不一样了，谈吐文雅，显得很成熟。他也说我变了，变胖了。
　　后来我到南京的一些年后，我们经常到一起聚聚，有时他也到我这边来坐坐。最近的是在今年三份月。他从美国回来后，我还叫了我们班刘晓兵、1班的王强几个一起小聚了一下。那次发现章维益谈论的话题和以前不一样了，他说现在参加了政协，还是什么主席的。也真为他高兴，他除研究学问外，也关心起社会来了。
　　目前他仍然在南大，早几年前就是博士生导师了。有他这个同学，我很为他骄傲。以下是他的论文（部分），我花了些时间打上一段，以飨读者：
　　
　
On the doping induced gap states
Of high-Tc oxides due to oxygen disorder

Weiyi Zhang ,K.H. Bennemann

Abstract

The photoemission and inverse photoemission spectra clearly show doping induced states inside the antiferromagnetic gap of high-Tc superconducting oxides. Experimental data indicate that these states have dominant oxygen character and result form the transfer of density of states form the lower and upper Hubbard bands. They also seem to be related to localized orbitals.It is important to determine the physical nature of these states and whether these states in the gap result solely form strong correlations or from a combination of strong correlation and oxygen disorder. We show in this paper that structural defects like excess oxygen and oxygen vacancies in the CuO2 plane will cause deep impurity states in the gap and which have approximately the observed characteristics. Furthermore, we find that copper disorder does not cause such states in the gaps. Despite its simplicity these results are interesting with regard to clarifying the physical origin of these states.

Photoemission and inverse photoemission experiments reveal interesting features of the quasiparticle excitation spectra of the high-Tc superconducting oxides〔1-3〕.The undoped compounds correspond to charge transfer insulators with a gap of the order of 2eV,as verified by experiments〔4〕.Doping the insulator by substituting for the trivalent elements divalent or tetravalent ones and by oxygen defects introduces nonrigid changes of the spectra.Especially, the photoemission experiments〔4－10〕indicate states with energy near the middle of the antiferromagnetic gap upon doping. These gap states have dominantly oxygen character and result form the transfer of density of states form both the upper and lower Hubbard bands. While an earlier experiment on La2-x SrxCuO 4-〔7〕seems to indicate the pinning of the Fermi energy upon doping, recent results on Bi2Sr2Ca1-xYxCu2O8+〔10〕show that the Fermi energy moves just like in doped simple semiconductors.A more recent study of the optical spectrum of lightly doped Cu2 plane of high- Tc superconductors〔11〕identifies further structures inside the insulating gap.Besides the usual major peak observed near the center of the gap, an absorption peak near the low Hubbard band with the excitation energy around 0.16 eV is also found.
The doping induced gap states have attracted great attention during the last several years. Among others, Jichu et al.〔12〕investigated this phenomenon using the slave boson technique. They interpreted the reduced quasihole band as the states occurring in the gap.(Note that the original lower and upper Hubbard bands have disappeared in their analysis.) Eskes et al.〔13〕studied the same problem using the exact diagonalization method for small clusters. Identifying the lower and upper Hubbard band edges for the half-filled case, they attribute states between the band edges occurring due to doping as states in the gap.The positions of band edges are not well defined as a function of doping.Recent calculations by Lorenzana and Yu〔14〕show that polarons and excitons of charge-transfer origin arise quite naturally in the p-d model of high- Tc superconductors and contribute states over the whole gap region. However,in all these studies,the position and, especially, the character of those gap states are not explained satisfactorily in comparison with experiments. Hence,the origin of those gap states remains somewhat an open question. Clearly, it is of great significance to find out whether such gap states result solely form strong correlation or from a combination of strong correlation and defects. Note that structural disorders such as grain boundaries, magnetic textures,interstitial oxygens, as well as oxygen vacancies may all contribute to such states in the gap.
As is well known now,oxygen defects in the high- Tc superconducting oxides are unavoidable.Experiments〔15-17〕show that for the sample prepared under pressure, at smaller doping some excess oxygens appear at interstitial sites in the orthorhombic La2CuO4 unit cell while at higher doping oxygen vacancy appears in the system. Furthermore, it is also observed in La2-x SrxCuO 4-that the doping processes induce oxygen dislocations〔18〕.The transport experiments〔19〕indicate that the oxygen defects create localized states in contrast to the mobile states created by the substitution of trivalent elements. The existence of localized states in the high- Tc superconducting oxides is also inferred form the phase diagram〔20,21〕showing a transition from localized states to metallic states at finite doping concentration. Therefore, it seems possible that those states in the gap are due to impurity levels as was already suggested by Takahashi〔8〕from the photoemission and inverse photoemission measurements. More recently,effects of impurities on the electronic structure of the one band t-J model have been studied by several groups〔22-24〕using the exact diagonalization of small cluster.They found that a combination of strong correlation and structural defects does result in the localized states below the upper Hubbard band band. However, the one band t-J model they used eliminates the oxygen degree of freedom on the outset, the question why those localized states are oxygen-like is still unresolved.
Although the origin of the localized states is not fully understood yet, there are speculations concerning its role on the physical properties of high- Tc superconductors.Bar-Yam〔25〕has shown that by including both the mobile and localized carriers in these high- Tc oxides, many unusual phenomena can be clarified. A recent study by Lee〔26〕shows also that some of the contradictory behavior can only be reconciled by assuming such localized states in the system.Therefore, it is rather interesting to know how these localized states arise from structural disorders and why they have a dominant oxygen character. Note that one expects on general grounds a transfer of density of states from bands to these gap states due to defects. This is so,since the doping will conserve the total density of states. Furthermore,it will involve both the valence and conduction bands as the gap states occur in both the hole and electron doped high- Tc superconducting compounds.
In this paper, we would like to study the effect of structural disorder on the electronic density of states of the CuO 2 plane; in particular, to determine how the position and character of the impurity states are related to the various defects2. We begin our study by estimating the impurity potential on the CuO 2 plane due to the excess oxygen and oxygen vacancies.Let us first consider excess oxygen defects outside of the CuO 2 plane, the impurity potential caused by the extra interstitial oxygen depends on whether there are intervening oxide layers(such as LaO) toward the CuO 2 plane. For the case that such intervening oxide layers exist, the impurity potential caused by the excess oxygen on the CuO 2 plane is screened. A simple estimate using a screened Coulomb potential gives electronic level shifts at Cu and O sites in the vicinity of the defect of the order of 0.82 eV〔11〕，whereis the distance between the excess oxygen core charge and Cu and O in the CuO 2 plane. is taken as the dielectric constant. Otherwise, the impurity potential at the nearest Cu or O sites on the CuO 2 plane is just given by the unscreened Coulomb potential 8 eV as the distance now is roughly half the size compared with the former. A similar analysis holds also for oxygen vacancies outside of the CuO 2 plane. For an oxygen vacancy in the CuO 2 plane we assume ............