第2章，我的同學章維益

　　章維益，是我的同學中的佼佼者，他是常州人，跟隨父母親下放到高淳，因此我們才有緣相識相知。
　　我們從初中開始就是同學，一直到高中畢業。他和我同年，個子也和我差不多，瘦瘦的，尖臉。
　　我們曾經坐過一桌，經常一起打籃球、學習、玩耍。但他的學習成績比我好，他一直是班上的尖子，老師一直把他作為榜樣。78年考取南京大學，他學的是物理專業，後又留學芬蘭。因為女朋友在德國留學，他又到德國工作了幾年，等到女朋友畢業後，90年又回到南京大學任教。回國時為博士後，到南京大學後為副教授。
　　章維益學習成績一直是很優秀，在我們眼中他是'書呆子'──一心研究學問，對外界的事管得很少。穿著樸素，人很隨和。
　　他從德國歸來，我94年去拜訪過他，那時他結婚不久，女兒才一歲，在他的宿舍裏我們聊了很多，十幾年沒有見麵了，非常親切。我真是羨慕他，他給我看了他的一些論文，全是英文。最讓我敬佩的是一本他的英文專著上的一行中文字：謹以此書獻給我的父親--章宇清。我翻開那書，他告訴我是他的論文專集（見後），專業的東西我是不大能看懂的。
　　我們交談時，有時用高淳話，有時用普通話。他和學生時又不一樣了，談吐文雅，顯得很成熟。他也說我變了，變胖了。
　　後來我到南京的一些年後，我們經常到一起聚聚，有時他也到我這邊來坐坐。最近的是在今年三份月。他從美國回來後，我還叫了我們班劉曉兵、1班的王強幾個一起小聚了一下。那次發現章維益談論的話題和以前不一樣了，他說現在參加了政協，還是什麽主席的。也真為他高興，他除研究學問外，也關心起社會來了。
　　目前他仍然在南大，早幾年前就是博士生導師了。有他這個同學，我很為他驕傲。以下是他的論文（部分），我花了些時間打上一段，以饗讀者：
　　
　
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 ............