a r X i v :c o n d -m a t /0312570v 1 [c o n d -m a t .s u p r -c o n ] 22 D e c 2003
Effect of chemical inhomogeneity in the bismuth-bad copper oxide superconductors
H.Eisaki,∗N.Kaneko,†D.L.Feng,‡A.Damascelli,§P.K.Mang,K.M.Shen,Z.-X.Shen,and M.Greven
Department of Applied Physics,Physics,and Stanford Synchrotron Radiation Laboratory,Stanford University,Stanford CA,94305
(Dated:February 2,2008)
permission是什么意思We examine the effect on the superconducting transition temperature (T c )of chemical inhomo-geneities in Bi 2Sr 2CuO 6+δand Bi 2Sr 2CaCu 2O 8+δsingle crystals.Cation disorder at the Sr crystal-lographic site is inherent in the materials and strongly affects the value of T c .Partial substitution of Sr by Ln (Ln =La,Pr,Nd,Sm,Eu,Gd,and Bi)in Bi 2Sr 1.6Ln 0.4CuO 6+δresults in a monotonic decrea of T c with increasing ionic radius mismatch.By minimizing Sr site disorder at the expen of Ca site disorder,we demonstrate that the T c of Bi 2Sr 2CaCu 2O 8+δcan be incread to 96K.Bad on the results we discuss the effects of chemical inhomogeneity in other bulk high-temperature superconductors.
PACS numbers:74.62.-c,74.62.Bf,74.62.Dh,74.72.Hs
I.INTRODUCTION
The possible existence of nanoscale electronic inho-mogeneity —the propensity of charge carriers doped into the CuO 2plane to form nanoscale structures —has drawn much attention in the field of high-T c su-perconductivity.Neutron scattering studies on Nd co-doped La 2−x Sr x CuO 4(Nd-LSCO)1and STM/STS stud-ies on Bi 2Sr 2CaCu 2O 8+δ(Bi2212)2have led to sug-gestions that such lf-organization may manifest it-lf as one-dimensional “stripes”in Nd-LSCO,or two-dimensional “patches”in Bi2212.In the former ca,the inter-stripe spacing in the superconducting regime is reported to be approximately four times the in-plane lat-tice constant,about 1.5nm,and in the latter ca the patches are estimated to be 1-3nm across.Many the-oretical studies suggest that the spatial electronic inho-mogeneity in the hole-doped CuO 2planes is an esntial part of high-T c physics 3.However,at prent,the im-portance of,or even the existence of generic nanoscale electronic inhomogeneity remains controversial 4,5.
If nanoscale electronic inhomogeneity exists in the su-perconducting cuprates,the doped holes will distribute themlves in the CuO 2planes so as to minimize their to-tal energy.In real materials,the C
uO 2planes are usually inhomogeneous due to local lattice distortions and/or the random Coulomb potential resulting from chemical disor-der,which differs from system to system.Therefore,even if electronic inhomogeneity may itlf be a genuine prop-erty of doped CuO 2planes,the spatial variation of doped holes will likely depend on the details of each material.For example,in the framework of the stripe model 1,in-commensurate spin and charge correlations are stabilized in Nd-LSCO by the long-range distortion of the CuO 6oc-tahedra in the low-temperature tetragonal pha,which creates one-dimensional potential wells.For Bi2212,it is argued that the random Coulomb potential caud by ex-cess oxygen atoms in the BiO planes pins the doped holes,thus creating patch-shaped inhomogeneities 2.The ob-rvations suggest that electronic and chemical inhomo-geneity are inparable from each other ,and that the un-
derstanding of the latter is imperative for an understand-ing of the former.
Motivated by this line of reasoning,we have exam-ined the effects of chemical inhomogeneity in single-layer Bi 2Sr 2CuO 6+δ(Bi2201)and double-layer Bi2212.Al-though widely ud for surface nsitive measurements such as STM 2and angle-resolved photoemission spec-troscopy (ARPES)6,a detailed understanding of their materials properties is very limited,when compared to other materials such as LSCO or YBa 2Cu 3O 7−δ.
The Bi-bad cuprates contain excess oxygens in BiO planes and one can change their carrier concentration by changing the amount,δ.The excess oxygen would engender a random Coulomb potential in the CuO 2planes.Besides the oxygen nonstoichiometry in BiO planes,there exists another source of chemical inhomo-geneity which inherently exists in typical samples.Al-though referred to as Bi2201and Bi2212,it is empir-ically known that stoichiometric Bi 2.0Sr 2.0CuO 6+δand Bi 2.0Sr 2.0CaCu 2O 8+δare very difficult to synthesize 7,8,even in a polycrystalline form.In order to more eas-ily form the crystal structure,one usually replaces Sr 2+ions by trivalent ions,such as excess Bi 3+ions or La 3+ions,forming Bi 2+x Sr 2−x CuO 6+δ,Bi 2Sr 2−x La x CuO 6+δ,and Bi 2+x Sr 2−x CaCu 2O 8+δ.As listed up in Ref.9,a typical Bi:Sr nonstoichiometry,x ,for Bi2212is around 0.1,which yields a T c =89-91K.To our knowledge,the highest T c reported in the literature is 95K (Ref.9(g),(i)).For Bi2201,T c of Bi 2+x Sr 2−x CuO 6+δis around 10K for x (Bi)=0.1,whereas La substituted Bi2201(Bi 2Sr 2−x La x CuO 6+δ)has a higher T c >30K for x (La)≈0.410.Since the Sr atom is located next to the apical oxygen which is just above the Cu atoms,the effect of Sr site (also referred to as the A-site)cation inhomogeneity is expected to be stronger than that of the excess oxy-gens in BiO planes.Note that BiO planes are located relatively far away from CuO 2planes,with SrO planes in between.
In this study,we evaluate the effect of chemical inho-mogeniety in the Bi-bad cuprates.For Bi2201,we have grown a ries of Bi 2Sr 1.6Ln 0.4CuO 6+δcrystals with var-
2
ious trivalent rare earth(Ln)ions.In this ries,the magnitude of the local lattice distortion can be changed systematically by making u of the different ionic radii of the substituted Ln ions.Wefind that T c monoton-ically decreas with increasing ionic radius mismatch. For Bi2212,a ries of Bi2+x Sr2−x CaCu2O8+δcrystals with varying values of x were grown in order to evalu-ate the effect of Bi:Sr nonstoichiometry.In addition,we also have grown Bi2Sr2Ca1−y Y y Cu2O8+δ,andfind that substitution of Y for Ca site helps to enforce Bi:Sr stoi-chiometry and to rai T c to96K for y=0.08.
Our results demonstrate that the cation disorder,in particular that located at the Sr site,significantly affects the maximum attainable T c(T c,max)in the Bi-bad su-perconductors.In order to explain our results we u a conceptual hierarchy that classifies and ranks the princi-pal kinds of chemical disorder possible in the systems. We then extend our arguments to other cuprates to ex-amine whether a general trend exists in the hole-doped high-T c superconductors.
This paper is organized as follows:Section II contains detailed information about sample preparation
and char-acterization.The experimental results are prented in Section III and discusd in Section IV,while the effects of disorder in other cuprates is addresd in Section V.
II.SAMPLE PREPARATION
Single crystals of Bi2201and Bi2212were grown us-ing the travelling-solventfloating-zone technique,which is now the preferred method for synthesizing high-purity single crystals of many transition metal oxides.This technique allows for greater control of the growth con-ditions than is possible either by standard solid state re-actions or by theflux method.
Powders of Bi2O3,SrCO3,CaCO3,Ln2O3(Ln=La, Pr,Nd,Sm,Eu,Gd,Y),and CuO(all of99.99%or higher purity)were well dried and mixed in the desired cation ratio(Bi:Sr:Ln:Cu=2:2−x:x:1for Bi2201and Bi:Sr:Ca:Cu=2+x:2−x:1:2for Bi2212),and then repeatedly calcinated at about800◦C with intermediate grinding.Eventually,the powder wasfinely ground and formed into a100mm long rod with a diameter of5mm. The crystal growth was performed using a Crystal Sys-tems Inc.infrared radiation furnace equipped with four 150W halogen lamps.Except for nearly-stoichiometric (x=0)Bi2212,the rods were premelted at18mm/h to form den feed rods.The crystal growth was carried out without the u of a solvent and at a growth speed of 0.3-0.4mm/h for Bi2201and0.15-0.2mm/h for Bi2212. T
he growth atmospheres adopted for the Bi2212growth are listed in Table1.Bi2201single crystals were grown in1atm offlowing O2.
The growth condition for the x=0Bi2212sample was more stringent than for the other samples.In or-der to obtain homogeneous polycrystalline feed rods,a mixture of starting powders with the stoichiometric ra-tio Bi:Sr:Ca:Cu=2:2:1:2was calcinated in stages,at tem-peratures increasing from770◦C to870◦C in10◦C incre-ments,with intermediate grindings.Thefinal calcina-tion temperature(870◦C)was t to be just below the composition’s melting temperature(875◦C).The dura-tion of each calcination was about20hours.To avoid possible compositionalfluctuation in the feed rod,in-stead of premelting,the feed rod was sintered four times in thefloating-zone furnace at a speed of50mm/h.This process allowed us to obtain den feed rods,approxi-mately95%of the ideal density.The atmosphere re-quired for stable crystal growth was7±3%O2,a range much narrower than for nonstoichiometric or Y-doped Bi2212.The grown crystal rod contained small amounts of a single-crystalline SrCuO2condary pha,indicat-ing that the sample still suffers from Bi:Sr nonstoichiom-etry.Single-pha Bi2212single crystals could be cleaved from the grown rod.No traces of impurity phas were found in other compositions.
Inductively coupled plasma(ICP)spectroscopy was carried out to determine the chemical compositio
ns of the crystals.Additional electron-probe microanalysis (EPMA)was also carried out on the Bi2201crystals.The results confirm that the actual compositions follow the nominal compositions,as listed in Table1for Bi2212. Hereafter,we basically denote the samples by nominal composition to avoid confusion.In order to determine the maximum T c for each cation ,to achieve optimal hole concentration),the Bi2212samples were annealed at various temperatures and oxygen par-tial pressures using a tube furnace equipped with an oxy-gen monitor and a sample transfer arm,which allowed us to rapidly quench the annealed samples from high tem-peratures within a clod environment.This procedure ensures that the variation of T c among the samples is primarily due to cation nonstoichiometry and not due to differing hole concentrations.Annealing conditions for obtaining optimal(OP),and typical underdoped(UD) and overdoped(OD)samples are listed in Table1.The results for Bi2201are on the as-grown crystals and ac-cordingly may not exactly reflect T c,max.However,by carrying out a ries of annealing studies,we have con-firmed that the systematic change of T c among our sam-ples is not due to different hole concentrations,but due to the different Ln ions.
Superconducting transition temperatures were deter-mined by AC susceptibility measurements using a Quan-tum Design Physical Properties Measurement System (PPMS).The transition temperatures r
eported here cor-respond to the ont of a diamagnetic signal.We note that the different definition of T c(such as the interecept between the superconducting transition slope and the χ=0axis)does not affect our conclusions due to the sharp superconducting transition(less than2K for most samples),as shown below.Although it is hard to de-termine the exact superconducting fraction due to the demagnetization factor of the plate-shaped crystals,the magnitude of the superconducting signal suggests the
3 TABLE I:Sample preparation conditions and crystal compositions derived from the ICP analysis for Bi2212single crystals. The ICP analysis on the third sample in the Table was done on cleaved,single-pha samples from an ingot containing a small amount of SrCuO2condary pha.
annealing condition nominal composition ICP results Bi:Sr ratio growth atmosphere UD OP OD
4
M /H (a r b .u n i t s )
Temperature (K)
FIG.2:Bi 2+x Sr 2−x Ca 1−y Y y Cu 2O 8+δsusceptibility curves,normalized to -1at the lowest temperature.Data for optimally-doped (OP),underdoped (UD),and overdoped (OD)samples are indic
ated for each cation composition by clod circles,open squares,and open triangles,respectively.
of Bi 2+x Sr 2−x CaCu 2O 8+δ.By adopting the methods de-scribed in Sec.II,we have managed to grow single crys-tals over the range 0.0<x ≤0.2.In Figs.2(a)-(c),we prent magnetic susceptibility data for three differ-ent crystals with compositions x =0.2,0.04,and ≃0,respectively (ǫin the chemical formula for the nominal x =0sample (Fig.2(c))implies the prence of resid-ual nonstoichiometry in our sample,as discusd in the previous ction).In the figures,OP indicates optimally-doped samples,which posss T c ,max for a given cation composition.Reprentative data for underdoped (UD)and overdoped (OD)samples,which were obtained by reducing and oxidizing OP samples,are also plotted to demonstrate successful control of the hole concentration over a wide range.
As the Bi:Sr ratio approaches 1:1,T c ,max increas from 82.4K for x =0.2,to 91.4K for x =0.07(not shown),92.6K for x =0.04,and eventually to 94.0K for the sample clost to the stoichiometric composition that we could grow.We note that most of the samples studied in the literature contain a nonstoichiometry of x ∼0.1with T c =89−91K 9,consistent with the prent results.Although T c of Bi2212can be raid by trying to en-force Bi:Sr stoichiometry,the preparation of nearly sto-ichiometric samples becomes much more difficult than when nonstoichiometry is allowed.This could be due to a
greater stability of the crystal structure when it contains additional positive charges,which are usually introduced by allowing the Bi 3+:Sr 2+ratio to be larger than one,as discusd in Ref.8.If this is indeed the ca,one might expect to be able to synthesize higher-T c ,max sam-ples more easily by introducing extra positive charges via cation substitution that caus disorder less vere than substitution of Bi 3+ions at the Sr site.
In the ca of Bi2201we obrved that the substitution of additional Ln atoms can eliminate excess Bi atoms from the unfavorable Sr site position,effectively lower-ing the magnitude of disorder and raising T c .In the double-layer material Bi2212,there is an additional crys-tallographic site,the Ca site located between the CuO 2planes,which can also accept trivalent dopant ions.One might expect Ln 3+ions at the Ca site to be a weaker type of disorder than Bi 3+ions at the Sr site,since there are no apical oxygens in the Ca planes that could couple to Cu atoms in the CuO 2planes.
To test this idea we have also grown Y-substituted Bi 2Sr 2Ca 1−y Y y Cu 2O 8+δcrystals.We find that this com-pound is as easy to prepare as ordinary (nonstoichiomet-ric)Bi2212,and that for Y-Bi2212the Bi:Sr ratio indeed tends to be stoichiometric.Furthermore,as shown in Fig.2(d),T c ,max for the y =0.08sample was incread to 96.0K,a value higher than for any other Bi2212sam-ple reported in the literature.9We also grew y =0.10and y =0.12samples and confirmed that T c ,max >9sife
5K in both cas.休闲服饰搭配
IV.DISCUSSION
The effect on T c of structural distortions associated with cation substitution has been extensively studied in LSCO-bad materials 13,and it is established that T c strongly depends on the A-site (La site)ionic ra-dius mismatch.For instance,Attfield et al.ud si-multaneous co-substitution of veral alkaline earth and Ln ions to hold the average A-site ionic radius constant while systematically controlling the variance of the A-site ionic radius,and found that T c is affected not just by the average radius,but also by the degree of disorder (the variance)at that crystallographic site.Our study of single-layer Bi2201continues this line of inquiry to a different superconducting material and demonstrates a similar nsitivity of T c to A-site disorder.We note that our results qualitatively agree with tho of a previous study on polycrystalline Bi2201samples 14.
One can e the same trend in Bi2212crystals with varying degrees of chemical inhomogeniety.As expected,we find that T c is strongly dependent on the A-site dis-order introduced by the Bi:Sr nonstoichiometry.Fur-thermore,we also demonstrate that by the emingly counter-intuitive method of introducing additional Y 3+ions,and hence a new type of disorder,we can rai T c ,max to 96K while minimizing A-site disorder.This suggests that,although the minimization of chemical dis-
5
order is important for raising T c,different types of dis-order are not equally harmful.This is consistent with the obrvation15that by carefully controlling disorder in the triple-layer material TlBa2Ca2Cu3O9+δ(Tl1223) T c can be raid from∼120K to133.5K,a new record for that system,and that Ba site(the A-site in this sys-tem)cation disorder(deficiency)has the strongest effect on T c.
Numerous experiments on Bi2212have suggested non-uniformity in its electronic properties.The include broad linewidths en in inelastic neutron scattering ex-periments16,residual low-energy excitations in the super-conducting state obrved in penetration depth measure-ments17,finite spin susceptibility at low temperatures obrved in NMR studies18,and short quasiparticle life-times detected by complex conductivity experiments19. The most recent of the are STM/STS measurements2 that purport to directly image patch-shaped,electroni-cally inhomogeneous regions.The Bi:Sr nonstoichiome-try which inherently exists in most samples may be par-tially responsible for the experimental obrvations. Although the prent results do not directly prove the prence of nanoscale electronic inhomogeneity,they can be taken as a circumstantial supporting evidence,since they successfully prove the existence of nanoscale chemi-cal inhomogen
eity which potentially pins down electronic inhomogeneity.To explain their STM/STS results,Pan et al.2attribute the source of pinning centers to excess oxygen in the BiO planes.Although the overall frame-work addresd by Pan et al.should still hold,we con-sider that the Bi ions on the Sr site are more effective as pinning centers since they are clor to the CuO2planes and affect T c more directly.Indeed,assuming a random distribution of Bi ions on the Sr site and a nonstoichiom-etry of x=0.10,the average paration between Bi ions is∼1−2nm,comparable with the length scale obrved in the STM/STS studies.
Recent89Y NMR experiments on YBCO indicate that the spatial inhomogeniety in this system is much less vere than in LSCO or Bi22125.This is reasonable since the latter two systems exhibit a much higher degree of disorder located at the A-site(La site(LSCO)and Sr site(Bi2212)),whereas YBCO(Ba site)is thought to be free from such cation disorder.Indeed,recent penetration depth measurements on the YBCO variant Nd1+x Ba2−x Cu3O7−δ,with cationic disorder at the Ba site,demonstrate that the superconducting properties of this system change quite nsitively with the degree of Nd/Ba nonstoichiometry20.
V.DISORDER EFFECTS IN THE CUPRATES The two main lessons to be learned from our Bi2201 and Bi2212ca studies are that(1)chemical inhomo-geneity affects T c,max and that(2)the effect of
disorder differs depending on its location.In the following,we attempt to classify the various sites at which chemical disorder is possible and categorize other superconducting families on the basis of which kind of disorder is prevalent
in each system.
In Fig.3,we classify25cuprate superconductors bad
on the pattern of the chemical disorder and the number of CuO2planes in the unit cell.21In thefirst row,we il-
lustrate three possible locations of chemical disorder rel-ative to the CuO5pyramids in multilayer materials,or
to the CuO6octahedra in single-layer materials.Pattern (a)corresponds to the Bi:Sr nonstoichiometry in Bi2201
and Bi2212,or Sr2+ions doped into the La site in LSCO, referred to as A-site disorder so far.The disorder is lo-
隐之书
cated next to the apical oxygen.Pattern(b)corresponds to Y3+substitution for Ca2+in Bi2212and reprents
disorder located next to the CuO2plane,but at a posi-tion where there are no apical oxygen atoms with which
to bond.There is no corresponding(b)site in single-layer materials.Pattern(c)disorder is further away
from the CuO2plane.We include excess oxygenδin Bi-and Tl-bad cuprates,oxygen defects in CuO chains in YBa2Cu3O7−δ,and Hg deficiency y as well as excess
oxygenδin Hg1−y Ba2Ca n−1Cu n O2n+2+δin this cate-gory.We note that the materials are catalogued bad
on the primary form of disorder that they are believed to exhibit.
As demonstrated in the prent ca study,the effect of the chemical disorder is expected to be stronger for pat-
tern(a)than for pattern(b),which is reasonable consid-ering the role of the apical oxygen atom in passing on the
effect of disorder to nearby Cu atoms.First,the random Coulomb potential caud by type(a)disorder changes
the energy levels of the apical oxygen orbitals,which can be transmitted to CuO2planes through the hybridization
between the apical O(2p z)orbital and the Cu(3d r2−3z2) orbital.Second,the displacement of the apical oxygen
caud by type(a)disorder brings about a local lattice distortion to the CuO2planes.The effect of pattern(c)
disorder is expected to be weakest since the disorder is located relatively far away from the CuO2plane.德语圣诞歌
The number of CuO2planes per unit cell may be re-
garded as another parameter that,in effect,determines the magnitude of the chemical disorder.As demonstrated in Bi2212,multilayer materials can accommodate het-erovalent ions by making u of type(b)substitution who effect on T c was en to be weaker than type(a) substitution.Furthermore,
the space between the CuO2 planes forming a multilayer may buffer the impact of the disorder.For instance,in single-layer materials,any dis-placement of the“upper”apical oxygen in a CuO6octa-hedron creates stress in the CuO2plane becau the mo-tion of the octahedron is constrained by the“lower”api-cal oxygen.Double-layer materials contain CuO5pyra-mids rather than CuO6octahedra,and the paration between CuO2planes relieves this stress,reducing the effects of type(a)disorder.This buffer zone between the outer CuO2planes is further incread in triple-layer ma-terials,with the additional benefit that the middle layer is somewhat“protected”from the direct effects of pat-
6
tern(a)(and(c))disorder.
Cursory examination of Fig.3reveals that T c,max gen-erally increas both across the rows and down the columns of the chart.Indeed,there is no material in (a-1)which posss a T c,max higher than50K.Fur-thermore,Bi2201in column(a)has a lower T c,max than Tl2201in column(c),despite their similar crystal struc-tures.Similarly,T c,max of TlBa1+x La1−x CuO5(Tl1201) is lower than that of HgBa2CuO4+δ(Hg1201).
This trend is cloly obeyed when one concentrates on the variation within a single family of materials,each denoted by a different color in the chart.For exam-ple,across thefirst row,oxygen-intercalated La2CuO4+δlocated in(c-1)has higher T c,max than Sr-substituted La2CuO4(a-1).Down the column,T c,max of the bilayer La-bad system La2−x Sr x CaCu2O6(a-2)is higher than that of its single-layer cousin.The classification suggests a negative correlation between the effective magnitude of chemical disorder and T c,max.Additional remarks are made in Ref.s22,23,24.
胡萝卜的英语We note that one may also have to consider other fac-tors which characterize the global materials properties and are likely to play a significant role as well in de-termining T c,max,such as Madelung potential26,bond valence sum25,band structure27,block layer28,multi layer29etc.Although the prent scheme is somewhat oversimplified and does not take account of the param-eters,we believe it rves as a uful framework within which to consider the chemical disorder effects prevalent in the materials,at least some of which,if ignored, have the potential to lead to the misinterpretation of ex-perimental data.Finally,similar to previous work on Tl122315and to the prent work on Bi2212,it might be possible to rai T c,max of certain other cuprates by minimizing the effects of chemical disorder.
VI.SUMMARY
where did you go
verticalalignmentIn summary,we prent ca studies of the effects of chemical disorder on the superconducting transition tem-perature of the single-layer and double-layer Bi-bad cuprate superconductors.Wefind that the supercon-ducting transition temperature of Bi2212can be in-cread up to96K by lowering the impact of Sr site disorder,the primary type of disorder inherent to the bismuth family of materials,at the expen of Ca site dis-order.Bad on the experimental results,we prent a qualitative hierarchy of possible disorder sites,and then proceed to categorize the hole-doped high-temperature superconductors on that basis.
Acknowledgments
We thank G.Blumberg,J.Burgy,E.Dagotto,J.C. Davis,D.S.Dessau,T.H.Geballe,E.W.Hudson,A.Iyo, A.Kapitulnik,G.Kinoda,S.A.Kivelson,R.B.Laugh-lin,B.Y.Moyzhes,D.J.Scalapino,T.Timusk,and J.M. Tranquada for helpful discussions.This work was sup-ported by the NEDO grant“Nanoscale phenomena of lf-organized electrons in complex oxides-new frontiers in physics and devices”,by the U.S.DOE under contract nos.DE-FG03-99ER45773and DE-AC-03-76SF00515, by NSF DMR9985067,DMR0071897,ONR N00014-98-0195and by the DOE’s Office of Basic Energy Science, Division of Material Science,Divison of Chemical Sci-ence,through the Stanford Synchrotron Radiation Lab-oratory(SSRL).H.Eisaki was supported by the Mar-vin Chodorow Fellows
hip in the Department of Applied Physics,Stanford University.
∗Prent address:Nanoelectronic Rearch Institute,AIST, Tsukuba305-8568,Japan
†Prent address:National Metrology Institute of Japan, AIST,Tsukuba305-8568,Japan
复活节的由来
‡Prent address:Department of Physics&Astronomy, The University of British Columbia,334-6224Agricultural Rd.Vancouver,B.C.V6T1Z1,Canada and Department of Physics,Fudan University,Shanghai,China
§Prent address:Department of Physics&Astronomy, The University of British Columbia,334-6224Agricultural Rd.Vancouver,B.C.V6T1Z1,Canada
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