中科大高等固体物理3尺度.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,第三章 尺寸,3.1 介观体系,3.2 纳米体系,3.3 原子团簇,3.1 介观体系,1,电子波的干涉,金属的电导率,输运弛豫时间包含了各种相互作用的贡献：,电子杂质，电子声子，电子电子,较纯金属：杂质散射贡献较小，电子电子相互作用由于传导电子的屏蔽效应而变得很弱。在温度较高时，声子散射起主要作用，它决定了电导率随温度变化的规律。随温度的降低，声子浓度不断减少，而杂质的数量不变，因此电导将趋于常数(剩余电阻).,电子被看作粒子，各种相互作用都被纳入相应的驰豫时间，电子作为波的运动特征相位被完全忽略了。,X,X”,简化的合理性：,电子沿不同的布朗运动路径从X,点到达X”点(假设所以路径上电子,经历的散射为弹性):,干涉效应,某些特殊条件下，干涉效应不为零：,沿一闭合路径反向运动的两电子分波，具有时间反演对称性。两电子分波的叠加在总平均中不抵消,电子散射的可能路径不是无限多，而是局限于若干个有限路径时,(a).弱局域化电导修正,闭合路径：电子在固体中扩散运动时以一定的概率返回它的出发点，这种路径称之为闭合路径。,0,1,2,3,4,5,6,7,8,9,10,11,12,态的电子从0点开始：0-1-2-3,-12-0 ,波函数为A,+,态的电子从0点开始：0-12-11-10,-1-0 ,波函数为A,-,|A,+,|=|A,-,|=A,等概率地：,这两个路径的顺序具有时间反演对称性，称之为时间反演路径,(time reversal path),对所有散射为弹性散射的情形，可证明，电子受相同的杂质散射从 态到 态和从 态到 态所附加的相移 是相同,A,+,与A,-,具有相同的振幅，相同的相位：,虽然巨大数量的电子扩散路径的电子分波的干涉趋向于相互抵消，但经过时间反演路径的电子波的干涉却相互增强。电子回到途中某一点几率的增加，意味着观察点N发现电子的几率下降，导致电导率的减小或电阻率的增加，呈现对经典电导率的量子力学改正,弱定域化的物理图象,，是量子力学波函数叠加原理导致宏观可观察后果的独特范例。,计及量子效应之后，电子似乎更趋向于呆在原点,N,M,O,电导也将以括号内的因子减少：,为弱局域化电导修正,低温下，一般金属薄膜的电导率0.010.1S。,在电子平均自由程较小的样品中容易观察到,这种现象：淬火薄膜或掺氧薄膜,(b).正常金属中的Aharonov-Bohm(AB)效应,经典电磁学：,量子力学：,电磁场中运动的粒子方程,规范变换,A,B,C,F,经典物理：电子束通路上没有磁场，没有磁力作用在电子上，螺线管中磁场不会产生任何影响。,量子力学：电子将感受到与磁通量相联系的矢势存在，波函数,将附加一与矢势A有关，依赖于路径的相位。,A,B,C,F,干涉强度依赖于两条路径封闭的磁通总量 ，并以周期,振荡。,观察AB效应：,电子束不受散射，相位相干不受破坏：高真空或超导体,正常金属扩散区？电子经多次散射，走着无规行走路径可观察,对一维理想金属环，如果有磁通 穿过中空区，这个环的所有,物理性质随 以 为周期变化,L,上述问题与周期为L的一维能带问题相似：,杂质Peierls,理想环,非理想环,实验：1983年，Au的平均直径为245nm,环宽30nm,AAS效应：除了观察到AB效应，还观察到周期为 的效应,振幅只有AB效应的4%,缘由：弱局域化效应,2,介观体系的电导,(1),Kubo（久保公式）,线性响应理论：非局域响应关联函数,V,I,I,电导系数g:,1,2,1,dS,1,C,1,2,dS,2,C,2,(2)Landauer,公式:,两电极视为理想导体，被测器件视为一势,垒，器件的电导系数就一定依赖于电子波的穿透系数T:,T,R,(3)Landauer-Buttiker,公式:,一根无穷长理想导线中独立电子的Shordinger方程：,Z,E,1,E,2,k,0,每条曲线代表一个横向子能带-容许通道,在每个容许通道中电子将以行波的方式,传播，从而引起电荷的流动。,给定波矢量k0，电荷既可沿+k(入射）,也可沿-k(反射)流动。,计算T=0K,导线中第 个通道上的入射电流,被测器件视为一块不均匀散射媒质，它将理想导线1中入射而来的一束渐近行波散射到导线2中的某些容许通道(透射波）及导线1中的某些容许通道(反射波)中。,a.计算两端单通道器件电导系数的Landauer-Buttiker公式,导线宽度很窄，各子能带之间的能差很大，最低子能带可被电子占据，成为唯一的容许通道。,1,2导线由相同导线组成：,Buttiker公式,b.计算两端多通道器件电导系数的Landauer-Buttiker公式,导线有限宽度，电子将填充其数个子能带(N),改写两端单通道器件的净电流表达式：,多通道：,R.A.Webb,et al,.Phys.Rev.Lett.,54,2696(1985),C.P.Umbach,et al,.,Phys.Rev.B,30,4048(1984),1,m,m,3,普适电导涨落(UCF),(1)一般特征,a.,与时间无关的非周期涨落，不是热噪声(和时间有关)。,b.,这种涨落是样品特有的(,sample-specific),涨落花样可重复(pattern)。,c.,涨落大小是e,2,/h量级(,4x10,5,S),普适量。与样品的材料、尺寸、无序程度无关，与样品的形状和空间维度只有微弱的关系，只要求样品具有介观尺度，并处于金属区：即,普适电导涨落的存在反映了介观体系和宏观体系本质上的差别,REPRODUCIBILITY,OF THE CONDUCTANCE FLUCTUATIONSMEASURED IN A GOLD RING,S.Washburn and R.A.Webb,Adv.Phys.,35,375(1986),(2)物理解释,从样品一边到另一边的透射几率幅是许多通过样品的费曼路径相应的几率幅之和。在金属区电子通过样品时经历多次与杂质的散射，其费曼路径是无规行走式的准经典“轨道”，不同的费曼路径之间的相位差是不规则的,随机干涉效应(Stochastic interference)，使电导呈现非周期的不规则涨落。,INTERFERENCE BETWEEN TWO POSSIBLEELECTRON PATHS WHICH PROPAGATE,ALONG THE SAME ARM OF THE RING,n,m,m,n,TWO DIFFERENT TRANSMISSION PATHS,THROUGH A DISORDERED SAMPLE,由统计力学，边长为L的宏观体系物理量x的相对涨落为：,系综平均，L,C,是某一关联长度，,d,是体系的维度,L,，,x,的相对涨落趋于零,经典自,平均行为(self-averaging),对于普适电导涨落：,电导的平均值满足欧姆定律：,d1个彼此独立的环，每个环的总电子数固定不变，但不同的环除总电子数可以不同外，其他参数(如 ）均相同。,对不同总电子数的系综的平均,(2).变型巨正则系综(Modified grand canonical ensemble),不同环的化学势可以不同，其他参数均相同。,对不同化学势的系综的平均,3.2 纳米体系,(1).纳米体系物理学(2).纳米化学(3).纳米材料学(4).纳米生物学(5).纳米电子学(6).纳米加工学(7).纳米力学,1,纳米结构单元,零维：团簇、量子点、纳米粒子,一维：纳米线、量子线、纳米管、纳米棒,二维：纳米带、二维电子气、超薄膜、多层膜、超晶格,体系的某个或数个特征长度在nm量级,2.纳米结构的自技术,(1).球磨和机械合金化工艺和技术(2).化学合成工艺和技术(3).等离子电弧合成技术(4).电火花制备技术(5).激光合成技术(6).生物学制备技术(7).磁控溅射技术(8).燃烧合成技术(9)喷雾合成技术,Bottom-up,Top-down,3.纳米体系的基本物理效应,(1).小尺寸效应：尺寸与光波波长、德布罗意波长以及相干长度等相当或更小时，导致声、光、电磁、热力学等物性呈现新的小尺寸效应。,(2).表面效应：,(3).量子尺寸效应：,T=1K,d=14nm,(4).宏观量子隧道效应：,微观粒子具有贯穿势垒的能力。,宏观量：微颗粒的磁化强度，量子相干器件中的磁通量，亦具有隧道效应。,Fe-Ni薄膜中畴壁运动速度在低于某一临界温度时基本上与温度无关。,限定了磁带、磁盘进行信息储存的时间极限。,(5).库仑阻塞与库仑台阶效应：,V,I,(6).介电限域效应：,纳米微粒分散在异质介质中由于界面引起的体系介电增强现象。,纳米粒子的光吸收带边移动(蓝移，红移)的Brus公式：,4,纳米材料的奇特物性,(1).热学性能,纳米粒子的熔点、开始烧结温度和晶化温度均比常规粉体的低得多。,(表体比大）,(2).磁学性质,(a).超顺磁性,起源：在小尺寸下，当各向异性能减少到与热运动能可想比拟时，磁化方向就不再固定在一个易磁化方向，易磁化方向作无规律的变化，结果导致超顺磁性的出现。,(b).矫顽力,纳米粒子尺寸高于超顺磁临界尺寸时通常呈现高的矫顽力,每个粒子是一个单磁畴,(c).居里温度,居里温度Tc与交换积分J成正比，并与原子构形和间距有关纳米粒子的Tc比固体相应的低。,纳米粒子中原子间距随着颗粒尺寸减少而减小。原子间距小将会导致J的减小，因而Tc下降。,5nm Ni:点阵参数缩小2.4%,(d).磁化率,纳米粒子的磁性与它所含的总电子数的奇偶性密切相关。,电子数为奇数的磁化率服从：,量子尺寸效应使磁化率遵从d,-3,规律(d平均颗粒直径),电子数为偶数的磁化率服从：,磁化率遵从d,2,规律,(3).光学性质,(a).宽频带强吸收,(b).蓝移和红移现象,量子限域效应：蓝移,表面效应：红移,(c).量子限域效应,激子带的吸收系数随粒径下降而增加，即出现激子增强吸收并蓝移,(d).纳米粒子的发光,(4).表面活性及敏感特性,Au纳米团簇的催化(CO+O2-CO2),(5).光催化性能,纳米半导体独特性能,nano-TiO2:,3.3 原子团簇,原子团簇：几个，几十个，成千上万的原子的聚合体。,0.1nm10nm,性质既不同于单个,原子、分子，也不同于固体或液体,王广厚,1994年6月，1998年3月,1.团簇研究的基本问题：,弄清团簇如何由原子、分子一步一步发展而成，以及随着这种发展，团簇的结构和性质如何变化。,2.团簇的产生与检测,物理制备法和化学合成法,真空、气相和凝聚相合成(生成条件),物理方法：溅射、热蒸法和激光蒸发等产生原子气，通过绝热气体膨胀或惰性气体冷凝得到中性团簇，再用各种方法使之电离，包括：电子电离、光电离和离子反应等。,团簇电离后可通过四极谱仪、静电或磁谱仪，以及飞行时间质谱仪(TOF)探测。,3.团簇的稳定结构和幻数,原子中的电子状态,原子核中的核子状态,幻数特征（壳层结构),原子团簇？YES,团簇的幻数序列与构成团簇,的原子键合方式有关：,金属键：自由价电子,共价键：Si,C,离子键：金属卤化物,范德瓦尔斯键：惰性元素,团簇结构中的序,:,(a),位置序是经典粒子的特征,(b)动量序则是德布罗依波的特征,(1).惰性元素团簇Mackay二十面体,位置序起主导作用（Ar,Kr,Xe),(2).碱金属卤化物团簇,位置序起主导作用(LiF,NaCl,CuBr,CsI),Graphite,-Soft and black and the stable,common,form of carbon.,-Very light and resistant,-Atom is at the corners of fused hexagon in parallel layers.,Diamond,-Hard and transparent and the unusual form of carbon.,-Strong thermal conductivity.,-Atom is bound to four other carbon atoms in a regular,repetitive pattern.,C60,-,A third allotropic form of very stable spheres(1985),-Formed when graphite is evaporated in an inert atmosphere.,-Assumed C60 consists of 12 pentagons and 20 hexagons with carbon atoms at each corner,as a soccer ball.,-Names,(3).C,60,团簇 共价键团簇,An idea from outer space,The serendipitous discovery,Prof.Kroto wanted,Long-chained carbon,which could form,red giant stars,Prof.Curl,Prof.Smalley,had built,an apparatus,which could analyze,evaporate almost any material with a laser beam,Collaboration,C60(Fall,1985),Contact,Fullerene Science,1985:C,60,-discovered(Nature,318,162),1990:C,60,-macroscopic scale synthesis (Nature,347,354),1991:Carbon nanotubes-discovered(Nature,354,56),1996:Noble prize for C,60,Prof.Robert F.Curl,Jr,Rice University,Houston,TX,USA,Prof Sir Harold W.Kroto,University of Sussex,Brighton,England,Prof.Richard E.Smalley,Rice University,Houston,TX,USA,Reference:www.nobel.se/chemistry/laureates/1996,The Nobel Prize in Chemistry 1996,for their discovery of fullerenes,C,50,Cl,10,的立体结构模拟图,Usefulness of hollow sphere structure,Filter,Superconductivity,Building material of objects,Expansion to,nanotube,Fullerene-based single molecule devices,Contents,Switch and Transistor,Rectifier,Magnetoresistance,Oscillator,NDR,Conduction and Others,Switch,Christian Joachim,et al.,PRL 74,2102(1995),Current I as a function of tip displacement,s,at 300K,Tunneling region to contact region,Deformation of C,60,contributes the,increase of current,Electrical resistance is 54.80 M,C,60,/Au(110)-1x2,C,60,cluster,measurement position,C,60,/Cu(100),Conductance vs tip displacement at 8K,J.Kroger,et al.,PRL 98,065502(2007),The conductance rapidly,increases to about 0.25,conductance quanta in,the transition region from,tunneling to contact.,Single-molecule on-off,Single-molecule electromechanical amplifier,J.K.Gimzewski,et al.,CPL 365,353(1997),CurrentVoltage(IV)curves obtained from a single-C,60,transistor at T=1.5 K,Hongkun Park,et al.,Nature 407,57(2000),Au-C,60,-Au system,Strongly suppressed,conductance near zero,bias voltage followed,by step-like current,jumps at higher voltages,The current through the,transistor and the voltage,width of the zero,conductance region can,be changed by changing,Vg reversibly.,Transistor,I-V curves from a C,140,single electron transistor for equally spaced Vg,C,140,AFM image of,continuous Au electrode,Au-C,140,-Au system,P.L.McEuen,et al.,Nano Lett.5,203(2005),Design of the experimental apparatus and STM,image of a MCBJ sample with a silicon substrate,gate,before breaking the gold bridge,D.C.Ralph,et al.,Nano Lett.5,305(2005),A device geometry for single-molecule,electronics experiments that,combines,both the,ability to adjust the spacing,between the electrodes mechanically,and the,ability to shift the energy levels,in the molecule using a gate electrode,Au-C,60,-Au system,Requirement:,The LUMO of the,acceptor should lie at or above,the Fermi level of the electrode,and above the HOMO of the donor,The energy(eV)of LUMO(,El,)and HOMO(,Eh,),calculated for C,60-n,X,n,(,X=,B,;,N)using B3LYP/6-31G(d),Acceptor/donor pairs,C,58,B,2,/C,58,N,2,C,54,B,6,/C,54,N,6,C,49,B,11,/C,51,N,9,C,48,B,12,/C,48,N,12,Rectifier,Double C60,Rui-Hua Xie,et al.,PRL 90,206602(2003),C,48,B,12,structure optimized,with B3LYP/6-31G(d),Calculated current through a rectifier C,48,B,12,/C,48,N,12,pair,A prototype for C,48,X,12,(17,0)SWNT-based,(,X=,B,;,N),p,-,n,junction,Single C59N Molecule as a Molecular Rectifier,J.Zhao,et al,.,Phys.Rev.Lett.,95,045502(2005),SET+C59NMolecular rectifier,Bing Wang,et al.,JPCB 110,24505(2006),Schematic drawing of the model of,the C,60,NPy on Au(111)surface,I-V,curve and its numerical d,I,/d,V,spectrum for C,60,NPy measured at,5 K taken at a gap voltage of 2.0 V,Rectifying effect,based on the,donor-barrier-acceptor(D-,-A),architecture,Gate-controlled,rectifying behavior,Gate-controlled rectifying,I,DS,-,V,DS,characteristics,after electrical breakdown,.,Inset:almost linear,I,DS,-,V,DS,curve for pristine device.,C,70,SWNT networks,Gate-controlled rectification behavior,at room temperature in air,The current rectification results from,highly asymmetric,Schottky,barriers,between semiconducting peapods,and the S/D electrodes,Yunyi Fu,et al.,JPCB 110,9923(2006),Magnetoresistance,Ni-C,60,-Ni system(experiment),(Left),Artists view of the C,60,quantum dot,between ferromagnetic nickel electrodes.,(Right),Differential conductance versus,bias voltage of the device for the parallel,(blue)and antiparallel state(red).,For parallel alignment,the,Kondo resonance is split by,the exchange fields of the two,electrodes.,For,antiparallel,alignment,the,exchange fields of the two,electrodes cancel each,other,and Kondo resonance,is restored at zero-bias voltage.,This leads to a large,magnetoresistance,MR,which exceeds the usual,tunneling,magnetoresistance,D.C.Ralph,et al.,Science 306,86(2004),Physical model of the magnetic CNT/C,60,/CNT junction,doped by Fe atoms,Transmission coefficients,as functions of energy,H.-P.Cheng,et al.,JCP 124,201107(2006),Magnetoresistance about 11%,DFT+nonequilibrium Greens function,Oscillator,Au-C,60,-Au system,multiple excitation,Two-dimensional plots of dI/dV as a function of both,V,and,V,g,Common,feature,Quantized excitation with,energy about 5meV,Hongkun Park,et al.,Nature 407,57(2000),Diagram of the centre-of-mass oscillation of C,60,The excitation is interpreted,as a centre-of-mass,oscillation of C,60,within the,confinement potential that,binds it to the gold surface,When an electron jumps on,to C,60,the attractive interaction,between the additional electron,and its image charge on gold,pulls the C,60,ion closer to the,gold surface by the distance d.,This electrostatic interaction,results in the mechanical motion,of C,60,.,Schematic illustration of the molecular junction,Au-C60-Au system,Transmission spectra,Resonance inelastic conduction in molecular-scale electronics can be used to,channel energy into a given mode of the molecular component to generate a,desired motion.,Dependence of the conductance properties on the molecular configuration leads,to a time-modulated current whose temporal properties are subject to control.,Tamar Seideman,et al.,PRL 94,226801(2005),Transmission spectra for,different C,60,orientation,6-6 bond,pentagon,hexagon,5-6 bond,Orientation dependent,Transmission spectra for different C,60,location:d=5.05(solid),5.13(dashed)and 5.23(dot-dash)a.u.,Spontaneously oscillating current vs time,Location dependent,A nanoscale generator of ac electromagnetic field,(frequency 0.8THz;ac/dc radio 0.26),Schematic diagram of,Au-C,20,-Au system,Scattering intensity due to molecular vibrations,Takahiro Yamamoto,et al.,PRL 95,065501(2005),total dI/dV,elastic component,Large discontinuous steps appear in the,dI/dV,curve when the applied bias voltage matches,particular vibrational energies.,The magnitude of the step varies with the,vibrational mode and to depend on the local,electronic states besides the strength of electron-,vibration coupling.,The electron density of Au-C,20,-Au,at(a)-1,.,5 eV and (b)0 eV(the Fermi,level),and(c)the scattering intensity,for the shuttle motion of C,20,.The,electron density is indicated by the,red shading on the atom spheres.,The excitation rate is expected to increase significantly when the electronic state,localized at C atoms adjacent to Au electrodes lie close to the Fermi level.,Such a localized state lies 1.5eV below the Fermi level(E,F,=0eV),and the,scattering intensity of,the shuttle motion,exhibits a maximum peak at-1.5eV.,The excitation rate can be enhanced by tuning the gate voltage to shift the,localized state to the Fermi level.,Structure model of the novel,oscillator.One C60 molecule,is inside a(10,10)SWNT of,length 50.05 Angstroms,Time(ps),Time(ps),Evolution of buckyball kinetic,energy between 120 and 170 ps,Evolution of potential energy of,buckyball between 120 and 170 ps,Haibin Su,et al.,Nanotechnology 17,5691(2006),Negative differential-resistance device involving two C60 molecules,C.G.Zeng,et al,.,Appl.Phys.Lett.77,3595(2000),NDR,NDR molecular device involving two C,60,molecules,TbC,82,system,I-V,curve at T=68 K,I-V,curve at T=13 K,Yutaka Majima,et al.,Nano Lett.5,1057(2005),The I-V curve shows no negative differential,conductance(NDC)at T=65K,NDC is observed in the I-V curve at T=13 K,Candidate schematic image of single,molecular orientation switching of TbC,82,NDC here is interpreted in terms of a,switching of the TbC,82,molecular,orientation caused by the interaction,between its electric dipole moment,and an external electric field.,At higher temperature,the electric,dipole moment of the TbC,82,molecule,tend to be oriented at random by,thermal energy,so no NDR appears.,Y.F.Li,et al.,APL 90,073106(2007),I,DS,-,V,DS,curve,V,G,=20 V at RT,I,DS,-,V,DS,curves with,V,G,ranging from 30 to 30 V,dI/dV curve,for empty DWNTs,peak-to-valley current ratio is about 1300,Gate voltage dependence characteristics,of,I,DS,-,V,DS,curves indicates that a threshold,voltage,V,th,for the appearance of current,peak is greatly affected by gate voltage.,NDR characteristic is symmetrical,C,60,-filled DWNT,NDR effect in,DyC82,molecules,Total charge density at Fermi level and total current distribution,(C,60,),2,(LiC,60,),2,Tomoya Ono,et al.,PRL 98,026804(2007),Conduction,Energy band structures of,chains with infinite length,C,60,Li,LiC,60,nonmetallic,metallic,nonmetallic,As electrons are inserted into the fullerenes from inserting atoms,the unoccupied state around the junction is filled and the conductivity can be significantly improved.,Channel transmissions at the Fermi level,Brian Larade,et al.,PRB 64,195402(2001),The I-V curves,Al(100)-C,80,-Al(100),system,Al(100)-Sc,3,NC,80,-Al(100),device of two orientation,The current through the Sc,3,NC,80,device is double that through a bare,C,80,device.,The presence of the Sc,3,N metal,complex and its associated charge,transfer to the C,8