Superconductivity Discovery of Superconductivity by H. Kamerlingh Onnes (1911) Brief History Characteristic of Superconductors Applications Important Superconductors How the Superconductivity Was First Discovered? (This story was told by Prof. P. Kes of Leiden in 1993 at a NATO summer school in Erice, Italy.) There were two assistants working for Onnes, Horst and Dorshman (these names need to be confirmed). The son of Dorshman told Prof. Kes in 1992 the story of the discovery of superconductivity his father used to tell to his son. They were studying the resistance of mercury with a resistance bridge. One day, by pumping on liquid He in the cryostat, they realized that for some reason the resistance bridge did not seem to be working properly because it was not giving any signal. After they stopped the pump, by mistake, they forgot to re-open the valve to release the evaporated He gas from the cryostat. The pressure increased beyond atmosphere and the temperature increased. It was THEN that they noticed that the resistance of mercury recovered! This is how the superconductivity was first discovered. (Not on cooling, but on warming mercury!) In the Leiden Communication article, there is a description that the tap (valve) Eak2 was used to increase the temperature. What Is a Superconductor? A superconductor is an element, intermetallic alloy, or compound that will conduct electricity without resistance below a certain temperature. Once set in motion, electrical current will flow forever in a closed loop of superconducting material making it the closest thing to perpetual motion in nature. 1
Superconductivity Materials become superconductors below some critical temperature, T C. The temperature dependent change between superconducting and normal conduction is abrupt! The temperature at which this drastic decrease in resistance occurs is the critical temperature of a superconductor. Abrupt change! Resistance goes to zero. This is the critical temperature. Superconductors Compared to Other Conductors Semiconductors show a increase in resistance as the temperature is decreased. Fewer electrons are excited from the donor band (in n-type extrinsic semi-conductors), into the acceptor band (in p-type extrinsic semiconductors), and from the valence band to the conduction band (in intrinsic semiconductors). Metal conductors show a decrease in resistance as the temperature is decreased. Fewer vibrations result in a more perfect lattice. Current Research Status on High Temperature Superconductors NMR Characteristics of Superconductors Loss of Resistance! Zero electrical resistivity. This means that an electrical current in a superconducting ring continues indefinitely (at least for a very long time ~ years ), without dissipation through the ring or until a force is applied to oppose the current. Meissner Effect! Superconductors expel all magnetic flux in a process called the Meissner effect. The magnetic field inside a bulk sample is zero. When a magnetic field is applied, current flows in the outer skin of the material, leading to an induced magnetic field that exactly opposes the applied field. The material is strongly diamagnetic as a result. A superconductor excludes magnetic flux. In this experiment, this is used to levitate a magnet above the surface of the superconductor. 2
Meissner Effect When a superconducting sample is cooled below Tc in the presence of an external magnetic field, the magnetic field (i.e., lines of the induction B) are pushed out. A superconductor is a perfect diamagnet! Two Easy Experiments Showing Meissner Effect Liquid nitrogen is added to a reservoir beneath the superconductor. (The superconductor is actually just out of sight beneath the rim of the cup.) A smaller magnet levitates about a centimeter above it. Superconductivity is a macroscopic quantum phenomenon. BCS (Bardee, Cooper & Schrieffer) 理论 1957, 金属超导性理论首先发现 Cooper pair 金属中的两个电子之间通过交换声子 ( 晶格振动量子 ) 而呈现吸引力 在 Fermi 面附近的电子, 两两配对, 构成 Cooper pair ( 类玻色子 ) Bardeen Cooper Schrieffer 1972 BCS theory Superconductivity is essentially a quantum phenomenon. Electrons in superconducting materials tends to pair up, forming a single quantum entity. At low enough temperature, all pairs coalesce into a ground state that can support a persistent current indefinitely. 在 Fermi 面附近, 能量在的一对电子 Cooper 对 Bardeen, Cooper, Schrieffer 著名 BCS 的理论 e - Normal Metal e - Cooper 对 D 能量守恒动量守恒电子 声子相互作用能泡利不相容原理 范围之内的自旋和动量都相反 Superconductor 2 ~ D 在连续的能带态下, 出现一条分离的能级 ( 基态 ), 它与激发态之间有一个能隙 (energy gap) Superconductivity ( 准粒子激发自由度被冻结 ) E F Electrons can attract via phonons Attraction leads to energy gap 1.76T c E F 3
超导电性的 BCS 理论 - 电声子相互作用 产生超导现象的关键在于超导体中的电子形成了电子对, 叫做 库柏对 在没有电流时, 每个 库柏对 由两个动量完全相反的电子所组成 在有电流的超导金属中, 每一个电子对都有一总动量, 这动量的方向与电流方向相反, 因而能够传送电荷 电子对通过晶格运动时不受阻力, 这是因为两个电子同时受到晶格的散射而发生相反的动量改变, 结果电子对的总动量不变 所以晶格既不能减慢也不能加快电子对的运动, 在宏观上就表现为直流电阻为零的超导行为 二级相变效应 超导体的其他物理特性 1932 年, 荷兰学者 Keesom 和 Kok 发现, 在超导转变的临界温度 T C 处, 比热出现了突变 Keesom-Kok 实验表明, 在超导态, 电子对比热的贡献约为正常态的 3 倍 如果发生相变时, 体积不变化, 也无相变潜热, 而比热 膨胀系数等物理量却发生变化, 则称这种相变为二级相变 正常导体向超导体的转变是一个二级相变 超导体的其他物理特性同位素效应同位素效应指出超导体的临界温度随同位素质量而变化 1 T c 1/ 2 M 同位素效应揭示出超导电性与电子和晶格的振动有关 超导体的其他物理特性 电子能通过两块超导体之间薄绝缘层的量子隧道效应 --- 超导电子学 Josephson effect (1962) : A current will flow through a superconductor-insulatorsuperconductor junction even when the voltage across the junction is zero. 1973 诺贝尔物理学奖 B.D. Josephson 发现固体中隧道现象, 理论上预言超导电流能够通过隧道阻挡层 ( 即约瑟夫森效应 ) S O V B S Josephson Junction Nb/Al 2 O 3 /Nb Pb/Al 2 O 3 /Pb j 4
Josephson effect 电子对能够以隧道效应穿过绝缘层, 在势垒两边电压为零的情况下, 将产生直流超导电流, 而在势垒两边有一定电压时, 还会产生特定频率的交流超导电流 直流约瑟夫森效应 : 结两端的电压 V=0 时, 结中可存在超导电流, 它是由超导体中的库珀对的隧道效应引起的 只要该超导电流小于某一临界电流 Ic, 就始终保持此零电压现象,Ic 称为约瑟夫森临界电流 Ic 对外磁场十分敏感, 甚至地磁场可明显地影响 Ic 交流约瑟夫森效应 : 结两端的直流电压 V 0 时, 通过结的电流是一个交变的振荡超导电流 S O V B S Josephson Junction Nb/Al 2 O 3 /Nb Pb/Al 2 O 3 /Pb j 直流约瑟夫森效应 直流电 I 存在临界电流 I C 绝超导体缘超导体层 若 I < I C, 结中通过超导电流 ; 若 I > I C, 结的两端出现电压 说明 直流约瑟夫森效应 临界电流 临界电流 I C 对于外加磁场十分敏感, 并随外加磁场呈周期性变化 I I C V C 约瑟夫森结 I-V 特性曲线 V 临界电流与外加磁场变化曲线两相邻最小之间的磁场强度间隔 H 0 与结面积的乘积等于磁通量子 0 h/ 2e 2.067 10 15 Wb 交流约瑟夫森效应在直流电压作用下超导隧道结约瑟夫森频率 2eV / h 483.6 10 6 Hz/μ 电磁波 ( 频率 v ' ) 照射约瑟夫森结若 v = n v ' ( n =1, 2, 3, ) 则照射的电磁波 ( v ' ) 共振结辐射的电磁波 ( v ) 说明在 V n nh ' 处有阶梯式变化 2 e 超导交流电流 辐射电磁波 约瑟夫森结 I - V 特性曲线 5
wire Application Existing wire - Energy loss by resistance - High voltage needed Wire with superconductor - No energy loss - No high voltage needed. - Storage of electricity. Wire with superconductor Cut end of superconductor wire Loss free power transmission (without cooling?) Uses of Superconductors Levitation MagLev trains have been under development in many countries for the past two decades The train floats above the track using superconducting magnets. There s no friction between the train and the rail, so less energy is lost and the train can reach much higher speeds. car with superconductor? 德国磁悬浮列车 西南交通大学研制成功的超导磁悬浮列车, 最高设计时速达 500 公里 1999 年 4 月, 日本研制的超导磁悬浮列车时速已达 552 公里, 创世界铁路时速最高纪录 实验性行驶 2002 年 4 月 5 日我国第一条磁悬浮列车试验线在长沙建成通车, 设计时速 150 公里 超导体的其他物理特性 电子能通过两块超导体之间薄绝缘层的量子隧道效应 --- 超导电子学 Josephson effect (1962) : A current will flow through a superconductor-insulatorsuperconductor junction even when the voltage across the junction is zero. 1973 诺贝尔物理学奖 B.D. Josephson 发现固体中隧道现象, 理论上预言超导电流能够通过隧道阻挡层 ( 即约瑟夫森效应 ) S O V B S Josephson Junction Nb/Al 2 O 3 /Nb Pb/Al 2 O 3 /Pb j 6
Application of Josephson Effect SQUIDs used to measure extremely small magnetic flux at the quantum level (human heart: ~10-10 T, brain: ~10-13 T); Rapid Single Flux Quantum integrated circuits; Build photon or particle detectors; Microwave detectors in the giga-and terahertz range; Quantum computer. Josephson effect and SQUID SQUID (Superconducting QUantum Interference Device ) A superconducting loop interrupted in 2 places by Josephson junctions. When sufficient electrical current is conducted across the SQUID body, a voltage is generated proportional to the strength of any nearby magnetic field. SQUIDs can be used to measure extremely small magnetic flux at the quantum level (human heart: ~10-10 T, brain: ~10-13 T); Uses of Superconductors Magnetic Resonance Imaging MRI is a technique developed in the 1940s that allows doctors to see what is happening inside the body without directly performing surgery. The development of superconductors has improved the field of MRI as the superconducting magnet can be smaller and more efficient than an equivalent conventional magnet. Application Super computer Without superconductor : large heat, large electric power use with superconductor : no heat, small electric power use 7
Application Particle Colliders Particle colliders are very large running tracks that are used to accelerate particles (i.e. electrons, positrons, hadrons and more) to speeds approaching the speed of light before they are collided with one another. The collision usually possess enough energy to split the particles into smaller particles. Particle colliders were used to discover many sub-nuclear particles such as taus and neutrinos. They do this by cycling the particle using magnetic fields, continually increasing the speed of the particle. U1 光刻 U4 红外与远红外 U7A 高空间分辨 X 射线成像 U7B X 射线衍射与散射 U7C 扩展 X 光吸收精细结构 U10 燃烧 U12B X 射线显微术 U14 原子与分子物理 U14C 真空紫外分析 U18 表面物理 U19 软 X 射线磁性圆二色 U20 光电子能谱 U24 真空紫外光谱 U25 光声与真空紫外圆二色光谱 U26 光谱辐射标准与计量 核聚变反应堆 磁封闭体 利用超导体产生的巨大磁场, 应用于受控制热核反应 核聚变反应时, 内部温度高达 1-2 亿 C, 没有任何常规材料可以包容这些物质 而超导体产生的强磁场可以作为 磁封闭体, 将热核反应堆中的超高温等离子体包围 约束起来, 然后慢慢释放, 从而使受控核聚变能源成为 21 世纪前景广阔的新能源 合肥等离子体所超导托卡马克 HT-7 巨大的电感线圈 Brief History of Superconductivity 1911 Kamerlingh Onnes discovered superconductivity in Hg at Tc=4K 1913 Kamerlingh Onnes won the Nobel Prize in Physics 1933 Meissner and Ochsenfeld discovered the Meissner Effect 1941 Superconductivity was reported in Nb nitride at Tc=16K 1953 Superconductivity was reported in V 3 Si at Tc=17.5K 1962 Development of first superconducting wire 1972 Bardee, Cooper & Schrieffer won the Nobel Prize in Physics 1986 Müller and Bednorz (IBM-Zurich) discovered high temperature superconductivity in La-Ba-Cu-O at Tc=35K! 1987 Müller and Bednorz won the Nobel Prize in Physics 1987 Superconductivity was found in YBCO copper oxide at Tc=92K!!! 1988 Tc was pushed to 120K in a ceramic containing Ca and Tl 1993 HgBa 2 Ca 2 Cu 3 O 8 was found to superconduct at Tc=133K 8
Superconducting Critical Temperature Tc = the temperature at which the system (sample) undergoes a phase transition from a normal conducting state into a superconducting state, characterized by zero dc electrical resistivity. supercondu ctor normal Three Temperatures Tc(onset) onset transition temperature, when the R T curve begin to departure from the linear relation of normal resistance Rn. Tc(min) the middle transition temperature, which corresponds the point that resistance drops to Rn/2. T the temperature when resistance drops to zero. For YBa 2 Cu 3 O 7- : Tc(onset)=95K, Tc(min)=91K T =90.5K and Tc=1K Three Barriers of Superconducting Materials 10 7 10 6 10 5 (A / cm 2 ) NbTi Nb 3 Sn 10 3 LaBaCuO A superconducting material exhibits superconductivity only below its critical temperature Tc, its critical magnetic field Hc, and its critical current density Jc. High Tc (critical temperature) High Hc (critical magnetic field) High Jc (critical current density) 100 T 40T 14T 24 T 9 K 18 K 40 K 90 K YBaCuO 9
Critical Magnetic Field (Hc) A sufficiently strong external magnetic field can destroy the superconducting state critical magnetic field Critical Current Density (Jc) The Critical Current Density (Jc) is the maximum current that a superconductor can carry. Above Jc the normal state is re-installed Critical current density, Jc, is the property that limits the industrial applications for high temperature superconductors. Jc is a function of temperature and magnetic field, it is also a microstructure-sensitive property and is influenced by many materials related factors. phase diagram of I- type superconductor experimental data Magnetic field destroys s/c Mercury Superconducting Transition H H c H H c Electric current destroys s/c I c B c 0 Mercury was historically the first to show superconductivity. Its practical usefulness is limited by the fact that its critical magnetic field is only 0.019 T, so the amount of electric current it can carry is also limited. 10
Superconductive Elements Table from Burns A15 compounds Materials Al Sn Pb Nb 3 Sn LaSrCuO YBaCuO BiSrCaCuO TlBaCaCuO HgBaCaCuO Transition temp.(k) 1.2 (-272 C) 3.4 (-270 C) 7.2 (-266 C) 23.8 (-249 C) 40 (-233 C) 90 (-178 C) 107 (-166 C) 125 (-148 C) 135 ~ 165K alloy 39K Superconductivity in MgB 2 In MgB 2, hexagonal honeycomb layers of boron atoms alternate with layers of magnesium atoms, centered on the hexagons. Nagamatsu et al. Nature 2001, 410, 63 MgB 2, like graphite, has strong bonds in the planes and weak bonds between them, but since boron atoms have fewer electrons than carbon atoms, not all the bonds in the boron planes are occupied. And because not all the bonds are filled, lattice vibration in the boron planes has a much stronger effect, resulting in the formation of strong electron pairs confined to the planes. 11
Li: Element With the Highest T C Superconductivity of Iron (Fe) Superconductivity at high temperatures is expected in elements with low atomic numbers. For example, it has been predicted that when hydrogen is compressed to its dense metallic phase (at pressures exceeding 400 GPa), it will become superconducting with a transition temperature above room temperature. Such pressures are difficult to produce in a laboratory setting, so the predictions are not easily confirmed. Under normal conditions lithium is the lightest metal of all the elements, and may become superconducting at lower pressures. In this work, Li shows superconducting at pressures greater than 30 GPa, with a pressure dependent transition temperature (Tc) of 20 K at 48 GPa. This is the highest observed Tc of any element; it confirms the expectation that elements with low atomic numbers will have high transition temperatures, and suggests that metallic hydrogen will have a very high Tc. K. Shimizu et al., Nature 2002, 419, 587. Shimizu et al., Nature 2001, 412, 316 The temperature dependence of the magnetization of iron under pressure obtained by cooling the sample at a magnetic field of 130 G. The signal at 21 GPa (the area enclosed by the dotted line is expanded in the upper inset) shows the appearance of diamagnetism at temperatures below 1.7 K, which is confirmed by the signal given by tin at 2.7 K. The lower inset shows the disappearance of the Meissner signal in iron when the pressure is decreased to 3.5 GPa in the b.c.c. phase. Temperature dependence of the electrical resistivity of iron at 25 GPa. A 10% drop in resistivity indicates the onset of superconductivity at around 1.5 K. Superconductivity in an iron-based layered compound LaO 1-x F x FeAs Superconductivity at 43 K in SmFeAsO 1-x F x Structural model of SmFeAsO 1-x F x with the tetragonal ZrCuSiAs-type structure. The quaternary equiatomic ZrCuSiAs-type structure is very simple, with only eight atoms in the tetragonal cell. The dashed lines represent a unit cell. Schematic crystal structure of LaOFeAs: Electron carriers generated by F-doping into oxygen sites are injected into FeAs metallic layers as a result of the large energy offset between these two layers. The carrier doping layer is spatially separated from the conduction layer. Temperature dependence of the electrical resistivity of LaO 0.95 F 0.05 FeAs below 3 GPa, using the piston cylinder device. Hiroki Takahashi Nature, 2008, 453, 376 Temperature dependence of resistivity with and without a magnetic field. Chen XH, Nature, 2008,453, 761 12
Smaller c First family of iron-based SC Crystal Structure: Tetragonal I4/mmm SmF xo 1-xFeAs x~0.2 d) Tc=55K, cm/0803.3603 a=3.933a, c=8.4287a R O 1-x F x FeAs R O 1-x FeAs Fe,Ni As,P PrF xo 1-xFeAs c) Tc=52K, cm/0803.4283 a=3.985a, c=8.595a F not important, vacancy fine 2D square lattice of Fe Fe - magnetic moment As-similar then O in cuprates La,Sm,Ce O CeF xo 1-xFeAs b) Tc=41 K, cm/0803.3790 a=3.996a, c=8.648a But As not in plane! a) Y. Kamihara et.al., Tokyo, JACS b) X.H. Chen, et.al., Beijing,arXiv: 0803.3790 c) Zhi-An Ren, Beijing, arxiv: 0803.4283 d) Zhi-An Ren, Beijing, arxiv: 0804.2053. LaF xo 1-xFeAs a) Tc=26 K, JACS-2008 a=4.036a, c=8.739 A La 1-xSr xofeas Tc=25K, cm/0803.3021, a=4.035a, c = 8.771A As Fe Rare earth s: Perfect tetrahedra 109.47 Phase diagrams SmFeAsO magneto-transport experiments SmFeAsO 1-x F x S.C. Riggs et.al., arxiv: 0806.4011 A. J. Drew et.al., arxiv:0807.4876. Very similar to cuprates, log (T) insulator due to impurities 13
Direct imaging of the coexistence of ferromagnetism and superconductivity at the LaAlO 3 /SrTiO 3 interface Nature Physics, 2011, 7, 767 a, LAO/STO magnetometry image mapping the ferromagnetic order. Inset: Scale image of the SQUID pick-up loop used to sense magnetic flux. b, δ-doped STO magnetometry image showing no ferromagnetic order. c, LAO/STO susceptometry image mapping the superfluid density at 40 mk. Inset: Scale image of the SQUID pick-up loop and field coil. d, δ-doped STO susceptometry image mapping the superfluid density at 82 mk. e, The temperature dependence of the susceptibility taken at the two positions indicated in c. f, The temperature dependence of the susceptibility taken at the two positions indicated in e. The arrow on each scan shows the scan fast axis and the SQUID orientation. a, Susceptometry scan on the patterned sample at 87 mk. A suppression of the diamagnetic susceptibility is visible near the edge of the pattern. b, Susceptibilityversus-temperature data from three positions on the patterned LAO/STO shown in a. Polymorphism control of superconductivity and magnetism in Cs 3 C 60 close to the Mott transition The crystal structure of fcc Cs 3 C 60 Nature, 2010, 466, 221 通过施加一定的压力, 改变 C 60 的晶体结构, 不同 C 60 晶体结构下的 Cs 3 C 60 能够从磁绝缘体转变为超导体, 而其超导转化温度也从 38K 转化为 35K Superconductivity in just four pairs of (BETS) 2 GaCl 4 molecules 由 4 对分子组成的世界上最小超导体 Superconductivity 1908, Kammerlingh-Onnes experiments on liquid He ( a few ml) Hg resistance: 0.08 ohm @ 5K to 0.000003 ohm @ 4.2 K 1986, J. G. Bednorz, K. H. Muller (IBM) La-Ba-Cu-O Oxide: Tc = 35 K Molecular superconductivity. S.-W. Hla*, Nature Nanotechnology, 2010, 5, 261 Size-dependent molecular superconductivity 14
At the extreme forefront of research in superconductivity is the empirical search for new materials. (1983) Discovery of Superconductivity in La-Ba-Cu-O (1986) High Temperature Superconductors Cuprate superconductors have been the focus of researchers because they conduct at relatively high temperature (T c > 77K). Compound Tc/K Compound Tc/K YBa2Cu3O7 93 Tl2CaBa2Cu2O8 119 YBa2Cu4O8 80 Tl2Ca2Ba2Cu2O7 128 Y2Ba4Cu7O15 93 TlCaBa2Cu2O7 103 Bi2CaSr2Cu2O6 92 TlCa2Ba2Cu3O8 110 Bi2Ca2Sr2Cu3O10 110 Tl0.5Pb0.5Ca2Sr2Cu3O9 120 In the Y, Ba, Cu, O compounds: Y, Ba, and O have oxidation states of +3, +2, and 2, respectively. This results in copper having mixed oxidation states +2 and +3. A similar result is obtained for the other materials. Their structures are related to that of perovskite (CaTiO 3 ). Perovskite Structure Perovskite Structure Octahedronal coordination of Ti Tolerance Coefficient If cation and anion keep contact, then R R ) 2(R R ) ( A X B X But in fact, only need to satisfy: ( R A R X ) t 2(RB R X ), 0.7 t 1 t is called tolerance coefficient. Ideal perovskite is cubic system, but many perovskites have been distorted to tetragonal, orthorhombic and monoclinic systems. 15
Perovskite structure: ABO 3 R: ionic radius: R(O 2- ) 1.40 Å a A and a B : natural size of each layer Rocksalt Structure and Fluorite Structure A O AO layer: R(A) R(O) a / A 2 BO 2 layer: B O R(B) R(O) a / 2 B tolerance factor: 1 R(A) R(O) a t 2 R(B) R(O) a A B Rocksalt Structure Fluorite Structure Oxides Superconductors vs Perovskite Structure YBa 2 Cu 3 O 7 as a Defective Perovskite Left: 3 perovskite unit cells, CaTiO 3 3 = Ca 3 Ti 3 O 9 Center: Replace Ca with Ba, Y; Replace Ti with Cu YBa 2 Cu 3 O 9 orthorhombic unit cell count Right: Removal of 2/9 of oxygens gives defect perovskite structure, YBa 2 Cu 3 O 7 - (x 0.2) 123 Superconductor C.N. Ba = 10, C.N. Y = 8 16
Oxides Superconductors vs Perovskite Structure Two types of Cu site Layers of CuO 5 square pyramids Chains of vertex-linked CuO 4 squares These are indicated in a Polyhedral Representation CuO2 BaO CuO BaO CuO2 Y CuO2 ABO 3 3 ABO 3 Y123 Crosses mark absent oxygen Yttrium-Barium-Copper Oxide This ceramic material was the first of the high temperature superconductors to make the phase change at a temperature above the liquid nitrogen temperature (77 K). value in YBa 2 Cu 3 O 7- As increases: 1) T c decreases 2) symmetry changes from orthorhombic to tetragonal (oxygen atoms rearrange in base) There has two crystal structures: i) <0.5, orthorhombic structure with a= 3.827, b= 3.882, and c= 11.682 Å; this phase is superconductive. ii) > 0.5, tetragonal structure with a= b= 3.9018, and c= 11.9403 Å; this phase is non-superconductive. Tc is a function of oxygen contents, an oxygen annealing is needed to ensure high oxygen contents in order to achieve the highest possible Tc. 17
Changing Properties? Can substitute many elements into YBa 2 Cu 3 O 7 structure: Y lanthanides no change in T c Y other elements decrease in T c Structure of Cuprate Superconductors Oxygen's from a CuO 2 layer are shared by the perovskite unit cell. In the perovskite cell, the Ba 2+ (Black) and Y 3+ (Gray) ions substitute for Ca 2+. The Cu (blue) centers substitute for Ti(IV). Ba Sr, Ca decrease in T c Cu transition metals decrease in T c Cu Au very slight increase? Ba La very slight increase? Generally detrimental! Cuprate Superconductors T c vs Number of CuO 2 Layers The CuO 2 layers are responsible for the superconducting properties. The other layers serve as sources of electrons. The copper 3d and oxygen 2p atomic orbitals are close enough to allow for significant orbital mixing band structure. This band is half filled because Cu(II) has a d 9 configuration The half-filled band is tuned electronically by the effects of the neighboring layers in the lattice. 18
Why Do They Superconduct? In compounds such as YBa 2 Cu 3 O 7-x, the metal ion (i.e. copper) is partially oxidized. But an individual metal ion cannot be partially oxidized. Instead, the lattice will be comprised of a ratio of Cu 2+ to Cu 3+ ions, depending on x. There will be holes' of positive charge (Cu 3+ ions) within the lattice. This type of superconductor is referred to as a p- type superconductor Compounds can also be doped to insert extra electrons into the lattice (i.e. a reduction), e.g. La 2 CuO 4+x This is called an n-type superconductor. Why Do They Superconduct? One explanation involves the use of holes within the superconductor. When a current is applied to the superconductor, the electrons travel along the ion planes in the lattice. As an electron passes a positive hole (due to oxidized cation, Cu 3+ ) in a neighboring plane, it will push negative charge from orbitals on a reduced cation (such as Cu 2+ ) towards the hole. This is due to electrostatic repulsion. The oxidized cation (Cu 3+ ) then reduces, and the reduced ion (Cu 2+ ) oxidizes Effectively, the hole moves backwards (as an electron moves forwards). This extra current that is caused by the normal current is the supercurrent. K 2 NiF 4 Structure (La,Sr) 2 CuO 4 (T Phase) K 2 NiF 4 structure and its (110) projection K 2 NiF 4 is a derivative structure of perovskite structure. This structure can be regarded as the alternate stacking of 2D perovskite layer and Rocksalt Layer. Ba x La 2-x CuO 4-y is K 2 NiF 4 structure,tc(0)=38k A superconductor with derivative structure of K 2 NiF 4 Can be regarded as the alternate stacking of perovskite structure unit containing Cu-O layer and rocksalt structure unit along c axis. The same structure with the first cupper oxide superconductor La 2-x Ba x CuO 4 (Tc=35K). 19
Lanthanum-Barium-Copper Oxide Superconductor This ceramic material was the first of a new class of high temperature superconductors. It is made by randomly substituting some barium atoms into the lattice of lanthanum-copper-oxide in what is termed a solid solution. Alternative Views of the La 2 CuO 4 Structure Doped La 2 CuO 4 {La 2-x Sr x CuO 4 and La 2-x Ba x CuO 4 } are the first (1986) High-T c Superconducting Oxide (T c ~ 40 K) for which Bednorz & Müller were awarded a Nobel Prize La 2 CuO 4 may be viewed as if constructed from an ABAB... arrangement of perovskite cells known as an AB Perovskite! Alternative Views of the La 2 CuO 4 Structure We may view the structure as based on: 1.Sheets of elongated CuO 6 octahedra, sharing only vertices 2.Layered networks of CuO 4 6-, connected only by La 3+ ions (Nd,Sr) 2 (Nd,Ce) 2 Cu 2 O 8 (T* Phase) Derivated from K 2 NiF 4 structure. CuO 6 octahedron lose one vertex and thus form CuO 5 square pyramids. (Nd,Sr) 2 (Nd,Ce) 2 Cu 2 O 8 can be regarded as the alternate stacking of CuO 5 square pyramids layers, fluorite layer and rocksalt layer along c axis. Tc=28K 20
(Nd,Ce) 2 CuO 4 (T Phase) TlBa 2 Ca n-1 Cu n O 2n+3 Superconductors Derivated from K 2 NiF 4 structure. CuO 6 octahedron lose two vertexes and thus form CuO 4 plane. (Nd,Ce) 2 CuO 4 can be regarded as the alternate stacking of CuO 4 plane and fluorite structure unit along c axis. Tc=24K TlBa 2 Ca n-1 Cu n O 2n+3 (n=1,2,3 ) series with single TlO layer, Tc is 50K,103K and 117K, respectively. They are built up by rocksalt layers and oxygendeficient perovskite layers. Ba Pb 2 Sr 2-x La x Cu 2 O 6 (Pb2202) Can be regarded as special K 2 NiF 4 structure, and derivated from La 2 CuO 4,in which one CuO 6 octahedron loss all oxygens and form liner coordination structure. There are two kinds of Cu,one in octahedron coordination structure (+2 valence) and the other in linear coordination structure (+1 valence). Tc=32K Comparison of Pb2202 and La 2 CuO 4 Pb 2 (Sr,La) 2 Cu 2 O 6 (La,Sr) 2 CuO 4 (T phase) 21
La 2 CaCu 2 O 6 Comparison of La 2 CaCu 2 O 6 and La 2 CuO 4 This structure contains two face-to-face CuO 5 square pyramid layers. It is a result of two-fold oxygen-deficient perovskite structure from two layers of CuO 6 octahedron losing the common vertex oxygen. This structure can also be regarded as the derivative in which the single perovskite layer is replaced by two layers of oxygen-deficient perovskite. La 2 CaCu 2 O 6 La 2 CuO 4 (T phase) YBa 2 Cu 3 O 7 the 123 Superconductor the first material to superconduct at liquid N 2 temperature, T c > 77 K YBa 2 Cu 3 O 7 can be viewed as an oxygen-deficient perovskite. Two types of Cu site: Layers of CuO 5 square pyramids Chains of vertex-linked CuO 4 squares YBa 2 Cu 4 O 8 (Y124 Phase) Y124 phase connects two CuO 5 square pyramids by structure units of Cu-O double chain. Cu-O double chain can be regarded as the common edges of CuO 6 octahedron of two layers of perovskites and lossing oxygens in the opposite planes. It is a 7-fold oxygendeficient perovskite structure (c~7a p ). Its superconducting transition temperature is 80K. 22
Comparison of Y124 and Y123 Y 2 Ba 4 Cu 7 O 14 (Y-247 phase) YBa 2 Cu 4 O 8 (Y124) YBa 2 Cu 3 O 7 (Y123) Besides oxygendeficient perovskite layers containing Cu-O plane, Y247 unit also contains Cu-O double chain and Cu-O linear structure. Can be regarded as the complex structure of Y123 phase and Y124 phase. Its superconducting temperature is 40K. Comparison of Y247 and Y124 and Y123 Bi 2 Sr 2 CuO Bi 2 Sr 2 CaCuO Bi 2 Sr 2 Ca 2 Cu 3 O Bi-Sr-Ca-Cu-O system 1988 by H. Meada (Japan) Bi2201 Tc< 30 K Bi2212 Tc= ~85 K Bi2223 Tc< 30 K Y 2 Ba 4 Cu 7 O 14 (Y247) YBa 2 Cu 4 O 8 (Y124) YBa 2 Cu 3 O 7 (Y123) Comparison between YBCO and BSCCO: i) Bi2223 has a higher Tc than YBCO; ii) BSCCO crystals cleave easily along (001) planes, making it easy to be textured with mechanical deformation; iii) No oxygenation process is needed because the oxygen content in BSCCO is relatively stable iv) BSCCO compounds have better stabilities in water containing environments 23
Bi 2 Sr 2 CuO 6 (Bi2201) Phase Bi 2 Sr 2 CuO 6 is the first layered cupper oxide superconductors which do not contain rare earth ions. Tc=7~22K Bi-2201 phase is formed by the ordered array of rocksalt structures of Bi 2 O 2 double layers and pervoskite structures along c axis. Bi 2 Sr 2 CaCu 2 O 8 (Bi2212) Ca CuO 2 SrO BiO BiO SrO CuO 2 Ca CuO 2 SrO BiO BiO SrO CuO 2 Ca Tc=85K Can be regarded as the 2-fold oxygendeficient pervoskite structure unit. Bi 2 Sr 2 Ca 2 Cu 3 O 10 (Bi2223) Enhancement of superconductivity by pressuredriven competition in electronic order CuO 2 Ca CuO 2 SrO BiO BiO SrO CuO 2 Ca CuO 2 Ca CuO 2 SrO BiO BiO SrO CuO 2 Ca CuO 2 Bi 2 Sr 2 Ca 2 Cu 3 O 10 can be regarded as 3-fold oxygendeficient pervoskite structure unit. Tc=110K Magnetic susceptibility measurement set-up. Russell J. Hemley, Nature 2010,466,950 Pressure dependence of Tc in optimally doped Bi 2 Sr 2 Ca 2 Cu 3 O 10+Δ. 对三层氧化铋 (Bi2223) 晶体施加两种不同程度的高压, 其临界温度也会相应发生变化, 过了某个 临界压力 后, 压力越高, 其临界温度也越高 24
Bi 2 Sr 2 (Ln,Ce) 2 Cu 2 O 10 (Bi2222) Comparison of Bi2212 and Bi2222 Bi2222 is formed from the insertion of one fluorite layer into two CuO 5 square pyramids. Its structure is the ordered array of three rocksalt layer, oxygendeficient pervoskite structure and fluorite layer along c-axis. Bi 2 Sr 2 CaCu 2 O 8 (Bi2212) Bi 2 Sr 2 (Ln,Ce) 2 Cu 2 O 10 (Bi2222) (Bi,M)Sr 2 YCu 2 O 7 (Bi1212) (Bi,M)Sr 2 (Ln,Ce) 2 Cu 2 O 7 (Bi1222) It is difficult to form a cupper oxide with intact single layer of BiO. Suitable metal ions such as Cd,Cu substitute Bi to stabilize BiO layer, resulting in (Bi,M)Sr 2 YCu 2 O 7 (Bi1212) with single layer of (Bi,M)O. Its structure is the ordered array of two rocksalt layers and oxygen-deficient pervoskite structure along c-axis. When M=Cu, Tc=60K. Insertion of one layer of fluorite structure unit into Bi1212 phase forms Bi1222. When M=Cd, Tc=27K (Bi,M)Sr 2 YCu 2 O 7 (Bi1212) 25
(Bi,M)Sr 2 (Ln,Ce) 3 Cu 2 O 7 (Bi1232) Pb 2 Sr 2 (Ln, Ca)Cu 3 O 8+ (Pb3212) Insertion of two-layers of fluorite structure into Bi1212 phase forms Bi-1232. When M=Cu,Tc=20K (Bi,M)Sr 2 YCu 2 O 7 (Bi1212) Pb 2 Sr 2 (Ln,Ca)Cu 3 O 8+ is the first Pb series of cupper oxide superconductor discovered by Cava. Tc=68K Can be regarded as the derivation in which the two-fold oxygen-deficient pervoskite structure units containing two CuO 5 square pyramids replace the CuO 6 octahedron in Pb 2 (Sr, La) 2 Cu 2 O 6+ (Pb2202). Comparison of Pb3212 and Pb2202 Pb 2 Sr 2 (Nd,Ce) 2 Cu 3 O x (Pb3222) Pb 2 Sr 2 (Ln, Ca)Cu 3 O 8+ Pb3212 Pb 2 Sr 2-x La x Cu 2 O 6 (Pb2202) The insertion of fluorite layer into the two CuO 5 square pyramids of Pb3212 phase can form Pb3222 phase. Pb 2 Sr 2 NdCu 3 O 8+ (Pb3212) 26
Pb(Sr,Ba) 2 (Y,Ca)Cu 3 O 7 (Pb2212) Pb(Sr,Ba) 2 (Nd,Ce) 2 Cu 3 O x (Pb-2222) Pb-2222 can be regarded as the insertion of fluorite structure into Pb-2212. Tc=60K Pb-2212 can be regarded as taken one PbO rocksalt phase from Pb-3212. In this unit cell, Ba,Sr,Pb distribute orderly. Pb 2 Sr 2 (Ln,Ca)Cu 3 O 8+ (Pb3212) Pb(Sr,Ba) 2 (Y,Ca)Cu 3 O 7 (Pb2212) Tl 2 BaCa n-1 CuO 2n+4 Another Series of Tl Superconductors Up to now, this kind of superconductors with n from 1 to 5 has been successfully synthesized. The lattice parameter a is similar while c increases with n. Such superconductors have single TlO layer. 27
Tl-Ba-Ca-Cu-O system discovered by Shen & Hermann with Tc= ~125 K; have a higher Tc than YBCO and BSCCO superconductors; Their crystal structures are similar with tetragonal unit cells; Jc and Hc are also high; Highly poisonous 28