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Transient multi-physics behavior of an insert high temperature superconducting no-insulation coil in hybrid superconducting magnets with inductive coupling 被引量:1
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作者 Xiang KANG Yujin TONG +1 位作者 Wei WU Xingzhe WANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第2期255-272,共18页
A transient multi-physics model incorporated with an electromagneto-thermomechanical coupling is developed to capture the multi-field behavior of a single-pancake(SP)insert no-insulation(NI)coil in a hybrid magnet dur... A transient multi-physics model incorporated with an electromagneto-thermomechanical coupling is developed to capture the multi-field behavior of a single-pancake(SP)insert no-insulation(NI)coil in a hybrid magnet during the charging and discharging processes.The coupled problem is resolved by means of the finite element method(FEM)for the magneto-thermo-elastic behaviors and the Runge-Kutta method for the transient responses of the electrical circuits of the hybrid superconducting magnet system.The results reveal that the transient multi-physics responses of the insert NI coil primarily depend on the charging/discharging procedure of the hybrid magnet.Moreover,a reverse azimuthal current and a compressive hoop stress are induced in the insert NI coil during the charging process,while a forward azimuthal current and a tensile hoop stress are observed during the discharging process.The induced voltages in the insert NI coil can drive the currents flowing across the radial turns where the contact resistance exists.Therefore,it brings forth significant Joule heat,causing a temperature rise and a uniform distribution of this heat in the coil turns.Accordingly,a thermally/mechanically unstable or quenching event may be encountered when a high operating current is flowing in the insert NI coil.It is numerically predicted that a quick charging will induce a compressive hoop stress which may bring a risk of buckling instability in the coil,while a discharging will not.The simulations provide an insight of hybrid superconducting magnets under transient start-up or shutdown phases which are inevitably encountered in practical applications. 展开更多
关键词 hybrid superconducting magnet high temperature superconducting(hts)no-insulation(NI)coil inductive coupling multi-physics field thermal stability
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Current Sharing Technology in Transmission Conductors of Cold Dielectric High Temperature Superconducting Cables Using Second-generation HTS Wires 被引量:3
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作者 ZHU Jiahui BAO Xuzheng QIU Ming 《中国电机工程学报》 EI CSCD 北大核心 2012年第13期I0022-I0022,205,共1页
冷绝缘高温超导电缆的导电层一般设计为多层结构以满足大电流载流特性,但伴随层数的增加,超导体上的集肤效应会引起电缆输电导体各层电流分布不均匀的问题,从而造成电缆损耗增加和传输性能下降。采用基于动态惯性权重因子的粒子群优... 冷绝缘高温超导电缆的导电层一般设计为多层结构以满足大电流载流特性,但伴随层数的增加,超导体上的集肤效应会引起电缆输电导体各层电流分布不均匀的问题,从而造成电缆损耗增加和传输性能下降。采用基于动态惯性权重因子的粒子群优化算法,提出了电缆导体层电流层间均流优化的设计方法。应用第2代高温超导材料钇钡铜氧涂层导体,通过建立超导电缆的等效电路模型,考虑电场、磁场等约束因素,对一根1km长,110kV/3kA等级的冷绝缘高温超导电缆进行优化设计,获得了电缆本体结构参数及输电导体层和屏蔽层的电流分布。比较优化前后层电流的结果可知,优化后超导电缆各导体层电流与平均电流相比最大不平衡率小于3.5%,各屏蔽层电流达到均布,较好地实现了电缆各导体层电流均匀分布的优化目标。最后,超导模型样缆载流特性实验也验证了优化设计方法的有效性。 展开更多
关键词 高温超导线材 高温超导电缆 共享技术 低电流 输电导线 介质 第二代 交流损耗
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Liquid nitrogen level meter for high-temperature superconductor (HTS) 被引量:1
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作者 PARK Heecheol JEONG Hwanjun +3 位作者 LEE Changyeung KIM Purn CHO Jangwon KIM Seokho 《Journal of Central South University》 SCIE EI CAS 2012年第11期3100-3104,共5页
Many kinds of high temperature superconductor (HTS) power machines such as HTS cable, HTS fault current limitcr and HTS magnet are cooled by liquid nitrogen. The level of liquid nitrogen should be monitored and cont... Many kinds of high temperature superconductor (HTS) power machines such as HTS cable, HTS fault current limitcr and HTS magnet are cooled by liquid nitrogen. The level of liquid nitrogen should be monitored and controlled to ensure the thermal stability and the dielectric strength as well. To measure the level, capacitance method and differential pressure method are usually used. However, each method has installation difficulties and measurement errors for unsteady state operation with varying system pressure. A new liquid level meter using a 2G HTS conductor is described, which has similar structure with the liquid helium level meter with NbTi filament. The level meter is fabricated with a parallel connected heater, which helps the separation of the superconducting region and normal region, considering the critical temperature, large heat capacity of conductor and cooling characteristics. The level of liquid nitrogen can be obtained from the measured voltage signal along the 2G HTS conductor. Design, fabrication and test results of the new liquid nitrogen level meter are presented. 展开更多
关键词 high temperature superconductivity liquid nitrogen level meter QUENCH
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High Temperature Superconducting Magnetic Energy Storage and Its Power Control Technology
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作者 Xiao-Yuan Chen Jian-Xun Jin +5 位作者 Kai-Meng Ma Ju Wen Ying Xin Wei-Zhi Gong An-Lin Ren Jing-Yin Zhang 《Journal of Electronic Science and Technology of China》 2008年第2期137-142,共6页
High temperature superconducting (HTS) power inductor and its control technology have been studied and analyzed in the paper. Based on the results of simulations and practical experiments, a controlled release schem... High temperature superconducting (HTS) power inductor and its control technology have been studied and analyzed in the paper. Based on the results of simulations and practical experiments, a controlled release scheme has been proposed and verified for developing a practical HTS SMES prototype. 展开更多
关键词 Electronic switch SMES high temperature superconducting (hts inductor uninterruptible power system (UPS).
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Induced current of high temperature superconducting loops by combination of exciting coil and thermal switch
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作者 Jia-Wen Wang Yin-Shun Wang +2 位作者 Hua Chai Ling-Feng Zhu Wei Pi 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第3期521-526,共6页
With its commercialization, the second-generation(2G) high temperature superconducting(HTS) RE–Ba–Cu–O(REBCO, RE is rare earth) tape is extensively applied to the superconducting magnets in the high magnetic fields... With its commercialization, the second-generation(2G) high temperature superconducting(HTS) RE–Ba–Cu–O(REBCO, RE is rare earth) tape is extensively applied to the superconducting magnets in the high magnetic fields. However,unlike low temperature superconducting(LTS) magnets, the HTS magnet cannot operate in the persistent current mode(PCM) due to the immature superconducting soldering technique. In this paper, an exciting method for two HTS sub-loops,so-called charging and load loops, is proposed by flux pump consisting of exciting coil and controllable thermal switch.Two HTS sub-loops are made of an REBCO tape with two slits. An exciting coil with iron core is located in one sub-loop and is supplied with a triangular waveform current so that magnetic field is generated in another sub-loop. The influence of magnetic flux on induced current in load loop is presented and verified in experiment at 77 K. The relationship between the induced magnetic flux density and the current on the sub-loops having been calibrated, magnetic flux density, and induced current are obtained. The results show that the HTS sub-loops can be excited by a coil with thermal switch and the induced current increases with magnetic flux of exciting coil increasing, which is promising for persistent current operation mode of HTS magnets. 展开更多
关键词 BRIDGE high temperature superconducting(hts)sub-loops induced current thermal switch
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The Superconducting Phases in Bi-Sr-Ca-Cu-O and Bi-Pb-Sr-Ca-Cu-O Superconductors at High Temperatures
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作者 He Qing Yu Dingan +2 位作者 Chang Shian Zhang Hong Sun Xu General Research Institute for Non-ferrous Metals,Beijing,100088,P.R.of China 《Rare Metals》 SCIE EI CAS CSCD 1989年第1期50-51,共2页
The addition Of Pb enhances the hightemperature stability as well as theproportion of the high Tphase in Bi-Sr-Ca-Cu-O superconductor.The sample A with nominal composi-tion of BiSrCaCuOwas synthesized bySolid state re... The addition Of Pb enhances the hightemperature stability as well as theproportion of the high Tphase in Bi-Sr-Ca-Cu-O superconductor.The sample A with nominal composi-tion of BiSrCaCuOwas synthesized bySolid state reaction.It was sintered in airat 1153K for 24h,followed by annealingat 773K for 24h and furnace-cooling.The sample B with a nominal compositionof BiPbSrCaCuOwas prepared bymixing PbO with the powder ofBiSrCaCuOwhich had been prefired at1113K for 24h,pressing,sintering at 展开更多
关键词 PB SR The superconducting Phases in Bi-Sr-Ca-Cu-O and Bi-Pb-Sr-Ca-Cu-O superconductors at high temperatures Cu Ca BI
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NI-HTS线圈不同波形电流自场交流损耗的计算
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作者 赵明菲 崔英敏 李琦 《河北科技大学学报》 CAS 北大核心 2024年第5期471-478,共8页
针对无绝缘高温超导线圈在交流传输和减小屏蔽电流采用的电流扫描反转等各种传输波形引起的自场交流损耗问题,基于E-J幂指数模型,提出采用磁矢势A和电流矢势T的T-A方法中的均质化模型方法,模拟计算传输电流、频率和n值对无绝缘高温超导... 针对无绝缘高温超导线圈在交流传输和减小屏蔽电流采用的电流扫描反转等各种传输波形引起的自场交流损耗问题,基于E-J幂指数模型,提出采用磁矢势A和电流矢势T的T-A方法中的均质化模型方法,模拟计算传输电流、频率和n值对无绝缘高温超导饼式线圈的电流密度分布和传输交流损耗的影响。定量计算了双饼线圈中方波、锯齿波和正弦波的瞬时交流损耗;采用等效电路模型模拟分析了充/放电速率对无绝缘高温超导线圈匝间电流分布的影响。结果表明:在几百至几千赫兹时,无绝缘线圈的交流损耗随频率的增加而增加;受线圈匝间电流径向流动的影响,无绝缘线圈快速充电初期可出现局部环向电流反向,急速放电初期产生局部环向电流增加的情况。所得结果可以为无绝缘高温超导线圈的稳定性和交流损耗研究提供一定的理论参考。 展开更多
关键词 超导物理学 高温超导磁体 无绝缘线圈 REBCO 交流损耗
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High-temperature superconducting filter using self-embedding asymmetric stepped impedance resonator with wide stopband performance and miniaturized size
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作者 王丹 魏斌 +1 位作者 衡勇 曹必松 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第10期477-482,共6页
In this study, a novel self-embedding asymmetric stepped impedance resonator (SE-ASIR) topology is proposed. By embedding asymmetric stepped impedance resonators in themselves, circuit sizes of ASIRs can be reduced ... In this study, a novel self-embedding asymmetric stepped impedance resonator (SE-ASIR) topology is proposed. By embedding asymmetric stepped impedance resonators in themselves, circuit sizes of ASIRs can be reduced effectively, while the ability to control spurious modes of ASIRs remains. Therefore, SE-ASIRs are suitable for being used to design filters with wide stopbands and miniaturized sizes. Furthermore, the construction process of the SE-ASIR is described in detail, and an equivalent model of the SE-ASIR is proposed. For demonstration, a high-temperature superconducting bandpass filter centered at 1112 MHz is designed and fabricated. The measured result agrees well with the simulation result and shows that the out-of-band rejection is better than 60 dB up to 4088 MHz, which is about 3.7 times the center frequency. The filter circuit size is 31 mm × 13 mm or 0.28λg × 0.12λg, where g is the guided wavelength at 1112 MHz. 展开更多
关键词 high-temperature superconducting bandpass filter microstrip filter wide stopband
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Summary of the First Generation High Temperature Superconducting Wire: Processing, Characterization and Applications
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作者 金建勋 郭远昌 +4 位作者 张刚 王厚军 徐红兵 田书林 童玲 《Journal of Electronic Science and Technology of China》 2006年第1期63-70,共8页
Silver-clad (Bi,Pb)2Sr2Ca2Cu3O10+x long wires produced by powder-in-tube techniques, which have been recognized as the first generation of the High Temperature Superconducting (HTS) wires, are expected to apply w... Silver-clad (Bi,Pb)2Sr2Ca2Cu3O10+x long wires produced by powder-in-tube techniques, which have been recognized as the first generation of the High Temperature Superconducting (HTS) wires, are expected to apply widely especially in strong current applications. In this work, the processing, characterization and application of the silver-clad (Bi,Pb)2Sr2Ca2Cu3Ol0+x HTS wires are summarized. The HTS wires are fabricated using the combination of powder-in-tube technique, and the resulting wires are fully characterized by the means of chemical analyses, microstructural observation, electrical and magnetic measurements. The relationship among fabrication parameters, chemical and microstructural characteristics, and electrical and magnetic properties are analyzed. Applications of the HTS wires have also been introduced according to their strong current behaviors with various prototype devices made. 展开更多
关键词 high temperature superconductors (hts Bi-2223 tapes critical currents high temperature superconductor applications
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Explanation of Pressure Effect for High Temperature Superconductors Using Pressure Dependent Schrodinger Equation and String Theory 被引量:2
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作者 Einas Mohamed Ahmed Mohamed Nagwa Idriss Ali Ahmed +3 位作者 Musa Ibrahim Babiker Hussein Rasha Abd Elhai Mohammad Taha Mohammed Idriss Ahmed Mubarak Dirar Abd-Alla 《Natural Science》 2020年第1期28-34,共7页
A pressure dependent Schrodinger equation is used to find the conditions that lead to superconductivity. When no pressure is exerted, the superconductor resistance vanishes beyond a critical temperature related to the... A pressure dependent Schrodinger equation is used to find the conditions that lead to superconductivity. When no pressure is exerted, the superconductor resistance vanishes beyond a critical temperature related to the repulsive force potential of the electron gass, where one assuming the electron total energy to be thermal, where applying mechanical pressure destroys Sc when it exceeds a certain critical value. However when the electron total energy is an assumed to be that of the free electron model and that the pressure is thermal and mechanical, the situation is different. The quantum expression for resistance shows that the increase of mechanical pressure increases the critical temperature. Such phenomenon is observed in high temperature cupper group. 展开更多
关键词 PRESSURE DEPENDENT SCHRODINGER Equation superconductivity Critical temperature PRESSURE high temperature superconductor
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Orbital Approach to High Temperature Superconductivity 被引量:1
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作者 Peter Love 《Natural Science》 2019年第1期1-7,共7页
High temperature superconductivity in cuprates is explained in terms of 3d-orbital capture in copper. In elemental Cu 3d-orbital capture abstracts an electron from the 4 s2 valence orbital, and leaves it as 4 s1. This... High temperature superconductivity in cuprates is explained in terms of 3d-orbital capture in copper. In elemental Cu 3d-orbital capture abstracts an electron from the 4 s2 valence orbital, and leaves it as 4 s1. This is known since Cu occurs in Group IB of the Periodic Table. This forms an electron vacancy, or hole, in the valence shell. Therefore, the energy of 3d-orbital capture is stronger than the energy of unpairing of a paired-spin 4 s2 orbital. In cuprates 3d-orbital capture abstracts an electron from a Cu-O covalent bond, and leaves a hole in the excited state orbital. By electron-hole migration the excited state orbital leads to a coordinate covalent bond. This leads to superconductivity. The 3d-orbital process accounts for superconductivity and insulator behavior in cuprates. These results lend credence to the statement that 3d-orbital capture in copper is the cause of high temperature superconductivity. 展开更多
关键词 high temperature superconductIVITY D-Orbital CAPTURE CUPRATES COORDINATE COVALENT Bonding
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Nonlocal Theory of High-Temperature Superconductivity 被引量:2
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作者 Boris V. Alexeev 《Journal of Modern Physics》 2021年第5期552-593,共42页
The Boltzmann local physical kinetics forecasts the destruction of SC regime because of the heat movement of particles. Then, the most fundamental distinction between a strange metal and a conventional metal is the ab... The Boltzmann local physical kinetics forecasts the destruction of SC regime because of the heat movement of particles. Then, the most fundamental distinction between a strange metal and a conventional metal is the absence of well-defined quasi-particles. Here, we show that the mentioned “quasi-particles” are solitons, which are formed as a result of self-organization of ionized matter. Shortcomings of the Boltzmann physical kinetics consist in the local description of the transport processes on the level of infinitely small physical volumes as elements of diagnostics. The non-local physics leads to the theory superconductivity including the high temperature diapason. The generalized non-local non-stationary London’s formula is derived. 展开更多
关键词 high temperature superconductivity Generalized London’s Formula Nonlocal Physics Transport Processes in superconductors Longitudinal Electromagnetic Waves Solitons in superconductors
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High Temperature Superconductivity in the Past Twenty Years Part 2——Towards to Practical Applications 被引量:1
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作者 Jian-Xun Jin 《Journal of Electronic Science and Technology of China》 2008年第2期237-254,共18页
After discovering high temperature superconducting materials 20 years ago, the preparation of applicable HTS materials has been pursued along with HTS mechanism and characteristic study. At present, the focus on the a... After discovering high temperature superconducting materials 20 years ago, the preparation of applicable HTS materials has been pursued along with HTS mechanism and characteristic study. At present, the focus on the applied HTS technology has been moving to the industrial preparations from the laboratory research stage, and the technology has been well verified for practical applications from small to large scales. The fabrication techniques of engineering HTS materials are being industrialized; and various HTS devices are also on the way towards practical applications. This paper provides a comprehensive summary on the applied high temperature superconductivity with regard to various applicable HTS materials, their preparation techniques and charac- terization, and applications in a wide range. 展开更多
关键词 high temperature superconductors(hts hts applications strong current applications critical currents magnetic fields.
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Superconducting Electronics Research at CSIRO Australia——20 Years after Discovery of HTS 被引量:1
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作者 Cathy P. Foley Keith L. Leslie 《Journal of Electronic Science and Technology of China》 2008年第2期216-224,共9页
CSIRO has had a long-term research effort in superconductivity, in particular, since the discovery of HTS which promised big prospects. Significant progress has been made in research and development of HTS electronic ... CSIRO has had a long-term research effort in superconductivity, in particular, since the discovery of HTS which promised big prospects. Significant progress has been made in research and development of HTS electronic devices and systems for practical applications such as mineral and exploration as well as some niche applications in emerging science and technology areas. This article presents an overview of the CSIRO research activities in HTS supercon- ducting electronics since 1987, outlining the HTS junction and device technology as well as various application systems developed by the group. 展开更多
关键词 high temperature superconductivity superconductor electronics superconductor applications step-edge Josephson junction superconductor quantuminterference device.
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Using the tight binding approximation in deriving the quantum critical temperature superconductivity equation
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作者 R. Abd Elhai M. H. M. Hilo +1 位作者 R. Abd Elgani M. D. Abd Allah 《Natural Science》 2013年第8期941-946,共6页
Superconductivity is one of the most important phenomena in solid state physics. Its theoretical framework at low critical temperature Tc is?based on Bardeen, Cooper and Schrieffer theory (BCS). But at high Tc above 1... Superconductivity is one of the most important phenomena in solid state physics. Its theoretical framework at low critical temperature Tc is?based on Bardeen, Cooper and Schrieffer theory (BCS). But at high Tc above 135, this theory suffers from some setbacks. It cannot explain how the resistivity abruptly drops to zero below Tc , besides the explanation of the so called pseudo gap, isotope and pressure effect, in addition to the phase transition from insulating to super-conductivity state. The models proposed to cure this drawback are mainly based on Hubbard model which has a mathematical complex framework. In this work a model based on quantum mechanics besides generalized special relativity and plasma physics. It is utilized to get new modified Schr?dinger equation sensitive to temperature. An expression for quantum resistance is also obtained which shows existence of critical temperature beyond which the resistance drops to zero. It gives an expression which shows the relation between the energy gap and Tc . These expressions are mathematically simple and are in conformity with experimental results. 展开更多
关键词 superconductIVITY high CRITICAL temperature TIGht BINDING APPROXIMATION
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High Temperature Superconductivity in the Past Twenty Years Part 1——Discovery, Material, and Theory
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作者 Jian-Xun Jin 《Journal of Electronic Science and Technology of China》 2008年第2期225-236,共12页
Twenty years after the discovery of hightemperature superconductors (HTSs), the HTS materials now have been well developed. Meanwhile the mechanism of superconductivity is still one of the topical interests in physi... Twenty years after the discovery of hightemperature superconductors (HTSs), the HTS materials now have been well developed. Meanwhile the mechanism of superconductivity is still one of the topical interests in physics. The achievements made on HTS materials and theories during the last twenty years are reviewed comprehensively in this paper. 展开更多
关键词 high temperature superconductivity high temperature superconductor high temperaturesuperconducting theory
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Announcing a Special Issue of the Journal of Electronic Science and Technology of China on High Temperature Superconductivity
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《Journal of Electronic Science and Technology of China》 2007年第2期191-191,共1页
Submission Deadline: 15 February 2008 Journal of Electronic Science and Technology of China (JESTC) invites manuscript
关键词 hts Announcing a Special Issue of the Journal of Electronic Science and Technology of China on high temperature superconductivity
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Announcing a Special Issue of the Journal of Electronic Science and Technology of China on High Temperature Superconductivity
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《Journal of Electronic Science and Technology of China》 2007年第3期288-288,共1页
Journal of Electronic Science and Technology of China (JESTC) invites manuscript submissions in the area of High Temperature Superconductivity (HTS). This special issue of
关键词 hts Announcing a Special Issue of the Journal of Electronic Science and Technology of China on high temperature superconductivity
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Announcing a Special Issue of the Journal of Electronic Science and Technology of China on High Temperature Superconductivity
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《Journal of Electronic Science and Technology of China》 2007年第4期378-378,共1页
Submission Deadline: 15 February 2008 Journal of Electronic Science and Technology of China (JESTC) invites manuscript submissions in the area of High Temperature Superconductivity (HTS). This special issue of JESTC w... Submission Deadline: 15 February 2008 Journal of Electronic Science and Technology of China (JESTC) invites manuscript submissions in the area of High Temperature Superconductivity (HTS). This special issue of JESTC will focus on recent experiment, theoretical, and application progress in HTS. It is intended to highlight and summarize the major developments that have occurred over the past few years. Topic scopes related to HTS to be covered include: 展开更多
关键词 hts Announcing a Special Issue of the Journal of Electronic Science and Technology of China on high temperature superconductivity
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Correlated-Electron Systems and High-Temperature Superconductivity
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作者 Takashi Yanagisawa Mitake Miyazaki Kunihiko Yamaji 《Journal of Modern Physics》 2013年第6期33-64,共32页
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-tempe... We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping. 展开更多
关键词 high-temperature superconductIVITY STRONGLY CORRELATED ELECTRONS Monte Carlo Methods HUBBARD Model CONDENSATION Energy Pair-Correlation Function
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