Please wait a minute...
Chin. Phys. B, 2022, Vol. 31(8): 087104    DOI: 10.1088/1674-1056/ac7a14
Special Issue: TOPICAL REVIEW — Celebrating 30 Years of Chinese Physics B
TOPICAL REVIEW—Celebrating 30 Years of Chinese Physics B Prev   Next  

Mottness, phase string, and high-Tc superconductivity

Jing-Yu Zhao(赵靖宇) and Zheng-Yu Weng(翁征宇)
Institute for Advanced Study, Tsinghua University, Beijing 100084, China
Abstract  It is a great discovery in physics of the twentieth century that the elementary particles in nature are dictated by gauge forces, characterized by a nonintegrable phase factor that an elementary particle of charge $q$ acquires from $A$ to $B$ points: $P \exp \left( \text{i} \frac q {\hbar c}\int_A^B A_{\mu}\text{d} x^{\mu}\right),$ where $A_{\mu}$ is the gauge potential and $P$ stands for path ordering. In a many-body system of strongly correlated electrons, if the so-called Mott gap is opened up by interaction, the corresponding Hilbert space will be fundamentally changed. A novel nonintegrable phase factor known as phase-string will appear and replace the conventional Fermi statistics to dictate the low-lying physics. Protected by the Mott gap, which is clearly identified in the high-$T_{\rm c}$ cuprate with a magnitude $> 1.5$ eV, such a singular phase factor can enforce a fractionalization of the electrons, leading to a dual world of exotic elementary particles with a topological gauge structure. A non-Fermi-liquid "parent" state will emerge, in which the gapless Landau quasiparticle is only partially robust around the so-called Fermi arc regions, while the main dynamics are dominated by two types of gapped spinons. Antiferromagnetism, superconductivity, and a Fermi liquid with full Fermi surface can be regarded as the low-temperature instabilities of this new parent state. Both numerics and experiments provide direct evidence for such an emergent physics of the Mottness, which lies in the core of a high-$T_{\rm c}$ superconducting mechanism.
Keywords:  mechanism of high-Tc superconductivity      doped Mott insulator      emergent organizing principle  
Received:  18 April 2022      Revised:  13 June 2022      Accepted manuscript online:  18 June 2022
PACS:  71.27.+a (Strongly correlated electron systems; heavy fermions)  
  74.20.-z (Theories and models of superconducting state)  
  74.72.-h (Cuprate superconductors)  
Fund: Stimulating discussions with Shuai Chen, Donna Sheng, Jan Zaanen, and Jia-Xin Zhang are acknowledged. A partial support of this work by the National Key R&D Program of China (Grant No. 2017YFA0302902) is also acknowledged.
Corresponding Authors:  Zheng-Yu Weng     E-mail:  weng@mail.tsinghua.edu.cn

Cite this article: 

Jing-Yu Zhao(赵靖宇) and Zheng-Yu Weng(翁征宇) Mottness, phase string, and high-Tc superconductivity 2022 Chin. Phys. B 31 087104

[1] Yang C N 1974 Phys. Rev. Lett. 33 445
[2] Wu T T and Yang C N 1975 Phys. Rev. D 12 3845
[3] Abrikosov A A, Gor'kov L P and Dzyaloshinskii E 1963 Method of Quantm Field Theory in Statistical Physics (Englewood Cliffs:Prentice-Hall)
[4] Pines D and Nozieres P 1965 Theory of Quantum Liquids (New York:Benjamin)
[5] Lee P A, Nagaosa N and Wen X G 2006 Rev. Mod. Phys. 78 17
[6] Anderson P W 1987 Science 235 1196
[7] Anderson P W 1997 The Theory of Superconductivity in the High Tc Cuprates (Princeton:Princeton Univ. Press)
[8] Ye C, Cai P, Yu R, Zhou X, Ruan W, Liu Q, Jin C and Wang Y 2013 Nat. Commun. 4 1365
[9] Keimer B, Kivelson S A, Norman M R, Uchida S and Zaanen J 2015 Nature 518 179
[10] Weng Z Y 2007 Intl. J. Mod. Phys. B 21 773; arXiv:0704.2875
[11] Weng Z Y 2011 Front. Phys. 6 370; arXiv:1110.0546
[12] Zaanen J and Overbosch B J 2011 Phil. Trans. R. Soc. A 369 1599; arXiv:0911.4070
[13] Anderson P W, Lee P A, Randeria M, Rice T M, Trivedi N and Zhang F C 2004 J. Phys.:Condens. Matter 16 R755 and references therein
[14] For a review, see, Edegger B, Muthukumar V N and Gros C 2007 Adv. Phys. 56 927
[15] Wen X G 2019 Science 363 eaal3099
[16] Sheng D N, Chen Y C and Weng Z Y 1996 Phys. Rev. Lett. 77 5102
[17] Wu K, Weng Z Y and Zaanen J 2008 Phys. Rev. B 77 155102
[18] Wu Y S 1984 Phys. Rev. Lett. 52 2103
[19] Zhang L and Weng Z Y 2014 Phys. Rev. B 90 165120
[20] Anderson P W 1990 Phys. Rev. Lett. 64 1839
[21] Anderson P W 1967 Phys. Rev. Lett. 18 1049
[22] Anderson P W 1967 Phys. Rev. 164 352
[23] Weng Z Y, Sheng D N, Chen Y C and Ting C S 1997 Phys. Rev. B 55 3894
[24] Weng Z Y, Sheng D N and Ting C S 1998 Phys. Rev. Lett. 80 5401
[25] Weng Z Y 2011 New J. Phys 13 103039
[26] Zhu Z, Jiang H C, Qi Y, Tian C and Weng Z Y 2013 Sci. Rep. 3 2586
[27] Wilczek F 1990 Fractional Statistics and Anyon Superconductivity (Singapore:World Scientific Publishing)
[28] Marshall W 1955 Proc. R. Soc. A 232 48
[29] Zheng W, Zhu Z, Sheng D N and Weng Z Y 2018 Phys. Rev. B 98 165102
[30] Zhu Z, Wang Q R, Sheng D N and Weng Z Y 2016 Nucl. Phys. B 903 51
[31] Zheng W and Weng Z Y 2018 Sci. Rep. 8 3612
[32] Zhu Z and Weng Z Y 2015 Phys. Rev. B 92 235156
[33] Zhu Z, Sheng D N and Weng Z Y 2018 Phys. Rev. B 98 035129
[34] Sun R Y, Zhu Z and Weng Z Y 2019 Phys. Rev. Lett. 123 016601
[35] He R Q and Weng Z Y 2016 Sci. Rep. 6 35208
[36] Zhu Z, Weng Z Y and Ho T L 2016 Phys. Rev. A 93 033614
[37] Shinjo K, Sota S and Tohyama T 2021 Phys. Rev. B 103 035141
[38] Zhu Z, Jiang H C, Sheng D N and Weng Z Y 2014 Sci. Rep. 4 5419
[39] Zhu Z, Sheng D N and Weng Z Y 2018 Phys. Rev. B 97 115144
[40] Jiang H C, Chen C and Weng Z Y 2020 Phys. Rev. B 102 104512
[41] Sun R Y, Zhu Z and Weng Z Y 2020 Phys. Rev. Res. 2 033007
[42] Jiang H C, Weng Z Y and Kivelson S A 2018 Phys. Rev. B 98 140505(R)
[43] Jiang Y F, Zaanen J, Devereaux T P and Jiang H C 2020 Phys. Rev. Res. 2 033073
[44] Jiang S, Scalapino D J and White S R 2021 Proc. Natl. Acad. Sci. USA 118 e2109978118
[45] Zhang J X, et al., 2022 in preparation.
[46] Ma Y, Ye P and Weng Z Y 2014 New J. Phys 16 083039
[47] Liang S, Doucot B and Anderson P W 1988 Phys. Rev. Lett. 61 365
[48] Wang Q R, Zhu Z, Qi Y and Weng Z Y 2015 arXiv:1509.01260
[49] Chen S, Wang Q R, Qi Y, Sheng D N and Weng Z Y 2019 Phys. Rev. B 99 205128
[50] Chen S A, Weng Z Y and Zaanen J 2022 Phys. Rev. B 105 075136
[51] Chen S, Zhu Z and Weng Z Y 2018 Phys. Rev. B 98 245138
[52] Zhao J Y, Chen S A, Zhang H K and Weng Z Y 2022 Phys. Rev. X 12 011062
[53] Note that here two twisted holes are defined by using the same sign of the phase-string factor in Eq. (21), a topological correction to the half-filling ground state should be included in|b-RVB> according to Ref.[52].
[54] Yang C N 1962 Rev. Mod. Phys. 34 694
[55] Kou S P, Qi X L and Weng Z Y 2005 Phys. Rev. B 71 235102
[56] Ye P, Tian C S, Qi X L and Weng Z Y 2011 Phys. Rev. Lett. 106 147002
[57] Ye P, Tian C S, Qi X L and Weng Z Y 2012 Nucl. Phys. B 854 815
[58] Zhang J H, Li S, Ma Y, Zhong Y, Ding H and Weng Z Y 2020 Phys. Rev. Res. 2 023398
[59] Mei J W and Weng Z Y 2010 Phys. Rev. B 81 014507
[60] Laughlin R B 1983 Phys. Rev. Lett. 50 1395
[61] Muthukumar V N and Weng Z Y 2002 Phys. Rev. B 65 174511
[62] Weng Z Y and Qi X L 2006 Phys. Rev. B 74 144518
[63] Qi X L and Weng Z Y 2007 Phys. Rev. B 76 104502
[64] Kou S P and Weng Z Y 2003 Phys. Rev. Lett. 90 157003
[65] Zhang J X, et al. 2022 in preparation
[66] Gu Z C and Weng Z Y 2005 Phys. Rev. B 72 104520
[67] Anderson P W 1972 Science 177 393
[68] Laughlin R B and Pines D 2000 Proc. Natl. Acad. Sci. USA 97 28
[1] CrAlGe: An itinerant ferromagnet with strong tunability by heat treatment
Zhaokun Dong(董昭昆), Zhen Wang(王振), Te Zhang(张特), Junsen Xiang(项俊森), Shuai Zhang(张帅), Lihua Liu(刘丽华), and Peijie Sun(孙培杰). Chin. Phys. B, 2022, 31(11): 117502.
[2] Kondo screening cloud in a superconductor with mixed s-wave and p-wave pairing states
Zhen-Zhen Huang(黄真真), Xiong-Tao Peng(彭雄涛), Wan-Sheng Wang(王万胜), and Jin-Hua Sun(孙金华). Chin. Phys. B, 2022, 31(10): 107101.
[3] Effect of f-c hybridization on the $\gamma\to \alpha$ phase transition of cerium studied by lanthanum doping
Yong-Huan Wang(王永欢), Yun Zhang(张云), Yu Liu(刘瑜), Xiao Tan(谈笑), Ce Ma(马策), Yue-Chao Wang(王越超), Qiang Zhang(张强), Deng-Peng Yuan(袁登鹏), Dan Jian(简单), Jian Wu(吴健), Chao Lai(赖超), Xi-Yang Wang(王西洋), Xue-Bing Luo(罗学兵), Qiu-Yun Chen(陈秋云), Wei Feng(冯卫), Qin Liu(刘琴), Qun-Qing Hao(郝群庆), Yi Liu(刘毅), Shi-Yong Tan(谭世勇), Xie-Gang Zhu(朱燮刚), Hai-Feng Song(宋海峰), and Xin-Chun Lai(赖新春). Chin. Phys. B, 2022, 31(8): 087102.
[4] Uniaxial stress effect on quasi-one-dimensional Kondo lattice CeCo2Ga8
Kangqiao Cheng(程康桥), Binjie Zhou(周斌杰), Cuixiang Wang(王翠香), Shuo Zou(邹烁), Yupeng Pan(潘宇鹏), Xiaobo He(何晓波), Jian Zhang(张健), Fangjun Lu(卢方君), Le Wang(王乐), Youguo Shi(石友国), and Yongkang Luo(罗永康). Chin. Phys. B, 2022, 31(6): 067104.
[5] Real-space parallel density matrix renormalization group with adaptive boundaries
Fu-Zhou Chen(陈富州), Chen Cheng(程晨), and Hong-Gang Luo(罗洪刚). Chin. Phys. B, 2021, 30(8): 080202.
[6] CeAu2In4: A candidate of quasi-one-dimensional antiferromagnetic Kondo lattice
Meng Lyu(吕孟), Hengcan Zhao(赵恒灿), Jiahao Zhang(张佳浩), Zhen Wang(王振), Shuai Zhang(张帅), and Peijie Sun(孙培杰). Chin. Phys. B, 2021, 30(8): 087101.
[7] Magnetic impurity in hybrid and type-II nodal line semimetals
Xiao-Rong Yang(杨晓容), Zhen-Zhen Huang(黄真真), Wan-Sheng Wang(王万胜), and Jin-Hua Sun(孙金华). Chin. Phys. B, 2021, 30(6): 067103.
[8] Resistivity minimum emerges in Anderson impurity model modified with Sachdev-Ye-Kitaev interaction
Lan Zhang(张欄), Yin Zhong(钟寅), and Hong-Gang Luo(罗洪刚). Chin. Phys. B, 2021, 30(4): 047106.
[9] Intercalation of van der Waals layered materials: A route towards engineering of electron correlation
Jingjing Niu(牛晶晶), Wenjie Zhang(章文杰), Zhilin Li(李治林), Sixian Yang(杨嗣贤), Dayu Yan(闫大禹), Shulin Chen(陈树林), Zhepeng Zhang(张哲朋), Yanfeng Zhang(张艳锋), Xinguo Ren(任新国), Peng Gao(高鹏), Youguo Shi(石友国), Dapeng Yu(俞大鹏), Xiaosong Wu(吴孝松). Chin. Phys. B, 2020, 29(9): 097104.
[10] Improved hybrid parallel strategy for density matrix renormalization group method
Fu-Zhou Chen(陈富州), Chen Cheng(程晨), Hong-Gang Luo(罗洪刚). Chin. Phys. B, 2020, 29(7): 070202.
[11] Lifshitz transition in triangular lattice Kondo-Heisenberg model
Lan Zhang(张欄), Yin Zhong(钟寅), Hong-Gang Luo(罗洪刚). Chin. Phys. B, 2020, 29(7): 077102.
[12] Point-contact spectroscopy on antiferromagnetic Kondo semiconductors CeT2Al10 (T=Ru and Os)
Jie Li(李洁), Li-Qiang Che(车利强), Tian Le(乐天), Jia-Hao Zhang(张佳浩), Pei-Jie Sun(孙培杰), Toshiro Takabatake, Xin Lu(路欣). Chin. Phys. B, 2020, 29(7): 077103.
[13] Electronic structure and spatial inhomogeneity of iron-based superconductor FeS
Chengwei Wang(王成玮), Meixiao Wang(王美晓), Juan Jiang(姜娟), Haifeng Yang(杨海峰), Lexian Yang(杨乐仙), Wujun Shi(史武军), Xiaofang Lai(赖晓芳), Sung-Kwan Mo, Alexei Barinov, Binghai Yan(颜丙海), Zhi Liu(刘志), Fuqiang Huang(黄富强), Jinfeng Jia(贾金峰), Zhongkai Liu(柳仲楷), Yulin Chen(陈宇林). Chin. Phys. B, 2020, 29(4): 047401.
[14] Electronic structure of correlated topological insulator candidate YbB6 studied by photoemission and quantum oscillation
T Zhang(张腾), G Li(李岗), S C Sun(孙淑翠), N Qin(秦娜), L Kang(康璐), S H Yao(姚淑华), H M Weng(翁红明), S K Mo, L Li(李璐), Z K Liu(柳仲楷), L X Yang(杨乐仙), Y L Chen(陈宇林). Chin. Phys. B, 2020, 29(1): 017304.
[15] Giant topological Hall effect of ferromagnetic kagome metal Fe3Sn2
Qi Wang(王琦), Qiangwei Yin(殷蔷薇), Hechang Lei(雷和畅). Chin. Phys. B, 2020, 29(1): 017101.
No Suggested Reading articles found!