Anomalous Symmetry Protected Topological States in Interacting Fermion Systems

被引：14

作者：

Wang, Qing-Rui ^{[1
]}

Qi, Yang ^{[2
,3
,4
]}

Gu, Zheng-Cheng ^{[1
]}

机构：

[1] Chinese Univ Hong Kong, Dept Phys, Shatin, Hong Kong, Peoples R China

[2] Fudan Univ, Dept Phys, Ctr Field Theory & Particle Phys, Shanghai 200433, Peoples R China

[3] Fudan Univ, State Key Lab Surface Phys, Shanghai 200433, Peoples R China

[4] Collaborat Innovat Ctr Adv Microstruct, Nanjing 210093, Jiangsu, Peoples R China

来源：

PHYSICAL REVIEW LETTERS | 2019年 / 123卷 / 20期

基金：

美国国家科学基金会;

关键词：

In this Letter; we systematically construct ASPT phases for 2D interacting fermion systems with total symmetry G f = G b × Z 2 f . Experimentally; 3D superconductivities with coplanar spin order can realize the T 2 = 1 symmetry. The surface of the He 3 B phase could also be a potential venue for finding such an ASPT state. We would like to thank Chenjie Wang for the insightful comments and suggestions. Z.-C. G. acknowledges Direct Grant No. 4053300 from The Chinese University of Hong Kong and funding from Hong Kong’s Research Grants Council (ECS No. 24301516). Y. Q. acknowledges support from Ministry of Science and Technology of China under Grant No. 2015CB921700; and from the National Science Foundation of China under Grant No. 11874115. [1] 1 Z.-C. Gu and X.-G. Wen; Phys; Rev; B; 80; 155131 ( 2009 ). PRBMDO 1098-0121 10.1103/PhysRevB.80.155131 [2] 2 M. Z. Hasan and C. L. Kane; Mod; 82; 3045 ( 2010 ). RMPHAT 0034-6861 10.1103/RevModPhys.82.3045 [3] 3 X.-L. Qi and S.-C. Zhang; 83; 1057; 2011; RMPHAT; 0034-6861; 10.1103/RevModPhys.83.1057; 4; C; Wang; A. C; Potter; and T. Senthil; Science; 343; 629 ( 2014 ). SCIEAS 0036-8075 10.1126/science.1243326 [5] 5 C. Wang and T. Senthil; 89; 195124 ( 2014 ). PRBMDO 1098-0121 10.1103/PhysRevB.89.195124 [6] 6 D. S. Freed and M. J. Hopkins; arXiv:1604.06527; 7; E; Witten; 88; 035001; 2016; 10.1103/RevModPhys.88.035001; 8; A; Kapustin; R; Thorngren; Turzillo; and Z. Wang; J. High Energy Phys. 12 ( 2015 ) 052 . JHEPFG 1029-8479 10.1007/JHEP12(2015)052 [9] 9 L. Fu; Lett; 106; 106802; PRLTAO; 0031-9007; 10.1103/PhysRevLett.106.106802; 10; X; Chen; Z.-C; Gu; Z.-X; Liu; and X.-G. Wen; 87; 155114; 2013; PRBMDO; 1098-0121; 10.1103/PhysRevB.87.155114; 11; 338; 1604 ( 2012 ). SCIEAS 0036-8075 10.1126/science.1227224 [12] 12 M. Levin and Z.-C. Gu; 86; 115109 ( 2012 ). PRBMDO 1098-0121 10.1103/PhysRevB.86.115109 [13] In many cases; the 2D boundary of 3D SPT states could realize the so-called anomalous topologically ordered states with ground state degeneracy on the torus; and we also refer to these topological degeneracies as gapless. [14] 14 A. Vishwanath and T. Senthil; 3; 011016 ( 2013 ). PRXHAE 2160-3308 10.1103/PhysRevX.3.011016 [15] 15 C. Wang and T. Senthil; 235122; 10.1103/PhysRevB.87.235122; 16; L; Fidkowski; and A. Vishwanath; 041016; PRXHAE; 2160-3308; 10.1103/PhysRevX.3.041016; 17; F. J; Burnell; Vishwanath; and L. Fidkowski; 5; 041013; 2015; 10.1103/PhysRevX.5.041013; 18; P; Bonderson; Nayak; and X.-L. Qi; J. Stat. Mech. ( 2013 ) P09016 . [!text type='JS']JS[!/text]MTC6 1742-5468 10.1088/1742-5468/2013/09/P09016 [19] 19 C. Wang; 115137; 10.1103/PhysRevB.88.115137; 20; 165132; 2014; 10.1103/PhysRevB.89.165132; 21; M. A; Metlitski; arXiv:1406.3032; 22; C. L; Kane; and M. P. A. Fisher; 92; 125111; 10.1103/PhysRevB.92.125111; 23; C.-H; Lin; and M. Levin; 6; 021015; 10.1103/PhysRevX.6.021015; 24; arXiv:1403.1467; 25; X.-G; Wen; 91; 205101 ( 2015 ). PRBMDO 1098-0121 10.1103/PhysRevB.91.205101 [26] 26 Z.-C. Gu and X.-G. Wen; 90; 115141;

D O I：

10.1103/PhysRevLett.123.207003

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The classification and construction of symmetry protected topological (SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there exists a new class of the so-called anomalous SPT (ASPT) states which are only well defined on the boundary of a trivial fermionic bulk system. We first demonstrate the essential idea by considering an anomalous topological superconductor with time-reversal symmetry T-2 = 1 in 2D. The physical reason for this is that the fermion parity might be changed locally by certain symmetry action, but it is conserved if we introduce a bulk. Then we discuss the layer structure and systematical construction of ASPT states in interacting fermion systems in 2D with a total symmetry G(f) = G(b) x Z(2)(f). Finally, potential experimental realizations of ASPT states are also addressed.

引用

页数：6

共 43 条

[1]

[Anonymous], ARXIV14063032

[2]

[Anonymous], ARXIV160406527

[3] Symmetry fractionalization, defects, and gauging of topological phases [J].

Barkeshli, Maissam ;

Bonderson, Parsa ;

Cheng, Meng ;

Wang, Zhenghan .

PHYSICAL REVIEW B, 2019, 100 (11)

[4] A time-reversal invariant topological phase at the surface of a 3D topological insulator [J].

Bonderson, Parsa ;

Nayak, Chetan ;

Qi, Xiao-Liang .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2013,

[5] Anomalous Symmetry Fractionalization and Surface Topological Order [J].

Chen, Xie ;

Burnell, F. J. ;

Vishwanath, Ashvin ;

Fidkowski, Lukasz .

PHYSICAL REVIEW X, 2015, 5 (04)

[6] Symmetry enforced non-Abelian topological order at the surface of a topological insulator [J].

Chen, Xie ;

Fidkowski, Lukasz ;

Vishwanath, Ashvin .

PHYSICAL REVIEW B, 2014, 89 (16)

[7] Symmetry protected topological orders and the group cohomology of their symmetry group [J].

Chen, Xie ;

Gu, Zheng-Cheng ;

Liu, Zheng-Xin ;

Wen, Xiao-Gang .

PHYSICAL REVIEW B, 2013, 87 (15)

[8] Symmetry-Protected Topological Orders in Interacting Bosonic Systems [J].

Chen, Xie ;

Gu, Zheng-Cheng ;

Liu, Zheng-Xin ;

Wen, Xiao-Gang .

SCIENCE, 2012, 338 (6114) :1604-1606

[9] Classification of symmetry-protected phases for interacting fermions in two dimensions [J].

Cheng, Meng ;

Bi, Zhen ;

You, Yi-Zhuang ;

Gu, Zheng-Cheng .

PHYSICAL REVIEW B, 2018, 97 (20)

[10] Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions [J].

Cheng, Meng ;

Tantivasadakarn, Nathanan ;

Wang, Chenjie .

PHYSICAL REVIEW X, 2018, 8 (01)

← 1 2 3 4 5 →