Topological order in interacting semimetals

Yi, Jinmin; Ying, Xuzhe; Gioia, Lei; Burkov, A. A.

doi:10.1103/physrevb.107.115147

Topological order in interacting semimetals

Journal Article · Fri Mar 24 00:00:00 EDT 2023 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.107.115147· OSTI ID:2423805

^[1]; ^[1]; Gioia, Lei ^[1]; ^[1]

University of Waterloo, ON (Canada); N2L 3G1 and Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a non-Abelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. Here, this may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED₃ to 3+1 dimensions. In addition we discuss a (3+1)-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.

View Accepted Manuscript (DOE)

Research Organization:: Ames Laboratory (AMES), Ames, IA (United States). Center for the Advancement of Topological Semimetals (CATS)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-07CH11358

OSTI ID:: 2423805

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 11 Vol. 107; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (80)

Fractons and Exotic Symmetries from Branes Geng, Hao; Kachru, Shamit; Karch, Andreas Fortschritte der Physik, Vol. 69, Issue 11-12 https://doi.org/10.1002/prop.202100133	journal	October 2021
(3+1)-TQFTs and topological insulators Walker, Kevin; Wang, Zhenghan Frontiers of Physics, Vol. 7, Issue 2 https://doi.org/10.1007/s11467-011-0194-z	journal	July 2011
Bosonization in higher dimensions Burgess, C. P.; Lütken, C. A.; Quevedo, F. Physics Letters B, Vol. 336, Issue 1 https://doi.org/10.1016/0370-2693(94)00963-5	journal	September 1994
Bosonization as duality Burgess, C. P.; Quevedo, F. Nuclear Physics B, Vol. 421, Issue 2 https://doi.org/10.1016/0550-3213(94)90332-8	journal	June 1994
Anyons in an exactly solved model and beyond Kitaev, Alexei Annals of Physics, Vol. 321, Issue 1 https://doi.org/10.1016/j.aop.2005.10.005	journal	January 2006
A duality web in 2 + 1 dimensions and condensed matter physics Seiberg, Nathan; Senthil, T.; Wang, Chong Annals of Physics, Vol. 374 https://doi.org/10.1016/j.aop.2016.08.007	journal	November 2016
Fermion–fermion duality in 3+1 dimensions Palumbo, Giandomenico Annals of Physics, Vol. 419 https://doi.org/10.1016/j.aop.2020.168240	journal	August 2020
Weyl Mott Insulator Morimoto, Takahiro; Nagaosa, Naoto Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep19853	journal	January 2016
Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase No authors listed New Journal of Physics, Vol. 9, Issue 9 https://doi.org/10.1088/1367-2630/9/9/356	journal	September 2007
A time-reversal invariant topological phase at the surface of a 3D topological insulator Bonderson, Parsa; Nayak, Chetan; Qi, Xiao-Liang Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 09 https://doi.org/10.1088/1742-5468/2013/09/P09016	journal	September 2013
Theory of the fractional quantum Hall effect in Weyl semimetals Thakurathi, Manisha; Burkov, A. A. Physical Review B, Vol. 101, Issue 23 https://doi.org/10.1103/PhysRevB.101.235168	journal	June 2020
Fermionic dualities with axial gauge fields Grushin, Adolfo G.; Palumbo, Giandomenico Physical Review B, Vol. 102, Issue 11 https://doi.org/10.1103/PhysRevB.102.115146	journal	September 2020
Charge density waves in Weyl semimetals Sehayek, Dan; Thakurathi, Manisha; Burkov, A. A. Physical Review B, Vol. 102, Issue 11 https://doi.org/10.1103/PhysRevB.102.115159	journal	September 2020
Topological polarization, dual invariants, and surface flat bands in crystalline insulators Nissinen, J.; Heikkilä, T. T.; Volovik, G. E. Physical Review B, Vol. 103, Issue 24 https://doi.org/10.1103/PhysRevB.103.245115	journal	June 2021
Emergent anomalies and generalized Luttinger theorems in metals and semimetals Wang, Chong; Hickey, Alexander; Ying, Xuzhe Physical Review B, Vol. 104, Issue 23 https://doi.org/10.1103/PhysRevB.104.235113	journal	December 2021
Toric-code insulator enriched by translation symmetry Tam, Pok Man; Venderbos, Jörn W. F.; Kane, Charles L. Physical Review B, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevB.105.045106	journal	January 2022
Dynamical effects from anomalies: Modified electrodynamics in Weyl semimetals Ying, Xuzhe; Burkov, A. A.; Wang, Chong Physical Review B, Vol. 107, Issue 3 https://doi.org/10.1103/PhysRevB.107.035131	journal	January 2023
Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces Wen, X. G.; Niu, Q. Physical Review B, Vol. 41, Issue 13 https://doi.org/10.1103/PhysRevB.41.9377	journal	May 1990
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect Read, N.; Green, Dmitry Physical Review B, Vol. 61, Issue 15 https://doi.org/10.1103/PhysRevB.61.10267	journal	April 2000
Z 2 gauge theory of electron fractionalization in strongly correlated systems Senthil, T.; Fisher, Matthew P. A. Physical Review B, Vol. 62, Issue 12 https://doi.org/10.1103/PhysRevB.62.7850	journal	September 2000
String-net condensation: A physical mechanism for topological phases Levin, Michael A.; Wen, Xiao-Gang Physical Review B, Vol. 71, Issue 4 https://doi.org/10.1103/PhysRevB.71.045110	journal	January 2005
Putting competing orders in their place near the Mott transition Balents, Leon; Bartosch, Lorenz; Burkov, Anton Physical Review B, Vol. 71, Issue 14 https://doi.org/10.1103/PhysRevB.71.144508	journal	April 2005
Superfluid-insulator transitions on the triangular lattice Burkov, A. A.; Balents, Leon Physical Review B, Vol. 72, Issue 13 https://doi.org/10.1103/PhysRevB.72.134502	journal	October 2005
Theory of a continuous Mott transition in two dimensions Senthil, T. Physical Review B, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevB.78.045109	journal	July 2008
Correlated topological insulators and the fractional magnetoelectric effect Swingle, B.; Barkeshli, M.; McGreevy, J. Physical Review B, Vol. 83, Issue 19 https://doi.org/10.1103/PhysRevB.83.195139	journal	May 2011
Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates Wan, Xiangang; Turner, Ari M.; Vishwanath, Ashvin Physical Review B, Vol. 83, Issue 20 https://doi.org/10.1103/PhysRevB.83.205101	journal	May 2011
Topological nodal semimetals Burkov, A. A.; Hook, M. D.; Balents, Leon Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235126	journal	December 2011
Weyl superconductors Meng, Tobias; Balents, Leon Physical Review B, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevB.86.054504	journal	August 2012
Continuous transitions between composite Fermi liquid and Landau Fermi liquid: A route to fractionalized Mott insulators Barkeshli, Maissam; McGreevy, John Physical Review B, Vol. 86, Issue 7 https://doi.org/10.1103/PhysRevB.86.075136	journal	August 2012
Topological response in Weyl semimetals and the chiral anomaly Zyuzin, A. A.; Burkov, A. A. Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115133	journal	September 2012
Superconductivity of doped Weyl semimetals: Finite-momentum pairing and electronic analog of the 3 He- A phase Cho, Gil Young; Bardarson, Jens H.; Lu, Yuan-Ming Physical Review B, Vol. 86, Issue 21 https://doi.org/10.1103/PhysRevB.86.214514	journal	December 2012
Three-dimensional topological lattice models with surface anyons von Keyserlingk, C. W.; Burnell, F. J.; Simon, S. H. Physical Review B, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevB.87.045107	journal	January 2013
Effective field theories for topological insulators by functional bosonization Chan, AtMa; Hughes, Taylor L.; Ryu, Shinsei Physical Review B, Vol. 87, Issue 8 https://doi.org/10.1103/PhysRevB.87.085132	journal	February 2013
Cancellation of quantum anomalies and bosonization of three-dimensional time-reversal symmetric topological insulators Zirnstein, Heinrich-Gregor; Rosenow, Bernd Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevB.88.085105	journal	August 2013
Gapped symmetry preserving surface state for the electron topological insulator Wang, Chong; Potter, Andrew C.; Senthil, T. Physical Review B, Vol. 88, Issue 11 https://doi.org/10.1103/PhysRevB.88.115137	journal	September 2013
Symmetry enforced non-Abelian topological order at the surface of a topological insulator Chen, Xie; Fidkowski, Lukasz; Vishwanath, Ashvin Physical Review B, Vol. 89, Issue 16 https://doi.org/10.1103/PhysRevB.89.165132	journal	April 2014
Superconductivity in Weyl metals Bednik, G.; Zyuzin, A. A.; Burkov, A. A. Physical Review B, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevB.92.035153	journal	July 2015
Symmetry-respecting topologically ordered surface phase of three-dimensional electron topological insulators Metlitski, Max A.; Kane, C. L.; Fisher, Matthew P. A. Physical Review B, Vol. 92, Issue 12 https://doi.org/10.1103/PhysRevB.92.125111	journal	September 2015
Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases Ye, Peng; Gu, Zheng-Cheng Physical Review B, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevB.93.205157	journal	May 2016
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators Metlitski, Max A.; Vishwanath, Ashvin Physical Review B, Vol. 93, Issue 24 https://doi.org/10.1103/PhysRevB.93.245151	journal	June 2016
Theory of a 3+1D fractional chiral metal: Interacting variant of the Weyl semimetal Meng, Tobias; Grushin, Adolfo G.; Shtengel, Kirill Physical Review B, Vol. 94, Issue 15 https://doi.org/10.1103/PhysRevB.94.155136	journal	October 2016
Topological surface superconductivity in doped Weyl loop materials Wang, Yuxuan; Nandkishore, Rahul M. Physical Review B, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevB.95.060506	journal	February 2017
Quasitopological electromagnetic response of line-node semimetals Ramamurthy, Srinidhi T.; Hughes, Taylor L. Physical Review B, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevB.95.075138	journal	February 2017
Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry Slagle, Kevin; Kim, Yong Baek Physical Review B, Vol. 96, Issue 19 https://doi.org/10.1103/PhysRevB.96.195139	journal	November 2017
Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials Shapourian, Hassan; Wang, Yuxuan; Ryu, Shinsei Physical Review B, Vol. 97, Issue 9 https://doi.org/10.1103/PhysRevB.97.094508	journal	March 2018
Quantum anomalies in nodal line semimetals Burkov, A. A. Physical Review B, Vol. 97, Issue 16 https://doi.org/10.1103/PhysRevB.97.165104	journal	April 2018
Composite Weyl semimetal as a parent state for three-dimensional topologically ordered phases Sagi, Eran; Stern, Ady; Mross, David F. Physical Review B, Vol. 98, Issue 20 https://doi.org/10.1103/PhysRevB.98.201111	journal	November 2018
From coupled wires to coupled layers: Model with three-dimensional fractional excitations Fuji, Yohei; Furusaki, Akira Physical Review B, Vol. 99, Issue 24 https://doi.org/10.1103/PhysRevB.99.241107	journal	June 2019
Limits on a Lorentz- and parity-violating modification of electrodynamics Carroll, Sean M.; Field, George B.; Jackiw, Roman Physical Review D, Vol. 41, Issue 4 https://doi.org/10.1103/PhysRevD.41.1231	journal	February 1990
Fractional Topological Insulators Levin, Michael; Stern, Ady Physical Review Letters, Vol. 103, Issue 19 https://doi.org/10.1103/PhysRevLett.103.196803	journal	November 2009
Fractional Topological Insulators in Three Dimensions Maciejko, Joseph; Qi, Xiao-Liang; Karch, Andreas Physical Review Letters, Vol. 105, Issue 24 https://doi.org/10.1103/PhysRevLett.105.246809	journal	December 2010
Weyl Semimetal in a Topological Insulator Multilayer Burkov, A. A.; Balents, Leon Physical Review Letters, Vol. 107, Issue 12 https://doi.org/10.1103/PhysRevLett.107.127205	journal	September 2011
Braiding Statistics of Loop Excitations in Three Dimensions Wang, Chenjie; Levin, Michael Physical Review Letters, Vol. 113, Issue 8 https://doi.org/10.1103/PhysRevLett.113.080403	journal	August 2014
Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( 2 + 1 ) Dimensions Mross, David F.; Alicea, Jason; Motrunich, Olexei I. Physical Review Letters, Vol. 117, Issue 1 https://doi.org/10.1103/PhysRevLett.117.016802	journal	June 2016
Exact Boson-Fermion Duality on a 3D Euclidean Lattice Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao Physical Review Letters, Vol. 120, Issue 1 https://doi.org/10.1103/PhysRevLett.120.016602	journal	January 2018
Topological Nodal Cooper Pairing in Doped Weyl Metals Li, Yi; Haldane, F. D. M. Physical Review Letters, Vol. 120, Issue 6 https://doi.org/10.1103/PhysRevLett.120.067003	journal	February 2018
Fractional Excitonic Insulator Hu, Yichen; Venderbos, Jörn W. F.; Kane, C. L. Physical Review Letters, Vol. 121, Issue 12 https://doi.org/10.1103/PhysRevLett.121.126601	journal	September 2018
Unpaired Weyl Nodes from Long-Ranged Interactions: Fate of Quantum Anomalies Meng, Tobias; Budich, Jan Carl Physical Review Letters, Vol. 122, Issue 4 https://doi.org/10.1103/PhysRevLett.122.046402	journal	February 2019
Fractional Quantum Hall Effect in Weyl Semimetals Wang, Chong; Gioia, L.; Burkov, A. A. Physical Review Letters, Vol. 124, Issue 9 https://doi.org/10.1103/PhysRevLett.124.096603	journal	March 2020
Foliated Quantum Field Theory of Fracton Order Slagle, Kevin Physical Review Letters, Vol. 126, Issue 10 https://doi.org/10.1103/PhysRevLett.126.101603	journal	March 2021
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations Laughlin, R. B. Physical Review Letters, Vol. 50, Issue 18 https://doi.org/10.1103/PhysRevLett.50.1395	journal	May 1983
Elasticity tetrads, mixed axial-gravitational anomalies, and ( 3 + 1 )-d quantum Hall effect Nissinen, J.; Volovik, G. E. Physical Review Research, Vol. 1, Issue 2 https://doi.org/10.1103/PhysRevResearch.1.023007	journal	September 2019
Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry Manjunath, Naren; Barkeshli, Maissam Physical Review Research, Vol. 3, Issue 1 https://doi.org/10.1103/PhysRevResearch.3.013040	journal	January 2021
Electric polarization as a nonquantized topological response and boundary Luttinger theorem Song, Xue-Yang; He, Yin-Chen; Vishwanath, Ashvin Physical Review Research, Vol. 3, Issue 2 https://doi.org/10.1103/PhysRevResearch.3.023011	journal	April 2021
Unquantized anomalies in topological semimetals Gioia, L.; Wang, Chong; Burkov, A. A. Physical Review Research, Vol. 3, Issue 4 https://doi.org/10.1103/PhysRevResearch.3.043067	journal	October 2021
Non-Fermi Liquids as Ersatz Fermi Liquids: General Constraints on Compressible Metals Else, Dominic V.; Thorngren, Ryan; Senthil, T. Physical Review X, Vol. 11, Issue 2 https://doi.org/10.1103/PhysRevX.11.021005	journal	April 2021
Layer Construction of 3D Topological States and String Braiding Statistics Jian, Chao-Ming; Qi, Xiao-Liang Physical Review X, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevX.4.041043	journal	December 2014
Composite Dirac Liquids: Parent States for Symmetric Surface Topological Order Mross, David F.; Essin, Andrew; Alicea, Jason Physical Review X, Vol. 5, Issue 1 https://doi.org/10.1103/PhysRevX.5.011011	journal	February 2015
Vortex-Line Condensation in Three Dimensions: A Physical Mechanism for Bosonic Topological Insulators Ye, Peng; Gu, Zheng-Cheng Physical Review X, Vol. 5, Issue 2 https://doi.org/10.1103/PhysRevX.5.021029	journal	June 2015
Is the Composite Fermion a Dirac Particle? Son, Dam Thanh Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031027	journal	September 2015
Dual Dirac Liquid on the Surface of the Electron Topological Insulator Wang, Chong; Senthil, T. Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevX.5.041031	journal	November 2015
Particle-Vortex Duality from 3D Bosonization Karch, Andreas; Tong, David Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031043	journal	September 2016
From Dirac Semimetals to Topological Phases in Three Dimensions: A Coupled-Wire Construction Raza, Syed; Sirota, Alexander; Teo, Jeffrey C. Y. Physical Review X, Vol. 9, Issue 1 https://doi.org/10.1103/PhysRevX.9.011039	journal	February 2019
Classification of 3 + 1 D Bosonic Topological Orders (II): The Case When Some Pointlike Excitations Are Fermions Lan, Tian; Wen, Xiao-Gang Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevX.9.021005	journal	April 2019
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Colloquium : Zoo of quantum-topological phases of matter Wen, Xiao-Gang Reviews of Modern Physics, Vol. 89, Issue 4 https://doi.org/10.1103/RevModPhys.89.041004	journal	December 2017
Weyl and Dirac semimetals in three-dimensional solids Armitage, N. P.; Mele, E. J.; Vishwanath, Ashvin Reviews of Modern Physics, Vol. 90, Issue 1 https://doi.org/10.1103/RevModPhys.90.015001	journal	January 2018
The Chern–Simons–Landau–Ginzburg Theory of the Fractional Quantum hall Effect Zhang, Shou Cheng International Journal of Modern Physics B, Vol. 06, Issue 01 https://doi.org/10.1142/S0217979292000037	journal	January 1992
The Dirac Composite Fermion of the Fractional Quantum Hall Effect Son, Dam Thanh Annual Review of Condensed Matter Physics, Vol. 9, Issue 1 https://doi.org/10.1146/annurev-conmatphys-033117-054227	journal	March 2018
Foliated field theory and string-membrane-net condensation picture of fracton order Slagle, Kevin; Aasen, David; Williamson, Dominic SciPost Physics, Vol. 6, Issue 4 https://doi.org/10.21468/SciPostPhys.6.4.043	journal	January 2019

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