Interactions and Topology in Quantum Matter: From frustrated magnets to fractional topological insulators
Final Report Abstract
The Emmy Noether project turned out very successful. In the project we significantly advanced the understanding of fractional topological (Chern) insulators and combining with insights from the field of frustrated magnetism we reached new surprising insights with broad implications for quantum materials. In the context of the fictional topological insulators I am especially proud of Ref. 6 which in my opinion settles pretty much everything there is to learn about Fractional Chern insulators in ideal lattice settings. It also opens up new avenues for studying even more intriguing physics in presence of wormhole-like lattice defects which are currently being explored. The highlight of the project was however serendipitous leading us in new unexpected directions. When combining frustration and topology we found a very general way of calculating exact boundary states of topological (and non-topological). While very unusual and interesting in itself, the exact solutions lead us to a large number of important insights. One such thing is that Fermi arc surface states can occur without the presence of Weyl nodes (monopoles of Berry flux) in the bulk. This seems indeed to have been realised in certain pyrochlore iridates (Eu2Ir2O7 and Nd2Ir2O7) where our exact solutions uncover this quite unexpected phenomena. Moreover, our work showed that Weyl Hamiltonians generally have an anisotropic and, more importantly, tilted dispersion. In fact, our work showed that the dispersion can in fact be “over-tilted” forming a compensated metal where the Weyl point is a singular point connecting two Fermi pockets. These systems were later popularly coined type-II Weyl semimetals in connection with their explicit materials prediction and were subsequently experimentally identified in a growing list of intriguing materials. This has now developed into one of the hottest topics in condensed matter physics and we have also continued to publish some of the central works in this field. Thus, while Weyl semimetals were not an initial focus of the Emmy Noether project, our investigations naturally lead us there and it has become a central theme of our research efforts within and beyond the Emmy Noether project. The project also enabled me to recruit and work with students and postdocs with whom I have had great success. In particular, key progress on combining topology and frustration was made together with my PhD student Maximilian Trescher. The grant also allowed me to attract Dr. Zhao Liu from Princeton University where he worked with Prof. Ravin Bhatt and Prof. Duncan Haldane (2016 Nobel laureate).
Publications
- “Bulk-edge correspondence in fractional Chern insulators”. Physical Review B 88, 081106(R) (2013)
Z. Liu, D.L. Kovrizhin and E.J. Bergholtz
(See online at https://doi.org/10.1103/PhysRevB.88.081106) - “Hierarchy of fractional Chern insulators and competing compressible states”. Physical Review Letters, 111, 126802 (2013)
A.M. Läuchli, Z. Liu, E.J. Bergholtz, and R. Moessner
(See online at https://doi.org/10.1103/PhysRevLett.111.126802) - “Topological equivalence of crystal and quasicrystal band structures”. Physical Review B 88, 125118 (2013)
K.A. Madsen, E.J. Bergholtz, and P.W. Brouwer
(See online at https://doi.org/10.1103/PhysRevB.88.125118) - “Topological Flat Band Models and Fractional Chern Insulators”. International Journal of Modern Physics B 27, 1330017 (2013)
E.J. Bergholtz and Z. Liu
(See online at https://doi.org/10.1142/S021797921330017X) - ”Non-Abelian Fractional Chern Insulators from Long-Range Interactions”. Physical Review B 88, 205101 (2013)
Z. Liu, E.J. Bergholtz and E. Kapit
(See online at https://doi.org/10.1103/PhysRevB.88.205101) - “Correlations and entanglement in flat band models with variable Chern numbers”. J. Stat. Mech. (2014) P10012. (Special Issue: Quantum Entanglement in Condensed Matter Physics)
M. Udagawa and E.J. Bergholtz
(See online at https://doi.org/10.1088/1742-5468/2014/10/P10012) - “Quantum transport of disordered Weyl semimetals at the nodal point”. Physical Review Letters 113, 026602 (2014)
B. Sbierski, G. Pohl, E. J. Bergholtz, and P. W. Brouwer
(See online at https://doi.org/10.1103/PhysRevLett.113.026602) - “Topological insulators with arbitrarily tunable entanglement”. Physical Review B 89, 195120 (2014)
J.C. Budich, J. Eisert and E.J. Bergholtz
(See online at https://doi.org/10.1103/PhysRevB.89.195120) - ”Search for localized Wannier functions of topological band structures via compressed sensing”. Physical Review B 90, 115110 (2014)
J. C. Budich, J. Eisert, E. J. Bergholtz, S. Diehl, and P. Zoller
(See online at https://doi.org/10.1103/PhysRevB.90.115110) - “Quantum critical exponents for a disordered three-dimensional Weyl node”. Physical Review B 92, 115145 (2015)
B. Sbierski, E.J. Bergholtz, and P.W. Brouwer
(See online at https://doi.org/10.1103/PhysRevB.92.115145) - “Quantum transport in Dirac materials: Signatures of tilted and anisotropic Dirac and Weyl cones”. Physical Review B 91, 115135 (2015)
M. Trescher, B. Sbierski, P.W. Brouwer and E.J. Bergholtz
(See online at https://doi.org/10.1103/PhysRevB.91.115135) - “Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to 𝒞>1 Fractional Chern Insulators”. Physical Review Letters 114, 016806 (2015)
E.J. Bergholtz, Z. Liu, M. Trescher, R. Moessner, and M. Udagawa
(See online at https://doi.org/10.1103/PhysRevLett.114.016806) - “Field-Selective Anomaly and Chiral Mode Reversal in Type-II Weyl Materials”. Physical Review Letters 117, 086401 (2016)
M. Udagawa and E.J. Bergholtz
(See online at https://doi.org/10.1103/PhysRevLett.117.086401) - “Model Fractional Chern Insulators”. Physical Review Letters 116, 216802 (2016)
J. Behrmann, Z. Liu, and E.J. Bergholtz
(See online at https://doi.org/10.1103/PhysRevLett.116.216802) - “Anatomy of Topological Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices”. Physical Review B 96, 085443 (2017)
F. Kunst, M. Trescher, and E.J. Bergholtz
(See online at https://doi.org/10.1103/PhysRevB.96.085443) - “Disordered Double Weyl Node: Comparison of transport and density-ofstates calculations”. Physical Review B 95, 115104 (2017)
B. Sbierski, M. Trescher, E.J. Bergholtz, and P.W. Brouwer
(See online at https://doi.org/10.1103/PhysRevB.95.115104) - “Josephson effect in a Weyl SNS junction”. Physical Review B 95, 064511 (2017)
K.A. Madsen, E.J. Bergholtz, and P.W. Brouwer
(See online at https://doi.org/10.1103/PhysRevB.95.064511) - “Tilted Disordered Weyl Semimetals”. Physical Review B 95, 045139 (2017)
M. Trescher, B. Sbierski, P.W. Brouwer, and E.J. Bergholtz
(See online at https://doi.org/10.1103/PhysRevB.95.045139)
