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DTSTART;TZID=America/New_York:20221012T090000
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UID:10001140-1665565200-1665568800@cmsa.fas.harvard.edu
SUMMARY:Engineering topological phases with a superlattice potential
DESCRIPTION:Topological Quantum Matter Seminar \nSpeaker: Jennifer Cano (Stony Brook and Flatiron Institute) \nTitle: Engineering topological phases with a superlattice potential\n\nAbstract: We propose an externally imposed superlattice potential as a platform for manipulating topological phases\, which has both advantages and disadvantages compared to a moire superlattice. In the first example\, we apply the superlattice potential to the 2D surface of a 3D topological insulator. The superlattice potential creates tunable van Hove singularities\, which\, when combined with strong spin-orbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. Thus\, the superlattice potential provides a new route to the long sought-after goal of realizing spontaneous magnetic order on the surface of a 3D TI. In the second example\, we show that a superlattice potential applied to Bernal-stacked bilayer graphene can generate flat Chern bands\, similar to in twisted bilayer graphene\, whose bandwidth can be as small as a few meV. The superlattice potential offers flexibility in both lattice size and geometry\, making it a promising alternative to achieve designer flat bands without a moire heterostructure.
URL:https://cmsa.fas.harvard.edu/event/tqms_101222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-10.12.22.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221019T160000
DTEND;TZID=America/New_York:20221019T173000
DTSTAMP:20240229T103702Z
CREATED:20230705T073706Z
LAST-MODIFIED:20240229T103702Z
UID:10001139-1666195200-1666200600@cmsa.fas.harvard.edu
SUMMARY:Symmetric Mass Generation
DESCRIPTION:Topological Quantum Matter Seminar \nSpeaker: Yizhuang You\, UC San Diego \nTitle: Symmetric Mass Generation\n\nAbstract: Symmetric mass generation (SMG) is a novel mechanism for massless fermions to acquire a mass via a strong-coupling non-perturbative interaction effect. In contrast to the conventional Higgs mechanism for fermion mass generation\, the SMG mechanism does not condense any fermion bilinear coupling and preserves the full symmetry. It is connected to a broad range of topics\, including anomaly cancellation\, topological phase classification\, and chiral fermion regularization. In this talk\, I will introduce SMG through toy models\, and review the current understanding of the SMG transition. I will also mention recent numerical efforts to investigate the SMG phenomenon. I will conclude the talk with remarks on future directions.
URL:https://cmsa.fas.harvard.edu/event/tqms_101922/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-10.19.22.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221026T090000
DTEND;TZID=America/New_York:20221026T100000
DTSTAMP:20240216T112155Z
CREATED:20230705T074050Z
LAST-MODIFIED:20240216T112155Z
UID:10001138-1666774800-1666778400@cmsa.fas.harvard.edu
SUMMARY:Kähler bands—Chern insulators\, holomorphicity and induced quantum geometry
DESCRIPTION:Topological Quantum Matter Seminar \n\n\nSpeaker: Bruno Mera\, Tohoku University\n\nTitle: Kähler bands—Chern insulators\, holomorphicity and induced quantum geometry\n\nAbstract: The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions\, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation\, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of band insulators refer not just to the topology\, but also to their geometry. Of particular interest is the momentum-space quantum metric and the Berry curvature. The latter is the curvature of a connection on the vector bundle of occupied states. The study of the geometry of band insulators can also be used to probe whether the material may host stable fractional topological phases. In particular\, for a Chern band to have an algebra of projected density operators which is isomorphic to the W∞ algebra found by Girvin\, MacDonald and Platzman—the GMP algebra—in the context of the fractional quantum Hall effect\, certain geometric constraints\, associated with the holomorphic character of the Bloch wave functions\, are naturally found and they enforce a compatibility relation between the quantum metric and the Berry curvature of the band. The Brillouin zone is then endowed with a Kähler structure which\, in this case\, is also translation-invariant (flat). Motivated by the above\, we will provide an overview of the geometry of Chern insulators from the perspective of Kähler geometry\, introducing the notion of a Kähler band which shares properties with the well-known ideal case of the lowest Landau level. Furthermore\, we will provide a prescription\, borrowing ideas from geometric quantization\, to generate a flat Kähler band in some appropriate asymptotic limit. Such flat Kähler bands are potential candidates to host and realize fractional Chern insulating phases. Using geometric quantization arguments\, we then provide a natural generalization of the theory to all even dimensions.\n\n\nReferences:\n[1] Tomoki Ozawa and Bruno Mera. Relations between topology and the quantum metric for Chern insulators. Phys. Rev. B\, 104:045103\, Jul 2021.\n[2] Bruno Mera and Tomoki Ozawa. Kähler geometry and Chern insulators: Relations between topology and the quantum metric. Phys. Rev. B\, 104:045104\, Jul 2021.\n[3] Bruno Mera and Tomoki Ozawa. Engineering geometrically flat Chern bands with Fubini-Study  Kähler structure. Phys. Rev. B\, 104:115160\, Sep 2021.
URL:https://cmsa.fas.harvard.edu/event/9062/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-10.26.22.png
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