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Bloch oscillations originate from the translational symmetry of crystals. These oscillations occur with a fundamental period that a semiclassical wave packet takes to traverse a Brillouinzone loop. We introduce a new type of Bloch oscillations whose periodicity is an integer multiple of the fundamental period, as has been observed in coldatomic experiments. The period multiplier is an invariant protected by the space groups of crystals, and has two complementary explanations: one from quantized BerryZak phases (acquired from adiabatic transport of Bloch functions in momentum space), and the other from the realspace distribution of Wannier functions. Building upon questions of what symmetries can be imposed on Wannier functions, we elucidate how obstructions to symmetric Wannier functions are realized in topological band insulators and photonic crystals. In particular, it is shown that an existing photonic crystal – that is touted to have robust Diraclike surface states [Nature, 565, 622] – actually exhibits a less robust, “fragile” topology.
References:
Phys. Rev. B 98, 024310 (2018)
Phys. Rev. B 98, 184305 (2018)
\n\nSPEAKER: Aris Alexandradinata, University of Illinois Urbana Champaign 190 ESB false
Institute for Condensed Matter Theory Seminar: "Topological revamp of band theory: from periodmultiplied Bloch oscillations to topological photonic crystals"
Speaker 
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Aris Alexandradinata, University of Illinois Urbana Champaign 

Date:  4/8/2019 
Time:  12 p.m. 
Location:  190 ESB 
Sponsor:  The Physics Department 
Event Type:  Seminar/Symposium 
Bloch oscillations originate from the translational symmetry of crystals. These oscillations occur with a fundamental period that a semiclassical wave packet takes to traverse a Brillouinzone loop. We introduce a new type of Bloch oscillations whose periodicity is an integer multiple of the fundamental period, as has been observed in coldatomic experiments. The period multiplier is an invariant protected by the space groups of crystals, and has two complementary explanations: one from quantized BerryZak phases (acquired from adiabatic transport of Bloch functions in momentum space), and the other from the realspace distribution of Wannier functions. Building upon questions of what symmetries can be imposed on Wannier functions, we elucidate how obstructions to symmetric Wannier functions are realized in topological band insulators and photonic crystals. In particular, it is shown that an existing photonic crystal – that is touted to have robust Diraclike surface states [Nature, 565, 622] – actually exhibits a less robust, “fragile” topology.
References: Phys. Rev. B 98, 024310 (2018) Phys. Rev. B 98, 184305 (2018)

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