2017/05/31 by Samuel Mugel, Alexandre Dauphin, Pietro Massignan +4 · 21 citations
Physics and Astronomy · #Boundary (topology) #Boundary value problem #Chern class #Displacement (psychology) #Periodic boundary conditions #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #STRIPS #Topological Materials and Phenomena #Transverse plane #Wave packet #cond-mat.mes-hall #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.21468/scipostphys.3.2.012
published in SciPost Physics 3(2) (SciPost.org) · v1: 17 pages, 10 figures; v2: minor changes, reference added, SciPost style, 26 pages, 10 figures; v3: published version
openalex created_date 2017/05/19 · arxiv created 2017/08/15 · openalex publication_date 2017/08/15 · arxiv updated 2017/08/16 · openalex updated_date 2026/08/05
Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wave packet exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.