SciPost Physics

SciPost Phys. 3, 012 (2017) · published 15 August 2017

• doi: 10.21468/SciPostPhys.3.2.012
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

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 wavepacket 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.

• Fraxanet et al.,
  1000, 85 (2023) [Crossref]
• Barbarino et al., Topological phases in frustrated synthetic ladders with an odd number of legs
  Phys. Rev. A 97, 013634 (2018) [Crossref]
• Mizoguchi et al., Blocking particle dynamics in a diamond chain with spatially increasing flux
  Phys. Rev. A 109, 053315 (2024) [Crossref]
• Szołdra et al., Determination of Chern numbers with a phase-retrieval algorithm
  Phys. Rev. A 99, 043611 (2019) [Crossref]
• Salamon et al., Quantum anomalous Hall phase in synthetic bilayers via twistronics without a twist
  Phys. Rev. B 102, 235126 (2020) [Crossref]
• Cabedo et al., Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices
  Eur. Phys. J. D 74, 123 (2020) [Crossref]
• Buser et al., Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics
  Phys. Rev. A 102, 053314 (2020) [Crossref]
• Genkina et al., Imaging topology of Hofstadter ribbons
  New J. Phys. 21, 053021 (2019) [Crossref]
• Mochol-Grzelak et al., Efficient algorithm to compute the second Chern number in four dimensional systems
  Quantum Sci. Technol. 4, 014009 (2018) [Crossref]
• Sun et al., Chiral current reversal induced by a quadratic field in the three-leg magnetic lattice
  J. Phys. A: Math. Theor. 53, 455301 (2020) [Crossref]
• Stenzel et al., Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders
  Phys. Rev. A 102, 023315 (2020) [Crossref]
• Johnstone et al., Interacting bosons on crystalline and quasiperiodic ladders in a magnetic field
  Phys. Rev. Research 5, 023195 (2023) [Crossref]
• Sajid et al., Localization, transport, and edge states in a two-strand ladder network in an aperiodically staggered magnetic field
  Phys. Rev. B 102, 134401 (2020) [Crossref]
• Bartel et al., Magnetotransport of Functional Oxide Heterostructures Affected by Spin–Orbit Coupling: A Tale of Two‐Dimensional Systems
  Physica Status Solidi (b) 259, 2100154 (2022) [Crossref]
• Argüello-Luengo et al., Synthetic dimensions for topological and quantum phases
  Commun Phys 7, 143 (2024) [Crossref]
• Buser et al., Finite-temperature properties of interacting bosons on a two-leg flux ladder
  Phys. Rev. A 99, 053601 (2019) [Crossref]
• Hudomal et al., Dynamics of weakly interacting bosons in optical lattices with flux
  Phys. Rev. A 98, 053625 (2018) [Crossref]
• Ozawa et al., Topological quantum matter in synthetic dimensions
  Nat Rev Phys 1, 349 (2019) [Crossref]
• Nandy et al., Few-particle dynamics of fractional quantum Hall lattice models
  Phys. Rev. B 101, 205305 (2020) [Crossref]
• Karnaukhov, Chern insulator with large Chern numbers. Chiral Majorana fermion liquid
  J. Phys. Commun. 1, 051001 (2017) [Crossref]