2013/05/22 by Sheng-Nan Ji, Bang-Fen Zhu, Bang‐Fen Zhu +5
Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Quantum optics and atomic interactions #Topological Materials and Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.48550/arxiv.1305.5289
5 pages, 4 figures
arxiv created 2013/05/22 · openalex publication_date 2013/05/22 · arxiv updated 2013/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Odd numbers of Dirac points and helical states can exist at edges (surfaces) of two-dimensional (three-dimensional) topological insulators. In the bulk of a one-dimensional lattice (not an edge) with time reversal symmetry, however, a no-go theorem forbids the existence of an odd number of Dirac points or helical states. Introducing a magnetic field can violate the time reversal condition but would usually lift the degeneracy at the Dirac points. We find that a spatially periodic magnetic field with zero mean value can induce a single Dirac point in a one-dimensional system with spin-orbit coupling. A wealth of new physics may emerge due to the existence of a single Dirac point and helical states in the bulk of a one-dimensional lattice (rather than edge states). A series of quantized numbers emerge due to the non-trivial topology of the 1D helical states, including the doubled period of helical Bloch oscillations, quantized conductance near the Dirac point, and 1/2-charge solitons at mass kinks. Such a system can be realized in one-dimensional semiconductor systems or in optical traps of atoms.