2020-08-05T23:15:45Zhttps://tsukuba.repo.nii.ac.jp/?action=repository_oaipmhoai:tsukuba.repo.nii.ac.jp:000334922020-08-04T05:39:40Z00003:00062:05598:0008200117:00483
Survival of sharp n=0 Landau levels in massive tilted Dirac fermions: Role of the generalized chiral operatorenghttp://hdl.handle.net/2241/00124354Journal ArticleHatsugai, YasuhiroKawarabayashi, TohruAoki, Hideo初貝, 安弘An anomalously sharp (δ-function-like) n=0 Landau level in the presence of disorder is usually considered to be a manifestation of the massless Dirac fermions in magnetic fields. This property persists even when the Dirac cone is tilted, which has been shown by Kawarabayashi et al. [Phys. Rev. B 83, 153414 (2011)] to be a consequence of a “generalized chiral symmetry.” Here we pose the question of whether this property will be washed out when the tilted Dirac fermion becomes massive. Surprisingly, the levels continue to be δ-function-like, although the mass term that splits n=0 Landau levels may seem to degrade the anomalous sharpness. This has been shown both numerically for a tight-binding model and analytically in terms of the Aharonov-Casher argument extended to the massive tilted Dirac fermions. A key observation is that, while the generalized chiral symmetry is broken by the mass term, the n=0 Landau level continues to accommodate eigenstates of the generalized chiral operator, resulting in the robustness against chiral-symmetric disorders. Mathematically, the conventional and generalized chiral operators are related to each other via a nonunitary transformation, with which the split, nonzero-energy n=0 wave functions of the massive system are just gauge-transformed zero-mode wave functions of the massless system. The message is that the chiral symmetry, rather than a simpler notion of the sublattice symmetry, is essential for the robustness of the n=0 Landau level.Physical review B9180851122015-021098-0121AA1118711310.1103/PhysRevB.91.085112©2015 American Physical Societypublisherhttps://tsukuba.repo.nii.ac.jp/?action=repository_action_common_download&item_id=33492&item_no=1&attribute_id=17&file_no=2基礎工学・応用物理学American Physical Society2015-04-22