Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912501943238656 |
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| author | Vela, A. Donís Beenakker, C. W. J. |
| author_facet | Vela, A. Donís Beenakker, C. W. J. |
| contents | The massless two-dimensional Dirac equation in a perpendicular magnetic field B supports a B-independent "zeroth Landau level", a dispersionless zero-energy-mode protected by chiral symmetry. On a lattice the zero-mode becomes doubly degenerate with states of opposite chirality, which removes the protection and allows for a broadening when the magnetic field is non-uniform. It is known that this fundamental obstruction can be avoided by spatially separating the doubly degenerate states, adjoining +B and -B regions in a system of twice the size. Here we show that the same objective can be achieved without doubling the system size. The key ingredients are 1) a chirality-preserving "tangent fermion" discretization of the Dirac equation; and 2) a boundary condition that ensures the zero-mode contains only states of a single chirality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_13658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice Vela, A. Donís Beenakker, C. W. J. Mesoscale and Nanoscale Physics The massless two-dimensional Dirac equation in a perpendicular magnetic field B supports a B-independent "zeroth Landau level", a dispersionless zero-energy-mode protected by chiral symmetry. On a lattice the zero-mode becomes doubly degenerate with states of opposite chirality, which removes the protection and allows for a broadening when the magnetic field is non-uniform. It is known that this fundamental obstruction can be avoided by spatially separating the doubly degenerate states, adjoining +B and -B regions in a system of twice the size. Here we show that the same objective can be achieved without doubling the system size. The key ingredients are 1) a chirality-preserving "tangent fermion" discretization of the Dirac equation; and 2) a boundary condition that ensures the zero-mode contains only states of a single chirality. |
| title | Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2505.13658 |