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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.14680 |
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| _version_ | 1866917345206730752 |
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| author | May-Mann, Julian Bhattacharjee, Sayak Raghu, Srinivas |
| author_facet | May-Mann, Julian Bhattacharjee, Sayak Raghu, Srinivas |
| contents | We consider the crystallization of a two-dimensional electron system in a perpendicular magnetic field using composite boson theory. There are three possible states to consider: the Hall liquid, the Wigner crystal, and the Hall crystal (a state with both broken translation symmetry and a quantized Hall response). Within composite boson theory, these states map onto a superconductor, a Mott insulator, and a supersolid of composite bosons respectively. We show that when a $ν= 1$ Hall liquid has a sufficiently soft roton, there is a first order transition to a triangular lattice Hall crystal. If we continue to decrease the roton mass, there is a continuous transition from the Hall crystal to a Wigner crystal. {When the Hall crystal exhibits the integer quantum Hall effect,} this transition {is} described by a free Dirac fermion and, at the critical point, the coupling to the phonons of the crystal is irrelevant, {in the {renormalization group} sense}. We extend this analysis to fractional $ν= 1/m$ Hall liquids. There, due to kinetic frustration arising from flux attachment, honeycomb lattice Hall crystals are preferred over triangular ones at intermediate interaction strength. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14680 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Composite boson theory of Hall crystals and their transitions to Wigner crystals May-Mann, Julian Bhattacharjee, Sayak Raghu, Srinivas Mesoscale and Nanoscale Physics We consider the crystallization of a two-dimensional electron system in a perpendicular magnetic field using composite boson theory. There are three possible states to consider: the Hall liquid, the Wigner crystal, and the Hall crystal (a state with both broken translation symmetry and a quantized Hall response). Within composite boson theory, these states map onto a superconductor, a Mott insulator, and a supersolid of composite bosons respectively. We show that when a $ν= 1$ Hall liquid has a sufficiently soft roton, there is a first order transition to a triangular lattice Hall crystal. If we continue to decrease the roton mass, there is a continuous transition from the Hall crystal to a Wigner crystal. {When the Hall crystal exhibits the integer quantum Hall effect,} this transition {is} described by a free Dirac fermion and, at the critical point, the coupling to the phonons of the crystal is irrelevant, {in the {renormalization group} sense}. We extend this analysis to fractional $ν= 1/m$ Hall liquids. There, due to kinetic frustration arising from flux attachment, honeycomb lattice Hall crystals are preferred over triangular ones at intermediate interaction strength. |
| title | Composite boson theory of Hall crystals and their transitions to Wigner crystals |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2603.14680 |