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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2508.13149 |
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| _version_ | 1866911621675220992 |
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| author | Kim, Kyung-Su |
| author_facet | Kim, Kyung-Su |
| contents | We study how an out-of-plane magnetic field $B({\bf r})$ and a Berry curvature $Ω({\bf k})$ modify the exchange interactions in a two-dimensional Wigner crystal (WC) using a semi-classical large-$r_s$ expansion. When only a magnetic field is present, ring-exchange processes arise from multi-particle tunneling through {\it complex} trajectories which constitute {\it complex instanton} solutions of the coordinate-space path integral. To leading order in $B$, each exchange constant $J_a$ acquires an Aharonov-Bohm phase along the zero-field tunneling trajectory. When a Berry curvature is present, the multi-particle tunneling must be considered in a complexified phase space $({\bf r}, {\bf k})$. To leading order in $Ω$, $J_a$ acquires a Berry phase along a {\it purely imaginary} momentum-space trajectory. When $B$ and $Ω$ are both present, in addition to having both Aharonov-Bohm and Berry phases, the exchange magnitude $|J_a|$ is also modified due to an effective-mass renormalization. These effects could be relevant for the WC and proximate phases recently observed in rhombohedral multilayer graphene. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exchange Interactions of a Wigner Crystal in a Magnetic Field and Berry Curvature: Multi-Particle Tunneling through Complex Trajectories Kim, Kyung-Su Mesoscale and Nanoscale Physics Strongly Correlated Electrons We study how an out-of-plane magnetic field $B({\bf r})$ and a Berry curvature $Ω({\bf k})$ modify the exchange interactions in a two-dimensional Wigner crystal (WC) using a semi-classical large-$r_s$ expansion. When only a magnetic field is present, ring-exchange processes arise from multi-particle tunneling through {\it complex} trajectories which constitute {\it complex instanton} solutions of the coordinate-space path integral. To leading order in $B$, each exchange constant $J_a$ acquires an Aharonov-Bohm phase along the zero-field tunneling trajectory. When a Berry curvature is present, the multi-particle tunneling must be considered in a complexified phase space $({\bf r}, {\bf k})$. To leading order in $Ω$, $J_a$ acquires a Berry phase along a {\it purely imaginary} momentum-space trajectory. When $B$ and $Ω$ are both present, in addition to having both Aharonov-Bohm and Berry phases, the exchange magnitude $|J_a|$ is also modified due to an effective-mass renormalization. These effects could be relevant for the WC and proximate phases recently observed in rhombohedral multilayer graphene. |
| title | Exchange Interactions of a Wigner Crystal in a Magnetic Field and Berry Curvature: Multi-Particle Tunneling through Complex Trajectories |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2508.13149 |