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| Paper IPM / P / 12962 |
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We have considered an AdS2R2 solution of an Einstein-Maxwell theory supported by a magnetic eld. Considering a charged Dirac fermion on this background, we
show that the charged fermion can make the background unstable, resulting in spontaneously formation of a vortex lattice. This is done by analytically solving the system of
coupled partial dierential equations of the metric, gauge eld, and the charged fermion at lowest order around the onset of lattice formation. We have shown that an electric eld emerges in the back-reacted solution due to vortex lattice constructed from spin polarized fermions. We also discuss about the correction to the free energy due to lattice formation.
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