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Field-Induced Kosterlitz-Thouless Transition in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>Landau Level of Graphene

Field-Induced Kosterlitz-Thouless Transition in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>Landau Level of Graphene

At the charge neutral point, graphene exhibits a very unusual high-resistance metallic state and a transition to a complete insulating phase in a strong magnetic field. We propose that the current carriers in this state are the charged vortices of the $XY$ valley-pseudospin order parameter, a situation which is dual …