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Analytical calculations of phase transitions in AdS3 Maxwell-scalar system,modeling a holographic superconductor, are performed in the probe limit of BTZblack hole background. Estimated values of the phase transition criticaltemperature and of the scalar boundary operator are compared with that obtainedin numerical simulations. We discuss extensions of the model to topologicallymassive QED3 and to inclusion of external magnetic field. The latter becomespossible through the Barnett-London and the Lense-Thirring effects, but theformer does not lead to any viable modifications. The standard setup of aholographic superconductor is extended to a rotating 2D holographicsuperconductor, and the main characteristics of the phase transition arecalculated in the probe limit and in the small angular momentum approximation.We evaluate the feedback of the superconductor rotation on the phase transitionand find the set of parameters, which lower the critical temperature in compareto the non-rotating case, or make it slightly higher.

Analytical approach to phase transitions in rotating and non-rotating 2D holographic superconductors