Specific heat anomaly in the d-density wave state and emergence of incommensurate orbital antiferromagnetic order

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We study the effect of finite chemical potential on the d-density wave state that has been proposed to explain the pseudogap phenomena in underdoped cuprates. We find that the specific heat anomaly at the transition temperature, below which the d-density wave state forms, gets weaker when finite chemical potential is introduced. This provides a useful ground for the proper interpretation of the specific heat measurement in regard to the existence of the d-density wave state below the pseudogap temperature. Further increase of the chemical potential leads to an incommensurate orbital antiferromagnetic state before the system eventually turns into the normal state. This is an inhomogeneous state characterized by novel charge ordering and an analog of the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in superconductivity.