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We study the effect of finite chemical potential on the d-density wave statethat has been proposed to explain the pseudogap phenomena in underdopedcuprates. We find that the specific heat anomaly at the transition temperature,below which the d-density wave state forms, gets weaker when finite chemicalpotential is introduced. This provides a useful ground for the properinterpretation of the specific heat measurement in regard to the existence ofthe d-density wave state below the pseudogap temperature. Further increase ofthe chemical potential leads to an incommensurate orbital antiferromagneticstate before the system eventually turns into the normal state. This is aninhomogeneous state characterized by novel charge ordering and an analog of theFulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in superconductivity.Comment: 4 pages, 2 figure

Specific-heat anomaly in theddensity wave state and emergence of inhomogeneous orbital antiferromagnetic order