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The shell-model-like approach is implemented to treat the cranking many-bodyHamiltonian based on the covariant density functional theory including pairingcorrelations with exact particle number conservation. The self-consistency isachieved by iterating the single-particle occupation probabilities back to thedensities and currents. As an example, the rotational structures observed inthe neutron-rich nucleus $^{60}$Fe are investigated and analyzed. Withoutintroducing any \emph{ad hoc} parameters, the bandheads, the rotationalspectra, and the relations between the angular momentum and rotationalfrequency for the positive parity band A, and negative parity bands B and C arewell reproduced. The essential role of the pairing correlations is revealed. Itis found that for band A, the bandcrossing is due to the change of the last twooccupied neutrons from the $1f_{5/2}$ signature partners to the $1g_{9/2}$signature partners. For the two negative parity signature partner bands B andC, the bandcrossings are due to the pseudo-crossing between the $1f_{7/2,~5/2}$and the $1f_{5/2,~1/2}$ orbitals. Generally speaking, the deformationparameters $\beta$ for bands A, B, and C decrease with rotational frequency.For band A, the deformation jumps from $\beta\sim0.19$ to $\beta\sim0.29$around the bandcrossing. In comparison with its signature partner band C, bandB exhibits appreciable triaxial deformation.

Shell-model-like approach based on cranking covariant density functional theory: bandcrossing and shape evolution in $^{60}$Fe