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Last year, we reported a perturbative theory of the Casimir-Lifshitz torquebetween planar biaxially anisotropic materials in the retarded limit [Phys.Rev. Lett. {\bf 120}, 131601 (2018)], which is applied here to study the changeof sign and magnitude of the torque with separation distance in biaxial blackphosphorus having excess charge carriers. The study is carried out both invacuum as well as in a background fluid medium. The presence of extra chargecarriers and that of an intervening fluid medium are both found to promoteenhancement of the magnitude of the torque between identical slabs. The degreeof enhancement of the magnitude of torque increases not only with an increasedcarrier concentration but also with separation distance. In the non-identicalcase when different planes of anisotropic black phosphorus face each other,owing to the non-monotonic characteristic of the sign-reversal effect of thetorque, the enhancement by carrier addition and intervening medium also becomesnon-monotonic with distance. In the presence of a background medium, thenon-monotonic degree of enhancement of the torque with distance is observedeven between identical slabs.

Effect of excess charge carriers and fluid medium on the magnitude and the sign of the Casimir-Lifshitz torqueP. Thiyam