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The position operator in a Bloch representation acquires a gauge correctionin the momentum space on top of the canonical position, which is called theanomalous position. We show that the anomalous position is generallyorbital-dependent and thus plays a crucial role in the description of theintrinsic orbital Hall effect in terms of Wannier basis. We demonstrate thisfrom the first-principles calculation of orbital Hall conductivities oftransition metals by Wannier interpolation. Our results show that consistenttreatment of the velocity operator by adding the additional term originatingfrom the anomalous position predicts the orbital Hall conductivities differentfrom those obtained by considering only the group velocity. We find thedifference is crucial in several metals. For example, we predict the negativesign of the orbital Hall conductivities for elements in the groups X and XIsuch as Cu, Ag, Au, and Pd, for which the previous studies predicted thepositive sign. Our work suggests the importance of consistently describing thespatial dependence of basis functions by first-principles methods as it isfundamentally missing in the tight-binding approximation.

First-principles calculation of orbital Hall effect by Wannier interpolation: Role of orbital dependence of the anomalous position