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

Dongwook Go, Hyun‐Woo Lee+3 more|arXiv (Cornell University)|Sep 25, 2023

Surface and Thin Film PhenomenaPhysics and Astronomy3 citations

TL;DR

This paper demonstrates that the anomalous position—a gauge-dependent correction to the position operator in momentum space—plays a critical role in first-principles calculations of the intrinsic orbital Hall effect (OHE) using Wannier interpolation. By accounting for orbital-dependent anomalous positions, the study reveals that OHE conductivities in transition metals, particularly in groups X and XI (e.g., Cu, Ag, Au, Pd), are predicted to be negative, contradicting prior studies that assumed positive values based on group velocity alone.

ABSTRACT

The position operator in a Bloch representation acquires a gauge correction in the momentum space on top of the canonical position, which is called the anomalous position. We show that the anomalous position is generally orbital-dependent and thus plays a crucial role in the description of the intrinsic orbital Hall effect in terms of Wannier basis. We demonstrate this from the first-principles calculation of orbital Hall conductivities of transition metals by Wannier interpolation. Our results show that consistent treatment of the velocity operator by adding the additional term originating from the anomalous position predicts the orbital Hall conductivities different from those obtained by considering only the group velocity. We find the difference is crucial in several metals. For example, we predict the negative sign of the orbital Hall conductivities for elements in the groups X and XI such as Cu, Ag, Au, and Pd, for which the previous studies predicted the positive sign. Our work suggests the importance of consistently describing the spatial dependence of basis functions by first-principles methods as it is fundamentally missing in the tight-binding approximation.

Motivation & Objective

• To address the lack of consistent treatment of spatial basis function dependence in first-principles OHE calculations.
• To investigate the role of the anomalous position—originating from dipole matrix elements between Wannier functions—in the intrinsic orbital Hall effect.
• To correct the long-standing assumption that only group velocity contributes to OHE, by including gauge-corrected velocity operators.
• To resolve discrepancies in sign predictions of OHE for transition metals, especially in groups X and XI.
• To demonstrate that the tight-binding approximation fails to capture this orbital-dependent correction, leading to quantitative errors.

Proposed method

• Employing first-principles density functional theory (DFT) with the full-potential linearized augmented plane wave (FLAPW) method to compute electronic structure.
• Using Wannier function interpolation to enable high-resolution k-space sampling for accurate response function evaluation.
• Incorporating the anomalous position as a gauge correction to the position operator in k-space, derived from inter-basis dipole matrix elements.
• Calculating the orbital Hall conductivity via the Kubo formula using the corrected velocity operator that includes the anomalous position term.
• Comparing results with and without the anomalous position correction to isolate its impact on OHE magnitude and sign.
• Systematically analyzing 3d, 4d, and 5d transition metals from groups IV to XI to assess the generality of the effect.

Experimental results

Research questions

• RQ1 How does the orbital-dependent anomalous position influence the intrinsic orbital Hall conductivity in transition metals?
• RQ2 Why do previous theoretical studies predict a positive sign for OHE in all transition metals, and is this assumption valid?
• RQ3 To what extent does the inclusion of the anomalous position correction alter the magnitude and sign of OHE in 3d, 4d, and 5d transition metals?
• RQ4 How does the Wannier interpolation method enable accurate treatment of the anomalous position in first-principles calculations?
• RQ5 What is the fundamental reason for the failure of the tight-binding approximation in capturing this correction?

Key findings

• The anomalous position is inherently orbital-dependent and arises from dipole matrix elements between Wannier functions, making it a non-trivial correction to the velocity operator.
• Including the anomalous position correction leads to significantly different orbital Hall conductivities compared to calculations based solely on group velocity.
• For elements in groups X and XI—such as Cu, Ag, Au, and Pd—the study predicts a negative orbital Hall conductivity, reversing the previously assumed positive sign.
• The correction is most pronounced in 4d and 5d transition metals, where the orbital dependence of the anomalous position strongly influences the OHE response.
• The sign reversal in OHE for Pd (σ_OH = -1870) and Au (σ_OH = -1020) is attributed to the orbital-specific nature of the anomalous position, not just spin-orbit coupling.
• The results demonstrate that the tight-binding approximation fundamentally misses this correction, leading to systematic errors in OHE predictions.