Uncovering vacuum level in infinite solid by real-space potential-unfolding

TL;DR

This paper presents a new real-space potential-unfolding method to determine the vacuum level in infinite solids, resolving longstanding ambiguities in band alignment by accounting for bulk quadrupole effects.

Contribution

The authors introduce an analytic approach that uncovers the vacuum level in infinite solids, addressing the controversy caused by finite-size assumptions in electronic structure theory.

Findings

Bulk band structure is offset by an orientation-dependent quadrupole.

The method clarifies the physical origin of band alignment.

Eliminates ambiguities in surface and interface property analysis.

Abstract

Although real materials are finite in size, electronic structure theory is built on the assumption of infinitely large solid, which led to a longstanding controversy: where is the vacuum level? Here, we introduce an analytic real-space potential-unfolding approach to uncover the vacuum level in infinitely large solid. First-principles calculations show that, in the absence of a physical surface, the bulk band structure, often measured with respect to an average bulk potential, is offset by a hereto unknown and orientation-dependent bulk quadrupole with respect to the vacuum level. By identifying intrinsic contributions of a bulk solid to its surface and interface properties, our theory eliminates the ambiguities surrounding the physical origin of the band alignment between matters.