# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1906.10162