Real-Space Imaging of Obstructed Atomic Bands

SPICE Workshop on Emergent Topology and Unconventional Order in Quantum Matter September 8th - 10th, 2026

Miguel Ugeda

The topology of electronic wavefunctions has reshaped how we classify crystalline solids. Yet even within topologically trivial bands, those admitting exponentially localized Wannier functions, there exists a sharp distinction between unobstructed atomic (UA) and obstructed atomic (OA) phases. In a UA phase, Wannier charge centers coincide with ionic sites; in an OA phase, at least one center is pinned by symmetry to an empty position in the unit cell. This seemingly subtle shift encodes quantized Berry phases, enhances the quantum geometric tensor, and can impact diverse phenomena ranging from superfluid weight in flat-band superconductors to electron–phonon coupling. Despite extensive theory, a quantitative and unambiguous experimental identification of an OA electronic band has remained elusive.

In this talk, I will show how STM/STS can provide evidence for OA phases in the family of transition metal dichalcogenides (TMDs), in particular in single-layer 1H-NbSe₂ and bulk NiS₂. For 1H-NbSe₂, we map the real-space charge-density distribution of the Fermi-level quasi-flat band (1). Combining these images with ab initio orbital wavefunctions, we deconvolve the STM signal to extract interorbital correlation functions from the local spectral function. The resulting correlators establish that the relevant band is an optimally compact OA band, with its Wannier charge center pinned to an empty site in the unit cell. Further measurements on dilute substitutional alloys provide an independent, controlled perturbation that yields the same real-space fingerprint.

I will then turn to NiS₂, where the origin of the long-known anomalous surface conductivity has remained unclear. Here, STM/STS plays a decisive role by directly identifying boundary-localized electronic states in real space and linking them to the bulk electronic structure (2). Together with first-principles calculations and topological analysis, our STM/STS observations support the picture of NiS₂ hosting an obstructed atomic phase whose obstructed charges manifest as robust boundary modes. Overall, our experiments highlight STM/STS as a powerful route to diagnose obstructed bands and to explore how real-space topology intertwines with strong correlations.

(1) Călugăru, et al., Nature Physics 22, 686 (2026)

(2) Iraola, et al., Nature Communications (accepted).