Probing the Quantized Berry Phases in 1H-NbSe$_2$ Using Scanning Tunneling Microscopy (2501.09063v1)

Abstract: Topologically trivial insulators are classified into two primary categories: unobstructed and obstructed atomic insulators. While both types can be described by exponentially localized Wannier orbitals, a defining feature of obstructed atomic insulators is that the centers of charge of these orbitals are positioned at empty sites within the unit cell, rather than on atoms. Despite extensive theoretical predictions, the unambiguous and quantitative experimental identification of an obstructed atomic phase has remained elusive. In this work, we present the first direct experimental evidence of such a phase in 1H-NbSe$_2$. We develop a novel method to extract the inter-orbital correlation functions from the local spectral function probed by scanning tunneling microscopy (STM), leveraging the orbital wave functions obtained from ab initio calculations. Applying this technique to STM images, we determine the inter-orbital correlation functions for the atomic band of 1H-NbSe$_2$ that crosses the Fermi level. Our results show that this band realizes an optimally compact obstructed atomic phase, providing the first unambiguous experimental identification of such a phase. Our approach of deconvolving the STM signal using ab initio orbital wave functions is broadly applicable to other material platforms, offering a powerful tool for exploring other electronic phases.

• The paper demonstrates the direct probing of obstructed atomic phases in monolayer 1H-NbSe2 using STM.
• It employs deconvolution of STM signals with ab initio wave functions to identify a quasi-flat band near the Fermi level indicative of OA phases.
• The findings enhance understanding of topological phases, paving the way for advances in quantum electronics and superconducting technologies.

Probing the Quantized Berry Phases in 1H-\ch{NbSe2} Using Scanning Tunneling Microscopy

The paper provides an intricate paper of the topological phases in materials by investigating the electronic properties of monolayer 1H-\ch{NbSe2} (niobium diselenide) using scanning tunneling microscopy (STM). The authors address a crucial question in condensed matter physics regarding the direct experimental identification of obstructed atomic (OA) phases, focusing on their tabletop manifestation within this transition metal dichalcogenide (TMD) monolayer.

Overview of Topological Atomic Insulators

The research presented classifies topologically trivial insulators into two categories: unobstructed atomic (UA) and obstructed atomic (OA) insulators. In UA insulators, the centers of the maximally localized Wannier functions align with the nuclear positions. Conversely, OA insulators possess charge centers positioned at vacant sites, thus exhibiting characteristics such as increased spread of Wannier orbitals and significant quantum geometric tensors.

1H-\ch{NbSe2}, a prototypical TMD, is leveraged due to its previously studied electronic and quantum properties such as charge-density wave (CDW) order and superconductivity. Despite being theoretically predicted in various systems, the unambiguous identification of an OA phase remains elusive. This distinction is pivotal since it directly impacts the quantum mechanical properties and potential applications in electronic and quantum computing technologies.

Methodology and Findings

The authors employ STM to measure the local spectral function—typically aligned with the charge distribution—of the monolayer \ch{NbSe2} at the Fermi level using a method that decomposes the STM signal into orbital contributions using ab initio wave functions. The significant findings include:

• The quasi-flat band near the Fermi level, central to the obstructed characterization, exhibits characteristics aligning with an OA phase.
• Through careful decomposition of electronic signals obtained from STM, the authors quantify orbital correlation functions, which fundamentally reflect an optimally compact OA phase with its Wannier charge center located at an empty lattice site.

STM was used to probe the electronic density features, and the results were deconvolved leveraging ab initio{} simulations, allowing an unprecedented quantitative analysis of the OA band, as opposed to more qualitative or indirect measurements historically utilized.

Implications of the Research

This work is importantly directed at understanding the real-space manifestation of topological phases. The distinction between UA and OA phases is not merely an academic exercise; it touches upon the fundamental quantum properties of materials, which can influence their suitability for building future quantum technologies. An OA phase’s unique characteristics imply potential utility in electronic devices where enhanced electron-phonon interactions play a critical role, such as in the material's superconducting and CDW states.

Potential Developments and Extensions

The method described, particularly the deconvolution technique, establishes a robust framework for analyzing complex materials where different electronic phases might coexist. The authors suggest that this could be applied to other TMD monolayers or similar materials, extending the framework to semiconductor physics where geometric phases play a critical role.

Future avenues of research could also explore the relationship between quantized Berry phases and the material's response to external perturbations, such as magnetic fields, which can further enrich understanding in complex band topology and help design materials with nontrivial topological invariants conducive to highly coherent quantum computing components.

In summary, the research provides a significant contribution to practical assessments of topological phases in materials, leveraging state-of-the-art STM techniques coupled with solid theoretical insights grounded in quantum mechanical principles.