🔬 materials science

Observation of Flat Bands in Type-II Weyl Semimetal TaRhTe $_{4}$

This paper reports the experimental discovery of unexpected flat bands near the chemical potential in the bulk noncentrosymmetric type-II Weyl semimetal TaRhTe $_4$ via angle-resolved photoemission spectroscopy, revealing a unique platform where nontrivial topology coexists with flat bands despite the absence of such features in theoretical predictions.

Original authors: Harry Rankin, Tyler J. Slade, Benjamin Schrunk, Yevhen Kushnirenko, Andrew Eaton, K. U. R. R. S. Rathnayaka, Maxwell Doyle, Lin-Lin Wang, Paul C. Canfield, Adam Kaminski

Published 2026-07-02

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CC BY 4.0

Original authors: Harry Rankin, Tyler J. Slade, Benjamin Schrunk, Yevhen Kushnirenko, Andrew Eaton, K. U. R. R. S. Rathnayaka, Maxwell Doyle, Lin-Lin Wang, Paul C. Canfield, Adam Kaminski

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the electrons inside a solid material as a massive crowd of people moving through a city. Usually, this city has hills and valleys. If an electron is in a valley, it's easy to move; if it's on a hill, it's harder. In physics, we call these paths "energy bands." Most of the time, these bands are sloped, meaning the energy changes as the electrons move.

But sometimes, nature builds a "flat plain" where the energy doesn't change no matter where the electron goes. Scientists call these flat bands. For decades, these were just a theoretical idea, like a map of a place that no one had ever visited. Recently, we found them in a few special materials, like twisted layers of graphene (which is like stacking two sheets of paper and twisting them at a very specific angle).

The Discovery: A New City with Flat Plains

In this paper, the researchers discovered that a material called TaRhTe4 (a crystal made of Tantalum, Rhodium, and Tellurium) has these flat plains right near the "ground level" where electrons usually hang out.

Here is the twist: TaRhTe4 is also a Type-II Weyl Semimetal. To use an analogy, imagine a city that is famous for its "Weyl points." These are like magical intersections where two roads (energy bands) cross each other perfectly, creating a special kind of traffic flow that follows the rules of Einstein's relativity. Usually, these "Weyl cities" are very bumpy and sloped. Finding a Weyl city that also has a giant, perfectly flat plain right next to the main intersection is extremely rare, especially in a solid chunk of crystal that isn't magnetic.

The Detective Work: Two Sides of the Same Coin

The researchers used a powerful tool called ARPES (Angle-Resolved Photoemission Spectroscopy). You can think of this as a high-speed, ultra-precise camera that takes snapshots of electrons as they fly off the surface of the crystal.

When they looked at the crystal, they found something tricky: the crystal has two different "sides" or surfaces (like the top and bottom of a layered cake, or two different ways a door can open).

Side A and Side B look slightly different.
The researchers compared their photos (experimental data) with computer simulations (theoretical predictions).
They found that while the computer models predicted the "Weyl intersections" correctly, the models completely missed the flat plains. The computer said, "There should be slopes here," but the camera said, "Nope, it's perfectly flat."

The "Flat" Surprise

The most exciting part of the discovery is the flat band itself.

Location: It sits just 4 "steps" (milli-electron volts) below the main energy level.
Shape: It stretches across a large part of the electron's map.
Why it matters: Because the energy is flat, the electrons aren't rushing around; they are "stuck" in a state where they have a huge density of states. This is like a parking lot that is completely full of cars that aren't moving. When you have a lot of electrons packed tightly in a flat energy state, it can lead to weird and exotic behaviors, like superconductivity (electricity flowing with zero resistance) or strange magnetic effects.

What They Did

Grew the Crystal: They melted Tantalum, Rhodium, and a lot of Tellurium together in a special furnace, then spun it in a centrifuge to separate the crystals, resulting in thin, flake-like pieces of TaRhTe4.
Shined Light: They broke the crystals open in a vacuum and hit them with a laser to knock electrons out, taking pictures of their energy and speed.
Compared Notes: They matched these pictures against computer calculations. The match was good for the "Weyl" parts, but the flat bands were a surprise that the computer didn't predict.

The Bottom Line

This paper reports that TaRhTe4 is a unique material where two very different and interesting physics phenomena coexist: the exotic, relativistic traffic of Weyl points and the stagnant, high-density traffic of flat bands.

The researchers emphasize that this is a rare find in a non-magnetic bulk crystal. Because these flat bands are so close to the main energy level, scientists might be able to "tune" them (like adjusting a radio dial) to move them exactly to the right spot to study new quantum effects. This makes TaRhTe4 a new playground for understanding how electrons behave when they are both topologically protected and stuck in a flat energy landscape.

Problem Statement
Flat bands—electronic bands with dispersionless energy over a range of momentum—have been theoretically predicted for decades but have only recently been realized in specific quantum materials, such as magic-angle twisted bilayer graphene, kagome and Lieb lattices, and certain rare-earth compounds. While these states are known to host exotic properties like superconductivity and magnetism due to their high density of states, they are rarely observed in Weyl semimetals, particularly in nonmagnetic bulk systems. Furthermore, existing platforms for flat bands (like twisted bilayer graphene) rely on external tuning mechanisms to align flat-band energies with the chemical potential. The isostructural compound TaIrTe4 has been extensively studied as a type-II Weyl semimetal, but its counterpart, TaRhTe4, remains underexplored regarding its electronic structure. A critical gap exists in understanding whether nontrivial topology and flat bands can coexist near the Fermi level in bulk, noncentrosymmetric Weyl semimetals without external tuning.

Methodology
The authors synthesized single crystals of TaRhTe4 using a solution/flux method with excess Tellurium. To characterize the electronic structure, they employed Angle-Resolved Photoemission Spectroscopy (ARPES) on in-situ cleaved single crystals at temperatures between 5 and 5.5 K. The measurements utilized a 6.6 eV photon source with high energy (0.7 meV) and momentum (0.001 Å⁻¹) resolution.

To interpret the experimental data, the authors performed Density Functional Theory (DFT) calculations including spin-orbit coupling (SOC) using the PBE functional with a modified Becke-Johnson (mBJ) exchange-correlation potential. They utilized the experimental lattice parameters and constructed tight-binding models via maximally localized Wannier functions to calculate surface spectral functions and two-dimensional Fermi surfaces. The study specifically addressed the two distinct surface terminations (labeled A and B) inherent to the noncentrosymmetric, layered crystal structure of TaRhTe4.

Key Results

Fermi Surface and Termination Identification: The ARPES measurements revealed two distinct electronic structures corresponding to the two surface terminations (A and B). By comparing experimental Fermi surfaces with DFT predictions, the authors successfully assigned specific data sets to each termination. Termination A showed excellent agreement with calculations, particularly regarding the "D" shaped surface states and specific band curvatures. Termination B displayed similar general features but with less pronounced agreement in certain regions, likely due to data limitations in the $k_y$ range.
Weyl Points: The study confirmed the presence of Weyl points (WPs) in TaRhTe4. DFT calculations predicted eight WPs: four located 13 meV above the Fermi energy ( $E_F$ ) and four located 50 meV below $E_F$ . The ARPES data captured Fermi arcs connecting WP pairs, particularly those 13 meV above $E_F$ , which were visible on the Fermi surface.
Discovery of Flat Bands: The most significant finding is the observation of flat bands near the chemical potential in Termination A. These bands appear as a structure extending throughout much of the Brillouin zone, with a peak intensity approximately 4 meV below $E_F$ . Crucially, the energy of these bands is effectively independent of momentum ( $k_x$ ).
Discrepancy with Theory: The observed flat bands were not predicted by the DFT calculations. While the theoretical band structure matched the experimental data well in many regions (especially below $E_F - 0.05$ eV), the flat bands appeared as an extra feature in the ARPES spectra that was absent in the theoretical models. In contrast, the corresponding cuts in Termination B showed only the bottom of electron-like bands in the same momentum regions, confirming the feature is specific to the surface termination and not an artifact of the measurement geometry.

Significance and Claims
The paper claims that TaRhTe4 provides a unique platform where nontrivial topology (Weyl points) coexists with flat bands near the Fermi level in a bulk, nonmagnetic system. This is significant because flat bands are rarely observed in Weyl semimetals, and their presence in a bulk crystal without the need for external tuning (such as twisting layers) offers a new avenue for study.

The authors emphasize that the flat bands are located very close to the Fermi energy (4 meV below), suggesting they could be tuned to the chemical potential via chemical or electronic means to influence transport and thermodynamic properties. The coexistence of flat-band physics and topological band structures in TaRhTe4 is presented as a promising platform for investigating anomalous transport and emergent quantum phenomena, particularly in regimes where independent-electron or weakly-interacting-electron models may fail. The work highlights a limitation of current DFT methods in predicting these specific flat bands in this material class, indicating a need for further theoretical development.

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