Electrons in ZrTe5 defy quantum limit under

Electrons in the topological material zirconium pentatelluride (ZrTe5) have exhibited unexpected quantum behavior under extreme conditions. A study published in Nature Communications reports that quantum oscillations continued in the material even after conventional physics predicted they should vanish, occurring at temperatures near 0.7 kelvin and magnetic fields reaching 60 tesla.

Led by scientists from the University of São Paulo, Los Alamos National Laboratory, and the University of Washington, the research combined high-field electrical transport experiments with theoretical calculations. Julio Larrea Jiménez, a professor at USP's Physics Institute and co-director of the Laboratory for Quantum Matter under Extreme Conditions, stated the work expands understanding of electron transport in exotic matter. "This work expands our understanding of electron transport in exotic phases of matter and suggests that topological insulators support the transport of not only electric charge, but also another fundamental degree of freedom: electron spin," he said.

A Material With Two Electronic Personalities

Topological insulators like ZrTe5 have insulating interiors but conductive surfaces, a property arising from the topology of their electronic bands. ZrTe5 is particularly valuable for study because it sits close to the boundary separating different topological phases. Small changes in temperature, mechanical deformation, or magnetic field can significantly alter its electronic behavior, making it a key material for investigating topological phase transitions.

When electrons move through a magnetic field, quantum mechanics restricts them to specific energy values known as Landau levels. In very pure metals, these levels crossing the Fermi level produce predictable oscillations in electrical resistance called Shubnikov-de Haas oscillations. These normally follow a periodic pattern related to the inverse of the magnetic field (1/B).

Quantum Oscillations That Refused To Disappear

The researchers found ZrTe5 did not follow this familiar pattern. Its magnetoresistance oscillations were not conventionally periodic in 1/B, and they continued well beyond the quantum limit where electrons should be restricted to the lowest Landau level and oscillations should disappear.

Cauê Kaufmann Ribeiro, the study's first author who performed experiments at the National High Magnetic Field Laboratory, explained the phenomenon. "In materials near topological phase transitions, electrons may cease to behave like ordinary particles within a metal." he said. The researchers propose a "back-bending" process where some Landau levels bend back toward the Fermi level and cross it again, generating additional oscillations where conventional theory predicts none.

Electron Spin Changes the Picture

The unusual behavior emerges from the interaction between cyclotron energy from electron orbital motion and the Zeeman effect from coupling between the magnetic field and electron spin. In ZrTe5, where spin-orbit interaction is strong, these contributions cannot be considered independently. Electron spin and orbital motion become coupled, causing Landau level energies to evolve nonlinearly as the magnetic field changes.

The study aimed to determine whether many-body effects from collective electron interactions or intrinsic topological properties caused the anomalous oscillations. The researchers found interactions among many electrons were not required. Instead, a single-particle model based on a three-dimensional Dirac Hamiltonian with strong spin-orbit coupling reproduced the experimental results. "What we saw is that the effect doesn't stem from many-body interactions, but rather from a nontrivial topology of the electronic bands," Larrea summarized.

Resolving Conflicting Results in ZrTe5

The findings may help clarify a long-running debate about ZrTe5 experiments where different samples produced different quantum oscillations. Some showed conventional oscillations periodic in 1/B, others showed non-periodic oscillations, and still others produced signals with logarithmic periodicity in B.

According to the new results, all these behaviors could arise from the same underlying Dirac electronic structure, with outcomes determined by carrier density and Fermi surface size in each sample. "In samples with low carrier density, such as the one investigated here, the Zeeman and cyclotronic effects become comparable in experimentally accessible magnetic fields," Larrea commented. This favors Landau level re-entry and makes anomalous oscillations visible. In samples with higher carrier density, conventional behavior dominates.

Two Spin Channels Interfere

The researchers identified two separate contributions to quantum oscillations linked to spin-separated states. These have different effective masses and can interfere with each other. This interference explains another unexpected feature: instead of oscillation amplitude steadily decreasing with temperature as predicted by the conventional Lifshitz-Kosevich model, the researchers observed a local minimum across certain temperature ranges.

Angular magnetoresistance measurements showed the Fermi surface appeared three-dimensional and roughly ellipsoidal under low magnetic fields. The experiments were performed at the National High Magnetic Field Laboratory using specialized equipment to test matter under extreme conditions.