A study published in Nature Communications has revealed that electrons in zirconium pentatelluride (ZrTe5) are basically the rebellious teenagers of the quantum world. When subjected to temperatures near absolute zero and magnetic fields powerful enough to make your fridge magnets weep, these particles displayed quantum oscillations that defy conventional expectations.
The research, led by scientists from the University of São Paulo (USP) in Brazil, Los Alamos National Laboratory, the University of Washington, and other U.S. institutions, combined electrical transport experiments in magnetic fields up to 60 tesla at temperatures around 0.7 kelvin (-272.45 °C) with detailed theoretical calculations. Because, you know, why not push the limits of physics while you're at it?
"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," says Julio Larrea Jiménez, a professor at USP's Physics Institute and co-founder/director of the Laboratory for Quantum Matter under Extreme Conditions.
Larrea served as the doctoral advisor of Cauê Kaufmann Ribeiro, the study's first author, who did much of the experimental work during an internship at the National High Magnetic Field Laboratory in Los Alamos, supported by a FAPESP Research Internship Abroad, and co-advised by Johanna Palmstrom and Sean Thomas.
Topological insulators are the oddballs of materials science: their interiors are electrical insulators, but their surfaces conduct electricity. This is due to the topology of their electronic bands, which are protected by crystal symmetries. ZrTe5 is particularly special because it sits near the boundary between different topological phases, meaning small changes in temperature, mechanical deformation, chemical composition, or magnetic field can dramatically alter its electronic behavior. It's the quantum equivalent of a moody artist.
When electrons move through a magnetic field, their energies are restricted to discrete values called Landau levels, named after Lev Landau (1908-1968). In pure metals, these levels can repeatedly cross the Fermi level, producing oscillations in electrical resistance known as Shubnikov-de Haas oscillations, which normally follow a predictable pattern in 1/B (B being the magnetic field). But ZrTe5 didn't get that memo.
The researchers found that its magnetoresistance oscillations were not conventionally periodic in 1/B and continued well beyond the quantum limit, where electrons should be stuck in the lowest Landau level and the oscillations should vanish. Instead, the oscillations persisted, like a bad habit.
"In materials near topological phase transitions, electrons may cease to behave like ordinary particles within a metal," explains Kaufmann. "Their electronic excitations begin to behave like quasiparticles similar to Dirac fermions - relativistic particles. In our work, we show that the spin of these quasiparticles plays a central role: when we apply strong magnetic fields, the interaction between spin and the magnetic field profoundly alters the energy levels of the electrons. As a result, Landau levels that would normally move away from the system's relevant energy can 'return' and cross it again. This unusual behavior is what we call reentrant Landau levels."
To explain this, the researchers propose a process called "back-bending" of Landau levels, where some levels bend back toward the Fermi level and cross it again, generating extra oscillations in a regime where they shouldn't exist. This happens because of the interplay between cyclotron energy (from orbital motion) and the Zeeman effect (spin-magnetic field coupling), which are entangled in materials with strong spin-orbit interaction like ZrTe5.
One of the study's goals was to determine whether the anomalous oscillations were due to many-body effects (collective interactions among electrons) or intrinsic topological properties. The verdict: many-body interactions were not required. A single-particle model using a three-dimensional Dirac Hamiltonian with strong spin-orbit coupling reproduced the experimental results perfectly. "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 summarizes.
These findings could also settle a long-standing debate about ZrTe5 experiments, where different samples showed different types of quantum oscillations: some periodic in 1/B, some not, some with logarithmic periodicity. The new results suggest all these behaviors can arise from the same Dirac electronic structure, with the outcome depending on carrier density and Fermi surface size. In low-carrier-density samples (like this one), Zeeman and cyclotronic effects become comparable, allowing Landau level re-entry and making anomalous oscillations visible. In higher-density samples, the conventional term dominates, and oscillations follow the usual 1/B periodicity.
The researchers also identified two contributions to the oscillations linked to spin-separated states, with different effective masses that can interfere. This interference explains a local minimum in oscillation amplitude at certain temperatures, defying the conventional Lifshitz-Kosevich model.
Angular magnetoresistance measurements revealed a three-dimensional, roughly ellipsoidal Fermi surface under low magnetic fields, and the carrier density was calculated at about 10^16 per cubic centimeter - very low, consistent with ZrTe5 being near a topological phase transition.
The experiments were performed at the National High Magnetic Field Laboratory in Los Alamos, one of the few places on Earth that can combine pulsed magnetic fields up to 60 tesla with temperatures below 1 kelvin. "This type of experiment can only be performed in a few places around the world. Access to those facilities is highly competitive," Larrea notes.
Beyond explaining the weird oscillations, the findings strengthen ZrTe5's case as a platform for exploring even more exotic topological phases, potentially involving Weyl quasiparticles, by tweaking symmetry, carrier density, stress, temperature, and magnetic field.
"Our experiment provided the first empirical demonstration of a process that had previously been shrouded in controversy," Larrea concludes.
The research was supported by FAPESP (including a Young Investigator Grant), Los Alamos National Laboratory, the National High Magnetic Field Laboratory, the National Science Foundation, and the U.S. Department of Energy. Materials provided by Fundação de Amparo à Pesquisa do Estado de São Paulo.