Quantum Oscillations in ZrTe5 Reveal Unexpected Electron Spin Behavior
Research published in Nature Communications has revealed an unusual form of quantum oscillation in the three-dimensional topological insulator zirconium pentatelluride, or ZrTe5. The findings show that electrons in the material can behave unexpectedly at temperatures close to absolute zero and under extremely strong magnetic fields.
The study was led by scientists from the University of São Paulo (USP), Los Alamos National Laboratory, the University of Washington, and other U.S. institutions. Researchers combined theoretical calculations with electrical transport experiments conducted in magnetic fields of up to 60 tesla and at temperatures as low as 0.7 kelvin (-272.45°C).
“This work expands our understanding of electron transport in exotic phases of matter and suggests that topological insulators support the transport not only of charge but also of another fundamental degree of freedom: electron spin,” said Julio Larrea Jiménez, a professor at the USP Institute of Physics and co-founder and director of the Laboratory for Quantum Materials under Extreme Conditions (LQMEC).
Larrea was the doctoral adviser of Kahue Kaufman Ribeiro, the study’s lead author. Ribeiro conducted most of the experimental research during an internship at the National High Magnetic Field Laboratory in Los Alamos, supported by a FAPESP Overseas Research Internship. During the project, Ribeiro also received guidance from Joanna Palmstrom and Sean Thomas.
ZrTe5: A Material with Two Electronic Personalities
Topological insulators are materials with an unusual combination of electrical properties. Their interiors behave as insulators, while their surfaces can conduct electricity. This behavior results from the topology of the electronic bands—the broad characteristics of a material’s quantum electronic structure that are protected by crystal symmetries.
ZrTe5 is especially valuable for studying topological physics because it lies close to the boundary between different topological phases. Small changes in temperature, mechanical strain, chemical composition, or magnetic field can significantly alter its electronic behavior.
This sensitivity makes ZrTe5 an important material for investigating topological phase transitions and relativistic quasiparticles in solids.
What Are Landau Levels and Quantum Oscillations?
When an electron moves through a magnetic field, its possible energies no longer form a continuous range. Instead, quantum mechanics confines the electron to specific energy values known as Landau levels, named after Soviet physicist and mathematician Lev Landau.
In very pure metals, Landau levels can repeatedly cross the Fermi level—the boundary between occupied and unoccupied electronic states. Each crossing can produce oscillations in electrical resistance known as Shubnikov–de Haas oscillations.
These oscillations normally follow a predictable pattern that is periodic in 1/B, where B represents the magnetic field.
Quantum Oscillations Continue Beyond the Quantum Limit
The researchers found that ZrTe5 does not follow this conventional pattern. Its magnetoresistance oscillations were not periodic in 1/B and continued well beyond the quantum limit.
This observation was unexpected. Beyond the quantum limit, electrons are generally expected to occupy only the lowest Landau level. Under conventional theory, the familiar quantum oscillations should therefore disappear.
“In materials near topological phase transitions, electrons may no longer behave like ordinary particles in metals,” Kaufman explained. “Their electronic excitations begin to behave like Dirac fermion-like quasiparticles, or relativistic particles. In our study, the spin of these quasiparticles plays a central role.”
According to the researchers, a strong magnetic field significantly changes the electron energy levels because of the interaction between spin and the magnetic field. As a result, a Landau level can return toward the Fermi level and cross it again. This unusual phenomenon is known as a reentrant Landau level.
Landau-Level Backbending Explains the Anomaly
To explain the continued oscillations, the research team proposed a process called Landau-level backbending. Instead of changing linearly as the magnetic field increases, some Landau levels curve back toward the Fermi level before crossing it again.
These additional crossings produce new resistance oscillations in magnetic-field regions where traditional models predict that the oscillations should have already disappeared.
Electron Spin Changes the Quantum Behavior
The unusual behavior results from the interaction between two physical effects. The first is the cyclotron energy associated with the orbital motion of electrons in a magnetic field. The second is the Zeeman effect, which describes the interaction between a magnetic field and electron spin.
In ZrTe5, strong spin–orbit coupling means these effects cannot be treated independently. Electron spin and orbital motion become linked, causing the Landau-level energy to evolve nonlinearly as the magnetic field changes.
The researchers also sought to determine whether the unusual oscillations were caused by collective, many-body interactions between electrons or by the intrinsic topological properties of the material’s electronic structure.
The results showed that many-body interactions were not necessary to explain the observations. A single-particle model based on a three-dimensional Dirac Hamiltonian and strong spin–orbit coupling successfully reproduced the experimental behavior.
“Our results show that the effect does not arise from many-body interactions, but from the nontrivial topology of the electronic bands,” Larrea said.
Resolving Conflicting Results in ZrTe5 Research
The discovery may help resolve a long-standing debate over quantum oscillation measurements in ZrTe5. Different samples of the same material have previously produced distinctly different results.
Some samples displayed conventional oscillations periodic in 1/B. Others showed nonperiodic oscillations, while some produced signals that appeared to be logarithmically periodic in the magnetic field.
The new findings suggest that these differences may not require separate explanations. Instead, they could all result from the same underlying Dirac electronic structure, with the observed behavior determined primarily by the carrier density and the size of the Fermi surface in each sample.
“In samples with low carrier densities, such as those studied here, the Zeeman and cyclotron effects become comparable within experimentally accessible magnetic fields,” Larrea explained. “This promotes reentry into the Landau level and makes the anomalous oscillations visible. In samples with higher carrier densities, the conventional cyclotron contribution dominates, and the oscillations retain their usual 1/B periodicity.”
Interference Between Two Spin Channels
The researchers also identified two separate contributions to the quantum oscillations associated with spin-separated electronic states. These two channels have different effective masses and can interfere with one another.
This interference may explain another unexpected feature of the measurements. According to the conventional Lifshitz–Kosevich model, the amplitude of quantum oscillations should decrease steadily as temperature rises. Instead, the researchers observed a local minimum in the oscillation amplitude over a specific temperature range.
The result indicates that the two electronic channels are not simply weakening in the standard way. Rather, they are interacting and interfering with one another.
Angular magnetoresistance measurements provided additional information about the electronic structure of ZrTe5. Under low magnetic fields, the Fermi surface appeared to be nearly ellipsoidal in three dimensions.
The researchers calculated a very low carrier density of approximately 1016 carriers per cubic centimeter. This value is consistent with ZrTe5 being located close to a topological phase transition.
Extreme Conditions Enable New Quantum Discoveries
The experiments were performed at the National High Magnetic Field Laboratory in Los Alamos, one of the few facilities worldwide capable of combining pulsed magnetic fields of up to 60 tesla with temperatures below 1 kelvin.
“Experiments of this type can only be conducted in a few locations around the world, and access to these facilities is highly competitive,” Larrea said.
The discovery not only explains the anomalous quantum oscillations observed in ZrTe5, but also strengthens the case for using the material as a platform for exploring new phases of matter.
The researchers suggest that more exotic electronic states could be created by carefully controlling factors such as crystal symmetry, carrier density, mechanical strain, temperature, and magnetic field. These states could include phases containing Weyl quasiparticles.
“Our experiment provides the first empirical demonstration of a process that has remained controversial,” Larrea said.
The research received support from FAPESP through a Young Investigator Grant awarded to Larrea. Additional funding came from U.S. agencies and institutions, including Los Alamos National Laboratory, the National High Magnetic Field Laboratory, the National Science Foundation, and the U.S. Department of Energy.
Source: www.sciencedaily.com