Magnetoconductance evolution across the topological-trivial phase transition in ${In_{x}}({Bi_{0.3}}{Sb_{0.7}})_{2-x}{Te_3}$ thin films

In the world of quantum materials, there exists a special class of substances known as topological insulators. Imagine a material that acts like a perfect electrical insulator on the inside, blocking the flow of electricity, while simultaneously acting like a highly efficient conductor on its very surface. This unusual behavior is not caused by the material's shape or size, but by a fundamental property of its internal electronic structure, protected by the laws of quantum mechanics. These surface currents are remarkably robust; they can flow around defects and impurities without scattering, a feature that makes them highly desirable for building future electronic devices that generate less heat and consume less power. However, this delicate state of matter is sensitive to its environment. If the material is disturbed too much, or if its chemical makeup is altered significantly, the special surface currents can vanish, and the material reverts to behaving like a normal, ordinary insulator. Understanding exactly how and when this transition happens, and how the material behaves as it loses its special properties, is a central question for physicists trying to harness these materials for real-world technology.

A team of researchers at the Indian Institute of Science Education and Research Kolkata has mapped out this journey in detail, studying a specific family of thin films made from indium, bismuth, antimony, and tellurium. By carefully adjusting the amount of indium in the mixture, they were able to steer the material through two distinct phases of change. First, they observed the material shifting from its exotic topological state into a standard, ordinary insulating state. Then, as they added even more indium, they pushed the material into a chaotic regime where electricity no longer flows freely but instead jumps in a series of tiny, random hops between trapped spots. The researchers found that the way electricity responds to a magnetic field changes dramatically at each of these stages, revealing a complex interplay between the material's internal quantum structure and the disorder introduced by the added atoms.

The scientists created a series of ultra-thin films, each about 100 nanometers thick, using a technique that fires a laser at a target to deposit atoms onto a crystal surface. They started with a film that had no indium, which behaved as a topological insulator with metallic surface currents. As they systematically increased the concentration of indium, replacing heavier atoms with lighter ones, they noticed a critical shift occurring around a concentration of roughly 7 percent. At this point, the material underwent a topological phase transition. The internal energy bands of the material, which had been inverted to create the special surface states, flipped back to their normal order. This change was signaled by a specific marker in the data: the strength of the quantum interference effects that usually protect the surface currents began to rise and then fall, peaking right at the moment the material lost its topological identity. This confirmed that the material had crossed from a topological class into a trivial, ordinary insulating class.

However, the story did not end there. As the researchers continued to add indium, the material became increasingly disordered. Around a concentration of 15 percent, a second, more dramatic transition occurred. The electrical resistance of the films skyrocketed, indicating that the electrons were no longer moving in a smooth, flowing stream. Instead, they had become trapped in localized pockets, forced to move by a mechanism known as variable-range hopping. In this regime, an electron does not flow continuously; it waits for a thermal jolt, then makes a sudden, random jump to a nearby site where it can exist, only to wait and jump again. This is a stark contrast to the smooth flow seen in the topological phase. The researchers identified this 15 percent threshold as the point where the material crossed from a diffusive, metal-like state into a strongly localized, insulating state.

Perhaps the most striking discovery was how the material reacted to magnetic fields as it moved through these different phases. In the early stages, when the material was still topological and the electrons were flowing freely, applying a magnetic field reduced the electrical conductivity. This is a well-known effect where the magnetic field disrupts the quantum interference that helps electrons avoid collisions. But once the material crossed the 15 percent threshold and entered the hopping regime, the response flipped completely. At low magnetic fields, the conductivity actually increased. This positive response was a surprise because standard theories of quantum interference usually predict a decrease in conductivity. The researchers found that this increase was caused by the magnetic field disrupting the random interference patterns between the different paths an electron could take while hopping. By breaking these patterns, the magnetic field made it slightly easier for electrons to find a successful path to their destination, effectively lowering the resistance.

As the magnetic field grew stronger, the behavior shifted again. The positive effect was eventually overwhelmed by a different mechanism where the magnetic field squeezed the electron's wave-like shape, making it harder for the electron to jump between sites. This caused the conductivity to drop, turning the response negative once more. The researchers observed that the point where this switch from positive to negative occurred depended on both the temperature and the amount of indium in the film. At higher temperatures, the positive effect dominated across the entire range of magnetic fields they tested. To explain this complex behavior, the team combined two different theoretical ideas: one that describes how magnetic fields affect the interference of hopping paths, and another that accounts for how the magnetic field changes the energy levels of the trapped sites. This combined model successfully described the entire landscape of the material's behavior, from the smooth flow of the topological phase to the chaotic hopping of the disordered phase.

The study provides a unified picture of how topology, disorder, and magnetic fields work together to determine the electrical properties of these materials. It establishes a clear experimental link between the loss of the topological state and the onset of incoherent hopping conduction. By pinpointing the exact concentrations where these transitions occur, the researchers have shown that the journey from a topological insulator to a disordered insulator is not a single event but a sequence of distinct physical changes. The findings suggest that while the special surface currents are robust against small amounts of disorder, they are eventually overwhelmed by the increasing chaos of the atomic structure. This work offers a detailed roadmap for understanding how quantum materials behave under stress, which is essential knowledge for anyone hoping to use these materials in future electronic devices that rely on the unique properties of topological states.