A team of Korean researchers, including the Korea Research Institute of Standards and Science (KRISS, President Dr. Lee Ho Seong) and the Gwangju Institute of Science and Technology (GIST, President Lim Kichul), has become the first in the world to identify the origin of the “beating*”signal that has long been a major obstacle to interpreting quantum signals in topological insulator (TI) nanowires. Their analysis confirmed that the beating arises when two different quantum oscillations overlap, where one created by the topological electronic states on the surface and the other by the ordinary electronic states inner the nanowire. This achievement provides a key criterion for interpreting the signals of topological quantum devices and for realizing desired electronic states.
* Beating: a phenomenon in which oscillations with slightly different periods overlap, causing the overall oscillation intensity to periodically grow stronger and weaker.
A topological insulator is a quantum material that conducts little electricity in its interior but hosts special electronic states on its surface. When such a material is made into a thin nanowire, the surface electrons travel around its perimeter, and when a magnetic field is applied, the electron waves that have passed through different paths interfere with one another, producing "Aharonov-Bohm (AB) oscillations," in which the conductance changes at regular intervals for varing magnetic fields. In real topological insulators, however, factors such as doping can create a thin layer just beneath the surface where electrons also flow. This layer, too, can serve as a path for electrons, but whether it participates in AB oscillations together with the topological surface states has remained unclear.
The clue to solving this question came from a thermoelectric experiment. While examining whether AB oscillations also appear in the thermoelectric effect of antimony (Sb)-doped bismuth selenide (Bi₂Se₃) nanowires, the researchers discovered "beating." Beating is a phenomenon in which oscillations with slightly different periods overlap and the signal intensity varies, much like two tuning forks producing a pulsing "wah-wah" sound; it was the decisive clue that captured the presence of another, unexpected oscillation component. Based on this, the researchers re-analyzed their earlier electrical conductance data and confirmed that the same beating phenomenon had been present all along.
After years of tracking and analysis, the researchers concluded that the beating arises when oscillation components originating from the “Topological Surface State (TSS*)” and the “Two-Dimensional Electron Gas (2DEG**), an ordinary electron layer beneath the surface, overlap.” They found that the electron paths passing through these two conduction states enclose slightly different cross-sectional areas of the nanowire, generating oscillations with different periods that superpose to produce the beating.
* Topological Surface State (TSS): A special electronic state formed on the outermost surface of a topological insulator.
** Two-Dimensional Electron Gas (2DEG): A common electronic state in which electrons gather and move in a thin layer beneath a material's surface.
The key to verification lay in the oscillation frequency. Because the frequency is determined by the area of the path along which electrons circle the nanowire, the frequency should remain the same even when the electronic state is changed by the gate voltage, as long as the path area stays constant. However, since neighboring oscillations overlapped, they were difficult to distinguish using conventional frequency analysis. To address this, the collaborating team led by Professor Song Taegeun of Kongju National University used machine learning to separate the oscillation components that had appeared clustered together in previous analyses, confirming that each frequency remained distinct even as the beating pattern changed with the gate voltage. Theoretical calculations also reproduced the observed characteristics, and the same phenomenon was verified in a separate nanowire device.
This study clearly demonstrated that ordinary electronic states can also take part in AB quantum interference, which has been used as a key signal for identifying topological surface states. In doing so, it established a clear criterion for accurately interpreting the quantum transport signals of topological insulators without error and for precisely controlling desired quantum states in the future.
Dr. Bae Myung-Ho, Principal Research Scientist in the Quantum Device Group at KRISS, said, “This achievement shows that electrons can undergo quantum interference by moving through not only topological states but also ordinary electronic states.” He added, “To make use of only the desired topological state, it is important to precisely control doping and the gate so that the ordinary conduction state does not intervene.”
Professor Choi Sang-Jun of the Department of Physics and Photon Science at the GIST said, “By bringing together the experimental, theoretical, and data-analysis capabilities of the research teams at each institution, this achievement explains, within a single physical picture, the origin of the beating that had gone unsolved for years.” He added, “The principle of understanding and controlling the interference between different electronic states could also be applied to the design of toological quantum devices in the future.”