Over a wide range of magnetic fields and temperatures, from well above the superconducting transition temperature to extremely low temperatures of 0.1 K, the full picture of superconductivity fluctuations has been revealed. For the first time, it was demonstrated that there is a crossing line between thermal (classical) and quantum fluctuations, and it was found that the quantum critical point at which the line reaches absolute zero exists within the anomalous metal region. Photo credit: Koichiro Ienaga
Weak fluctuations in superconductivity are a precursor phenomenon of superconductivity and have been successfully detected by a research team at the Tokyo Institute of Technology (Tokyo Institute of Technology). This breakthrough was achieved by measuring the thermoelectric effects of superconductors over a wide range of magnetic fields and temperatures, from well above the superconducting transition temperature to extremely low temperatures close to absolute zero. The findings were published online in Nature Communications on March 16, 2024.
This reveals the full picture of the fluctuations of superconductivity relative to temperature and magnetic fields, and proves that the origin of anomalous metallic states in magnetic fields – a problem that has been unanswered in the field of two-dimensional superconductivity for 30 years – is the existence of quantum tipping points, with the strongest quantum fluctuations.
Superconducting films
A superconductor is a material where electrons pair up at low temperatures, resulting in zero electrical resistance. It is used as a material for powerful electromagnets in medical MRI and other applications.
They are also considered to be vital tiny logic elements in quantum computers operating at low temperatures, and when superconductors are miniaturized, the properties of superconductors at low temperatures need to be elucidated.
Atomically thin two-dimensional superconductors are strongly affected by fluctuations and therefore exhibit significantly different properties than thicker superconductors.
There are two types of fluctuations: thermal (classical) and quantum (more important at very low temperatures). The latter can give rise to all sorts of interesting phenomena. For example, when the magnetic field is perpendicular to a two-dimensional superconductor at absolute zero degrees and increases, the transition from zero-resistance superconductivity to an insulator with local electrons occurs.
This phenomenon, known as the magnetic field-induced superconductor-insulator transition, is a classic example of a quantum phase transition caused by quantum fluctuations. However, since the 1990s, it has been known that for samples with relatively weak localization effects, abnormal metallic states occur in intermediate magnetic field regions where the resistance is orders of magnitude lower than normal.
The origin of this anomalous metal state is thought to be a liquid-like state in which magnetic flux lines penetrating superconductors move around due to quantum fluctuations.
However, this prediction has not been confirmed, as most previous experiments on two-dimensional superconductors have used resistivity measurements to examine the response of voltage to current, making it difficult to distinguish between a voltage signal from the movement of magnetic flux lines and a voltage signal from the scattering of conductive electrons from the normal.
In 2020, a research team led by Assistant Professors Koichiro Ienaga and Satoshi Okuma from the Department of Physics, Faculty of Science, Tokyo Institute of Technology, reported in Physical Review Letters that the quantum motion of magnetic flux lines occurs in an abnormal metal state by utilizing the thermoelectric effect, where voltage is generated relative to heat flow (temperature gradient) rather than current.
In order to further elucidate the origin of the anomalous metal state, it is necessary to elucidate the mechanism by which the superconducting state is disrupted by quantum fluctuations and transitions to a normal (insulated) state.
In this study, they performed measurements aimed at detecting the dynamics of superconducting waves, which are the precursor states of superconductivity and are thought to exist in a normal state.
(Left) In a medium-sized magnetic field, magnetic flux lines penetrate in the form of defects accompanied by vortex of superconducting currents. Conceptual diagram of the state of the (center) "superconducting wave", which is a precursor to superconductivity. Formation of time-changing, spatially inhomogeneous, bubble-like superconducting regions. (Right) Schematic diagram of thermoelectric effect measurement. Magnetic flux line motion and superconducting fluctuations produce a voltage (temperature gradient) perpendicular to the heat flow. Photo credit: Koichiro Ienaga
Research Results
In this study, a thin film of molybdenum-germanium (MoxGe1-x) with an amorphous structure was prepared and used, called a two-dimensional superconductor with a homogeneous structure and disorder. It is 10 nanometers thick (1 nanometer is one billionth of a meter) and is expected to have wave effects characteristic of two-dimensional systems.
Since the wave signal is buried in the signal scattered by the positive electrons and therefore cannot be detected by resistivity measurements, the researchers made thermoelectric effect measurements that can detect two types of waves: 1) superconducting waves (fluctuations in the amplitude of superconductivity) and 2) magnetic flux line motion (fluctuations in the superconducting phase).
When a temperature difference is applied in the longitudinal direction of the sample, the superconducting fluctuations and the movement of the magnetic flux lines produce a voltage in the transverse direction.
On the contrary, normal electronic motion mainly produces voltage in the longitudinal direction. In samples such as amorphous materials where electrons do not move easily, the voltage generated by electrons in the transverse direction is negligible, so the fluctuation contribution can be selectively detected by measuring the transverse voltage.
The thermoelectric effect is measured at a wide range of magnetic fields and at a wide range of temperatures, from 2.4 K (Kelvin), well above the superconducting transition temperature, to very low temperatures of 0.1 K (1/3000 of 300 K, room temperature), close to absolute zero. This shows that superconducting fluctuations exist not only in the liquid region of magnetic flux, where the superconducting phase fluctuations are more pronounced, but also in the farther wide temperature magnetic field region, which is considered to be the normal state region, where superconductivity is destroyed.
Notably, for the first time, the crossing line between thermal (classical) and quantum fluctuations was successfully detected. When the crossed line reaches absolute zero, the magnetic field value may correspond to the quantum critical point where the quantum fluctuations are strongest, and the point is clearly within the magnetic field range, and an anomalous metallic state is observed in the resistance.
Until now, it has not been possible to detect the existence of this quantum critical point from resistivity measurements. This result shows that the anomalous metallic state in the absolute zero magnetic field of a two-dimensional superconductor that has been unsolved for 30 years stems from the existence of a quantum critical point. In other words, anomalous metal states are broadened quantum-critical ground states of the superconductor-insulator transition.
Thermoelectric effect measurements of amorphous conventional superconductors can be considered as standard data for the thermoelectric effect of superconductors, as they purely capture the effects of superconductivity fluctuations without the contribution of normal electrons.
The application of the thermoelectric effect in electric cooling systems, etc., is very important, and it is necessary to develop materials that exhibit large thermoelectric effects at low temperatures to extend the limit of the cooling temperature. At low temperatures in some superconductors, the thermoelectric effect has been reported to be unusually large, and comparisons with available data may provide clues to their origins.
Future studies can demonstrate the theoretical prediction that the magnetic flux lines will be in quantum condensed states in 2D superconductors with stronger local effects than existing samples. Going forward, the researchers plan to use the methods of this study to deploy experiments to detect them.
更多信息: Koichiro Ienaga 等人,无序超导薄膜中的扩展量子临界基态,Nature Communications (2024)。 DOI: 10.1038/s41467-024-46628-7
期刊信息：Physical Review Letters 自然通讯