Quantum breakthrough reveals hidden nature of superconductors

Researchers at Tokyo Tech have identified the critical quantum point in superconductors, solving a three-decade-old mystery and advancing understanding of superconductivity fluctuations. Credit: SciTechDaily.com

The thermal effect reveals the full picture of fluctuations in superconductivity.

Weak fluctuations in superconductivity,[1] The phenomenon of superconductivity was successfully discovered by a research group at the Tokyo Institute of Technology (Tokyo Tech). This feat was achieved by measuring the thermal effect[2] In superconductors over a wide range of magnetic fields and over a wide range of temperatures from well above the superconducting transition temperature to very low temperatures near Absolute zero.

This revealed the full picture of fluctuations in superconductivity with respect to temperature and magnetic field, and demonstrated the origin of the anomalous metallic state in magnetic fields, which had been an unsolved problem in the field of 2D superconductivity.[3] For 30 years, a critical quantum point exists[4] Where quantum fluctuations are at their strongest.

Understanding superconductors

A superconductor is a material in which 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 crucial as small logic elements in quantum computers that operate at low temperatures, and there is a need to elucidate the properties of low-temperature superconductors when they are miniaturized.

Atomically thin 2D superconductors are strongly affected by fluctuations and thus exhibit properties that differ significantly from those of thicker superconductors. There are two types of fluctuations: thermal (classical), which is more pronounced at high temperatures, and quantum, which is more significant at very low temperatures, the latter causing a variety of interesting phenomena.

For example, when a magnetic field is applied perpendicular to a two-dimensional superconductor at absolute zero and increasing, a transition from a superconductor with zero resistance to an insulator with localized electrons occurs. This phenomenon is called magnetic field-induced superconducting insulator transition and is a typical example of a quantum phase transition[4] Caused by quantum fluctuations.

Two types of fluctuations in superconductors

Figure 1. (Left) In a mesoscale magnetic field, lines of magnetic flux break through in the form of defects accompanied by eddies of superconducting currents. (Center) Conceptual diagram of the “superconductivity fluctuation” state, a precursor to superconductivity. Time-varying, spatially non-uniform, bubble-like superconducting regions are formed. (Right) Schematic diagram of thermal effect measurement. Magnetic flux line motion and superconductivity fluctuations generate a voltage perpendicular to the heat flow (temperature gradient). Credit: Koichiro Inaga

However, it has been known since the 1990s that for samples with relatively weak localization effects, an anomalous metallic state appears in the intermediate magnetic field region where the electrical resistance is several orders of magnitude lower than the normal state. The origin of this anomalous metallic state is thought to be a liquid-like state, in which magnetic flux lines (Figure 1 left) that penetrate the superconductor are moved by quantum fluctuations.

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However, this prediction has not been proven because most previous experiments on 2D superconductors used electrical resistance measurements that examine the response of voltage to current, making it difficult to distinguish between voltage signals arising from the movement of magnetic flux lines and those arising from the scattering of electrons with normal conduction.

A research team led by Assistant Professor Koichiro Inaga and Professor Satoshi Okuma from the Department of Physics, Faculty of Science, Tokyo Tech University reported in Physical review letters 2020 Quantum motion of magnetic flux lines occurs in an anomalous metallic state using the thermoelectric effect, where an electric voltage is generated with respect to heat flow (temperature gradient) rather than a current.

However, to further clarify the origin of the anomalous metallic state, it is necessary to elucidate the mechanism by which the superconducting state is destroyed by quantum fluctuation and transitions to the normal (insulating) state. In this study, they performed measurements aimed at detecting the fluctuation state of superconductivity (center of Figure 1), a precursor state to superconductivity that is thought to exist in the natural state.

Color map of the thermoelectric signal capturing fluctuations in superconductivity

Figure 2. The full picture of fluctuations in superconductivity is revealed over a wide magnetic field range and over a wide range of temperatures, from well above the superconducting transition temperature to as low as 0.1 K. The existence of a line of intersection between heat (classical) and quantum fluctuations was demonstrated for the first time, and the quantum critical point at which this line reaches absolute zero was found to be located within the anomalous metallic region. Credit: Koichiro Inaga

Research achievements and techniques

In this study, molybdenum germanium (MosGee1-s) thins With amorphous structure,[5] Known as a two-dimensional superconductor with a uniform and chaotic structure, it has been manufactured and used. It is 10 nanometers thick (one nanometer is a billionth of a meter), and promises to have fluctuation effects characteristic of 2D systems.

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Since fluctuation signals cannot be detected by electrical resistance measurements because they are buried in the normal conduction electron scattering signal, we performed measurements of the thermoelectric effect, which can detect two types of fluctuations: (1) superconductivity fluctuations (fluctuations in superconductivity capacitance) and ( 2) Movement of the magnetic flux line (fluctuations in the superconducting phase).

When a temperature difference is applied in the longitudinal direction of the sample, the fluctuations of superconductivity and the movement of magnetic flux lines generate a voltage in the transverse direction. In contrast, normal electron motion generates voltage mainly in the longitudinal direction. Especially in samples such as amorphous materials, where electrons do not move easily, the voltage generated by the electrons in the transverse direction is small, so the fluctuation contribution alone can be selectively detected by measuring the transverse voltage (Figure 1, right).

The thermoelectric effect has been measured in a variety of magnetic fields and at a variety of temperatures ranging from well above the superconductivity transition temperature of 2.4 kelvin (K) to as low as 0.1 K (1/3000 of 300 K, ° Room temperature), which is close to absolute zero. This reveals that superconductivity fluctuations remain present not only in the liquid region of the magnetic flux (dark red region in Figure 2), where the superconducting phase fluctuations are most evident, but also over a wide region of the temperature magnetic field farther outward which is considered to be The normal state region, where superconductivity is destroyed (the region of high magnetic field and high temperature above the upper convex solid line in Figure 2). Notably, the intersection line between thermal (classical) and quantum fluctuations was successfully discovered for the first time (thick solid line in Figure 2).

The value of the magnetic field when the intersection line reaches absolute zero likely corresponds to the quantum critical point where quantum fluctuations are strongest, and that point (white circle in Figure 2) clearly lies within the magnetic field range where an anomalous metallic state exists. It was observed in electrical resistance. The existence of this quantum critical point has not been detected from electrical resistance measurements until now.

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This result reveals that the anomalous metallic state in the magnetic field at absolute zero in 2D superconductors, which has remained unresolved for 30 years, arises from the existence of a quantum critical point. In other words, the anomalous metallic state is an expanded quantum critical ground state for the transition from superconductor to insulator.


Measurements of the thermoelectric effect obtained for conventional amorphous superconductors can be considered as standard data for the thermoelectric effect on superconductors, because they capture the effect of fluctuations in superconductivity without the contribution of normal-state electrons. The thermal effect is important in terms of its application to electrical refrigeration systems, etc., and there is a need to develop materials that exhibit a significant thermal effect at low temperatures to extend the maximum cooling temperatures. Unusually large thermoelectric effects at low temperatures have been reported in some superconductors, and comparison with existing data may provide a clue to their source.

Future developments

One of the academic interests to be developed in this study is to clarify the theoretical prediction that in 2D superconductors with stronger localization effects than the present sample, magnetic flux lines will be in a quantum condensed state6. Going forward, we plan to publish experiments using the methods of this study to find out.

The results of this study were published online in Nature Communications On March 16, 2024.


  1. Fluctuations in superconductivity: The strength of superconductivity is not uniform and fluctuates in time and space. It is normal for thermal fluctuations to occur, but near absolute zero, quantum fluctuations occur based on the uncertainty principle of quantum mechanics.
  2. Thermal effect: Effect of thermal and electrical energy exchange. A voltage is generated when a temperature difference is applied, while a temperature difference is produced when a voltage is applied. The former is being studied for use as a power generation device and the latter as a cooling device. In this study, it was used as a way to detect fluctuations in superconductivity.
  3. 2D superconductivity: Ultra-thin superconductor. When the thickness becomes smaller than the distance between the pairs of electrons responsible for superconductivity, the effect of fluctuations in superconductivity becomes stronger, and the properties of superconductors are completely different from those of thicker superconductors.
  4. Quantum critical point, quantum phase transition: The phase transition that occurs at absolute zero when a parameter such as the magnetic field is changed is called a quantum phase transition, and is distinguished from the phase transition caused by a temperature change. The quantum critical point is the phase transition point where quantum phase transition takes places They occur where quantum fluctuations are strongest.
  5. Amorphous structure: A structure of matter in which the atoms are arranged in an irregular manner and do not have a crystalline structure.
  6. Condensed quantum state: A condition in which a large number of particles are in the lowest energy state and behave as a single macroscopic wave. In superconductivity, many pairs of electrons are condensed. Liquid helium also condenses when cooled to 2.17 K, resulting in superior fluidity with no stickiness.

Reference: “Extended quantum critical ground state in a disordered superconducting thin film” by Koichiro Inaga, Yutaka Tamoto, Masahiro Yoda, Yuki Yoshimura, Takahiro Ishigami, and Satoshi Okuma, 16 March 2024, Nature Communications.
doi: 10.1038/s41467-024-46628-7

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