International team of physicists including scientists from University of Grenoble, Landau Institute for Theoretical Physics, Weizmann Institute of Sciences and University of Utah explained anomalous low temperature behavior of ‘dirty’ superconductors. These materials possess various non-trivial properties which make them necessary part of quantum computers with superconductive qubits. In a paper published in Nature Physics, scientists report how ‘dirty’ superconductors can violate the conventional theory of superconductivity. With these results, it becomes possible to engineer superconductive qubits that are perfectly isolated from the outer disturbances and thus can be fully used for quantum computing.
Superconductors are materials that lose electrical resistance under special circumstances. When resistance falls to zero, an electrical current circulates within a superconductor without any dissipation of energy, while in wires made of conventional materials a lot of energy is lost as heat. Superconductivity has been discovered in early XX century, but the first phenomenological theory that explained superconductive properties was proposed only in 1950 by Soviet physicists Lev Landau and Vitaly Ginzburg. The complete microscopic theory of superconductivity was created seven years later by John Bardeen, Leon Cooper and John Schrieffer in the USA. For this theory dubbed BCS after their initials, they were awarded Nobel Prize in 1972.
Among other things BCS theory predicts the behavior of superconductors in a magnetic field. In a weak applied field superconductor expels magnetic flux while staying superconductive – this is called the Meissner effect. In a large class of materials (known as ‘type-II’ superconductors), at higher magnitudes of magnetic fields it penetrates into the bulk of superconductor in the form of quantized ‘tubes’ of magnetic flux, called Abrikosov vortices. Such a ‘mixed state’ is superconducting if vortices are pinned to the underlying atomic structure by disorder, which creates potential energy wells where vortices prefer to sit. But if magnetic field is increased further, at the point called upper critical magnetic field (Bc2) the sample loses its superconductivity and behaves like normal metal. When the temperature of the sample is relatively high and gets closer to critical temperature (Tc), superconductivity can be destroyed even by weak magnetic field. In different materials Tc varies from several to several dozen kelvins. The lower the temperature, the stronger magnetic field must be applied to ‘shut down’ the superconductivity. However, when the temperature gets below one fifth of Tc, further cooling of the sample does not lead to increase of Bc2. In other words, at a range of very low temperatures the magnetic field required to destroy superconductivity is stable and does not depend on the temperature of superconductive sample.
“This classical behavior is violated in ‘very dirty’ superconductors”, says Mikhail Feigelman, head of the Quantum Mesoscopics Department of Landau Institute for Theoretical Physics. “By ‘very dirty’ we mean superconductors made of some metal alloys with highly disordered crystal structure – i.e., they are almost amorphous. In these superconductors critical magnetic field continues to increase almost linearly even at very low temperatures. This abnormal behavior has been observed previously, but there was no decent explanation for it at the time”.
Low-temperature anomaly of the critical field Bc in 'very dirty' superconductors. These materials prevail in vortex-glass condition and thermal fluctuations of the vortex-glass are the key ingredient that causes the linear tepmerature dependance of Bc.
In their new research scientists made several experiments and proposed theoretical explanation of the continued Bc increase in ‘very dirty’ superconductors at near-zero temperatures. Key experimental findings were made while measuring critical current density. Along with critical temperature and critical magnetic field, critical current density is a fundamental characteristic of a superconductor. It is the maximum electrical transport current density that the superconductor is able to maintain with zero resistance. When the critical current density is exceeded, the sample ceases to superconduct and starts to heat. Authors of the new paper worked with amorphous indium oxide films of various levels of disorder – a prototypical disordered superconductor. They applied different currents to samples and measured critical magnetic fields required to destroy the superconductive state.
Though similar experiments have been performed earlier, this research is the first to feature systematic measurements of the critical magnetic fields and currents in the ‘very dirty’ superconductor at near critical magnetic fields and near-zero temperatures. “Surprisingly, it turned out that critical current density depends in a very simple way on how close the magnetic field is to its critical value. It is a power-law dependence and the exponent is 3/2”, says Feigelman. In addition to that, authors also measured the temperature dependence of the critical magnetic field value for indium oxide films.
“Comparing findings made in these two experiments, we managed to understand the connection between them. When strong magnetic field is applied to ‘very dirty’ superconductors and they still stay superconductive, thermal fluctuations of Abrikosov vortices occur inside disordered superconductor samples”, explains Feigelman. “And we’ve found a way to describe these Abrikosov vortices thermal fluctuations”. Predictions of the theory proposed by Feigelman and his colleagues are in good agreement with experimental data.
‘Very dirty’ superconductors are the cutting edge of modern superconductive physics. They differ from conventional metals in many ways. Under normal conditions, any disorder introduced in a usual metal decreases its ability to conduct electrical current. The more the disorder, the greater is the electrical resistance. When cooled, resistance of such disordered conventional metals decreases. ‘Very dirty’ superconductors at room temperature behave as weak dielectrics and become less and less conductive with temperature decrease. But when critical temperature is reached, they leap into superconductive state. “Superconducting and dielectric states are directly opposed to each other. This is why such a transition is amazing. ‘Very dirty’ superconductors have been studied for 25 years, but we still lack a complete theory to explain their unconventional behavior”, tells Feigelman.
In recent years disordered superconductors have been extensively studied as it turned out that these materials can have a lot of practical applications. ‘Very dirty’ superconductors are the best materials to isolate superconductive qubits – basic units of the quantum computer – from the external disturbances. That is due to their strong inductance – sort of electrical ‘inertia’ that determines the intensity of magnetic flux created by the electric current circulating inside the material. The more disordered is the superconductor, the stronger is it’s inductivity, and components with strong inductance serve as perfect ‘noise insulators’ that protect fragile quantum entanglement of the qubits.