Physicists from Germany and the United States have acquired new evidence related to the probable source of high-temperature superconductivity and similar phenomena. They achieved this by accurately quantifying the entropy of a cerium copper gold alloy (that has perplexing electronic characteristics) by cooling it close to absolute zero.
Qimiao Si. (Credit: Rice University)
This demonstration provides a foundation to better understand how novel behaviors like high-temperature superconductivity are brought about when certain kinds of materials are cooled to a quantum critical point.
S i, D irector of the Rice Center for Quantum Materials, Rice University
The experimental study was headed by Hilbert von Löhneysen from the Karlsruhe Institute of Technology in Karlsruhe, Germany. Löhneysen and his colleagues, including Kai Grube, the lead author of the study, spent a year performing numerous experiments on a compound formed of gold and cerium copper. After investigating the effect of stress or pressure exerted in particular directions, and by making the materials extremely cold, the researchers slightly altered the spacing between the atoms constituting the crystalline metallic compounds, consequently modifying their electronic characteristics.
The cerium copper gold alloys are “heavy fermions,” a type of quantum material that exhibits exotic electronic properties when very cold. The best known of these are high-temperature superconductors, termed so for their potential to conduct electrical current at zero resistance at temperatures well above those of conventional superconductors. Heavy fermions exhibit a different oddity: Their electrons appear to be effectively hundreds of times more massive than normal and, equally unusual, the effective electron mass seems to vary strongly as temperature changes.
These odd characteristics defy conventional physical theories. They are also observed at really cold temperatures and are noted when the materials are adjusted to a “quantum phase transition,” that is, a transition from one state to the other, similar to ice melting. In the year 2001, Si and his team devised a new theory, which states that electrons, at the quantum critical point, oscillate between two absolutely disparate quantum states, such that their effective mass becomes infinitely huge. The theory has speculated specific suggestive signs once the quantum critical point is attained. Moreover, Si has collaborated with experimental physicists for the last 16 years to gather evidence to support their theory.
Liquid water and ice are two of the classical states in which H2O can exist. Ice is a very ordered phase because the H2O molecules are neatly arranged in a crystal lattice. Water is less ordered compared with ice, but flowing water molecules still have underlying order. The critical point is where things are fluctuating between these two types of order. It’s the point where H2O molecules sort of want to go to the pattern according to ice and sort of want to go to the pattern according to water. It’s very similar in a quantum phase transition. Even though this transition is driven by quantum mechanics, it is still a critical point where there’s maximum fluctuation between two ordered states. In this case, the fluctuations are related to the ordering of the ‘spins’ of electrons in the material.
Quimiao Si, Director of the Rice Center for Quantum Materials, Rice University
Similar to eye color, spin is an innate characteristic, and the spin of each electron is classified as “up” or “down.” Spins in magnets such as iron are aligned in the same direction. However, a number of materials tend to have the opposite behavior, that is, their spins occur in a repeated up-down, up-down pattern. Physicists refer to this pattern as “antiferromagnetic.”
Numerous experiments performed on high-temperature superconductors, heavy fermions, as well as other quantum materials have revealed that there is a difference in magnetic order on either side of a quantum critical point. In general, experiments reveal antiferromagnetic order in one area of chemical composition, and a new state of order on the other side of the critical point.
A reasonable picture is that you can have an antiferromagnetic order of spins, where the spins are quite ordered, and you can have another state in which the spins are less ordered. The critical point is where fluctuations between these two states are at their maximum.
Si, Director of the Rice Center for Quantum Materials, Rice University
The research carried out by von Löhneysen’s team has rendered the cerium copper gold compound to be a prototype heavy fermion material for quantum criticality.
In 2000, we did inelastic neutron scattering experiments in the quantum critical cerium copper gold system,” stated von Löhneysen. “ We found a spatial-temporal profile so unusual that it could not be understood in terms of the standard theory of metal.”
According to Si, that study motivated him and his colleagues to devise their 2001 theory, which greatly assisted in interpreting von Löhneysen’s confusing results. In the following research works, Si and his team also speculated that entropy (which is a classical thermodynamic characteristic) increases when quantum fluctuations near a quantum critical point increases. According to Si, the well-documented characteristics of cerium copper gold offered a peculiar chance to investigate the theory.
Replacing trace amounts of gold for copper in cerium copper-six enables physicists to subtly increase the spacing between the atoms. The alloys, while in the critical composition, experience an antiferromagnetic quantum phase transition. Investigation of the composition and measurement of the entropy a number of times under differing conditions of stress enabled the Karlsruhe group to develop a 3D map that revealed the way in which entropy steadily increased at very low but finite temperature when the system reached the quantum critical point.
Although there is no direct measure of entropy, the ratio of the change in entropy with respect to stress is directly proportional to the ratio of expansion or contraction of the amount of sample due to changes in temperature, which is measurable. To enable the measurements at the extraordinarily low temperatures, the Karlsruhe group devised a technique for the precise measurement of changes in lengths of less than 1/10th of a trillionth of a meter, that is, nearly one-thousandth of radius of a single atom.
We measured the entropy as a function of stress applied along all the different principal directions,” stated Grube, a senior researcher at Karlsruhe Institute of Technology. “ We made a detailed map of the entropy landscape in the multidimensional parameter space and verified that the quantum critical point sits on top of the entropy mountain.”
According to von Löhneysen, the thermodynamic measurements also offer in-depth knowledge related to the quantum fluctuations at the critical point.
Surprisingly, this methodology allows us to reconstruct the underlying spatial profile of quantum critical fluctuations in this quantum critical material. This is the first time that this kind of methodology has been applied.
Hilbert von Löhneysen, Karlsruhe Institute of Technology, Karlsruhe
According to Si, it was surprising that they were able to achieve this just through entropy measurements.
It is quite remarkable that the entropy landscape can connect so well with the detailed profile of the quantum critical fluctuations determined from microscopic experiments such as inelastic neutron scattering, all the more so when both end up providing direct evidence to support the theory,” stated Si.
Si stated that in general, the revelation of a marked increase in entropy at a quantum critical point in a multidimensional parameter space provides new understanding of the manner in which electron-electron interactions cause high-temperature superconductivity.
One way to relieve the accumulated entropy of a quantum critical point is for the electrons in the system to reorganize themselves into novel phases,” stated Si. “ Among the possible phases that ensue is unconventional superconductivity, in which the electrons pair up and form a coherent macroscopic quantum state.”
Sebastian Zaum of Karlsruhe and Oliver Stockert of the Max-Planck Institute for Chemical Physics of Solids in Dresden, Germany, were the other co-authors of the study. The German Science Foundation, the National Science Foundation, the Humboldt Foundation, the Army Research Office, the Welch Foundation, and the Rice Center for Quantum Materials supported the study.