Freezes water at absolute zero

Matter close to absolute zero of temperature

In the metal-insulator transition and other quantum phase transitions, the quantum properties of matter play the decisive role. These quantum phenomena can only be studied experimentally at very low temperatures, in the range of a few degrees Kelvin, near absolute zero.

The transition from electrically insulating to metallic behavior is a special case of a large class of fascinating phenomena known as phase transitions. This includes the freezing of water to ice as well as the transition between the non-magnetic and the magnetic phase of a substance such as iron. The latter phenomena are classic phase transitions. Thermal fluctuations are decisive, i.e. the random movements of the atoms due to the heat. In the metal-insulator transition and other quantum phase transitions, however, the quantum properties of matter play the decisive role. These quantum phenomena can only be studied experimentally at very low temperatures, in the range of a few degrees Kelvin, near absolute zero.

The phase transition from water to ice and many other liquid-solid transitions are often discontinuous: the density of the changing substance changes abruptly. When it freezes, as in the case of ice, it shrinks by leaps and bounds. Another example of a phase transition is the evaporation of water under normal pressure at the critical temperature of 100 degrees Celsius. Phase transitions are heralded by fluctuations: even above the critical temperature, tiny drops of liquid form for a short time during cooling, but they quickly dissolve again. As the critical point approaches, these fluctuations expand spatially and become slower. The droplets become correspondingly larger and last longer until the transition into the other phase takes place. With further cooling one then has gaseous areas in the liquid, which gradually disappear. The continuous phase transitions are “driven” by such fluctuations.

Quantum phase transitions

Quantum phase transitions are also often continuous. They are also accompanied by fluctuations, but not by those known from classical statistical physics. Rather, it is a question of quantum fluctuations that are caused by the quantum nature of matter, as expressed in Heisenberg's uncertainty principle. The uncertainty principle is the basic principle of quantum mechanics and states that certain physical quantities such as the position and speed of a particle cannot be measured at the same time with unlimited accuracy. At the absolute zero point, the movements of all particles would normally freeze. The particles would then get stuck at certain points. The uncertainty principle says, however, that the velocities of the particles would then have to be arbitrarily large. However, this is not possible at absolute zero. This is why quantum objects necessarily have to fluctuate: they just can't get stuck in a certain place without moving.

Quantum fluctuations are not only decisive for the continuous phase transitions at absolute temperature zero. They also have a very strong influence on the behavior of certain substances at finite temperatures. This goes so far that well-known ideas about the properties of the atomic building blocks of matter have to be questioned. There are clear indications that in certain substances - for example in the exotic alloy CeCu6-xAux made of cerium, copper and gold (x assumes different values, depending on the composition of the alloy) - the electrons at absolute temperature zero completely lose their usual identity as Fermi particles. This can be concluded from the course of the specific heat of such substances as a function of temperature. The specific heat indicates how much thermal energy a substance can absorb if its temperature is increased by 1 degree Kelvin. With the alloy mentioned, the specific heat at the transition point between the magnetic and non-magnetic phase increases logarithmically with falling temperature, instead of decreasing proportionally to the falling temperature, as is the case with non-magnetic metals in which the electrons behave like “normal” Fermi particles.

The proportionality of the specific heat to the temperature in normal metals is due to the fact that the electrons are Fermi particles, of which only one can occupy a certain quantum state. Although in one metal around 1023 there are different quantum states for every cubic centimeter and although a similar number of electrons interact with each other due to their charge, it never happens that two or more of them are in the same quantum state!

The experimental result described is of fundamental importance: The fact that CeCu6-xAux the specific heat is not proportional to the temperature, suggests that the electrons in this substance must have other properties than the well-known Fermi particles. The interactions can drastically intervene in the nature of the elementary building blocks of matter and lead to a complete breakdown of the “normal” particle identity.

Another fundamental discovery is that in some of these non-Fermi fluid systems, superconductivity also occurs at the quantum phase transition. This is a clear indication of a new type of superconductivity, for which magnetism is an important prerequisite. This is surprising, because in classical superconductors, magnetic order is more in conflict with superconductivity and can even destroy it. Magnetic coupling effects are also considered to explain the high temperature superconductors.

The metal-insulator transition mentioned at the beginning, as it occurs, for example, in silicon doped with phosphorus atoms as a function of the phosphorus concentration, is very difficult to observe because, strictly speaking, it only occurs at absolute temperature zero. At any absolute temperature, no matter how small and different from zero, there is a certain probability that the originally immobile electrons will “hop” from one place to another due to the addition of thermal energy. The material is then no longer an insulator in the strict sense. The investigation of this quantum phase transition therefore poses an extreme challenge to the art of experimenters and theorists, because it seems to result in drastic changes in the identities of the electrons. Only now are physicists able to understand why some elements of the periodic table are metals, while others are insulators.