Quantum ‘umbilical cord’ links metal and insulator states in many materials, study shows

A kind of umbilical cord between different quantum states can be found in some materials. Researchers at TU Wien have now shown that this “umbilical cord” is generic to many materials.

It is a basic principle of quantum theory: sometimes certain physical quantities can only assume very specific values; all the values in between are simply not permitted by physics. This fact plays a decisive role in the behavior of materials. Certain energy ranges are possible for the electrons of the material, while others are not. Among other things, this explains the difference between electrically conductive metals and non-conductive insulators.

Sometimes, however, surprising connections can arise between permitted ranges, through which electrons can switch from one range to the other. One such unusual transition region was discovered in 2007 in certain copper-containing materials, known as cuprates.

Scientists at TU Wien (Vienna) have now been able to demonstrate that these are not exotic special cases; in fact, this effect is bound to occur if the interaction between the electrons is large enough. This means that there is an additional state between the metal and the insulator. The findings are published in the journal Nature Communications.

Quantum leaps between permitted energies

“An electron moving around the nucleus of an atom can only assume very specific energy values. Everything in between is forbidden; it can only switch from one permitted energy value to another permitted energy value, which is known as a quantum jump,” says Prof Karsten Held from the Institute of Solid State Physics at TU Wien. “It’s a bit more complicated with electrons in solids, where not just certain energy values are permitted, but entire energy ranges—we call them energy bands.”

Both the energy and the momentum (or speed) of the electrons play a role here: the electron can assume different momentum values, which means that its energy also varies—but only within a certain range. In order to move from one permitted energy range to the next, a larger portion of additional energy is required.

Insulators and conductive metals

In insulators, these permitted energy bands are separated from each other by a wide “forbidden” energy range. This prevents the electrons from switching from a band with low energy, in which each electron remains bound to its atomic nucleus, to a band with higher energy, in which it could move from atom to atom through the material. This means that all electrons remain in place and no electric current can flow. In an electrically conductive material, on the other hand, there is no such forbidden energy range, the electrons can move easily.

“How these allowed and forbidden energy bands are arranged depends on the material, especially on how strongly the electrons interact in this material,” says Held. This strength of the electron interaction can be adjusted by doping the material with a certain number of a different type of atom. This technique is routinely used in semiconductor production.

A new energy band is born—and remains connected by an ‘umbilical cord’

If this interaction strength is changed continuously, it can happen that one allowed energy range splits into two separate allowed energy ranges. “In this case, it is particularly interesting to see what structure arises here and what possible combinations of energy and momentum result from this,” says Held.

“We found that during the process of separation into two allowed energy bands, these two bands initially remain connected to each other by a kind of quantum umbilical cord,” says Held.

At most momentum values, the electron has to make a decision: It can only be in either the upper or the lower energy band. But there is one momentum value for which a wide range of energy values is possible—it connects both bands. Such anomalies, with one momentum value but many energy values, have been found in experiments before, but the cause initially remained unclear.

Held and Juraj Krsnik from TU Wien have now succeeded in showing that this phenomenon is not an exotic isolated case, but that this “umbilical cord effect” is bound to occur when the interaction strength between the electrons falls within a certain range. This means that a further class of states must now be taken into account when categorizing solids.

This is nothing new in solid-state physics: in 2016, for example, the Nobel Prize in Physics was awarded for so-called “topological states” in superconductors, another new set of states, which are also defined by a very specific relationship between energy and momentum values.

Nevertheless, the result is quite surprising: “We were able to show quite clearly that this umbilical cord-like connection must occur quite naturally when one energy band splits off from another,” says Held. “This opens up a whole new perspective on technologically highly interesting classes of materials and shows us that there is more to materials science between electrical conductors and insulators than previously thought.”