Crystal structure (left) and part of the band structure (right) of iridium tetrafluoride. The particular symmetry of the crystal lattice leads to the nodal chains (blue) in the band structure. (from Bzdusek et al. Nature, 2016)
The electronic energy states permitted by quantum mechanics determine whether a solid conducts electric current as a metal or whether it is an insulator. Recently, ETH researchers have theoretically predicted a unique material whose energy states display an unknown peculiarity.
Using a super-microscope to look deep into three diverse solids, in principle the same thing would be observed: atomic nuclei arranged in electrons and a crystal lattice, where a few orbit the atomic nuclei and others criss-cross the whole crystal lattice. However, those three materials might act in an extremely different manner when an electric voltage is used on them.
It is possible for the first solid to conduct an electric current, the second could be an insulator, and the third solid could be a material whose electric conductivity increases with an increase in temperature instead of diminishing, which is the case for metals. This is considered the basis for computer chips and transistors.
A group of physicists headed by Manfred Sigrist, Alexey Soluyanov, and Andreas Rüegg at the Institute for Theoretical Physics of the ETH in Zurich have recently predicted a novel type of solid they call a “nodal chain metal.” The solid is expected to consist of unknown properties that were unknown until now. They also earlier detected a potential candidate among the available materials.
Band Structure and Fermi Level
Two quantities establish how and if a solid conducts electric current: its Fermi level and band structure. The band structure is the possible energy states that can be occupied by the electrons present inside it.
However, a free electron accumulates kinetic energy as its traveling speed increases, and the electrons implanted in a crystal lattice can only accept energy values that are placed inside specific bands or intervals.
This follows from their quantum mechanical wave nature, which is also accountable for the fact that a few values of the motional energy are considered to be off limits for electrons; those are also known as band gaps. The Fermi level is obtained from the fermionic nature of electrons, which highlights that two of them can never occupy the same energy state.
The possibility of building one solid particle at a time would result in each of the newly added electrons trying to occupy higher and higher energy levels, starting from zero energy. The Fermi level would be considered as the energy of the last electron.
It is easy to predict whether a material is an insulator or a metal if its Fermi level and energy bands are known. Movement of the most energetic electrons will take place easily if the Fermi level is present inside a band, resulting in the conduction of electric current.
If the Fermi level corresponds with a band gap, then one has an insulator. Other materials, by the same token, may be metals based on that definition, however they will comprise only some energy states at the Fermi level.
The material we predict is, if you will, a cousin of such so-called semimetals.
Tomàš Bzdušek, PhD student, ETH
Nodes in the Semimetal
Graphene is a semimetal that has gained immense popularity. The way in which the energy bands of graphene’s electrons move toward each other at the Dirac points is responsible for the thermal and electrical conductivities of this unusual material.
In 2010, the discoverers of graphene were awarded the Nobel Prize in Physics. As the band gap actually disappears at the Dirac points, they are also called nodes, (in analogy with the nodes of a standing wave).
In various other semimetals the energy bands do not touch at isolated points but instead touch at well-defined lines or surfaces.
The peculiarity of our new material is that its energy bands touch along interconnected nodal loops, and those nodal loops form a chain. That may sound strange and rather theoretical, but we have actually found a real material that is likely to have those properties. That such nodal chains should appear is not an accident, but dictated by the symmetries of the material’s crystal lattice.
Alexey Soluyanov, ETH
Physicists have also been able to draw an exciting analogy between high energy and solid state particle physics. Nodal chains are impossible in high-energy theories due to the vacuum’s high level of symmetry. In contrast, a crystal has limited symmetries, developing a specific type of novel vacuum.
The researchers took a winding and long road in order to detect the nodal chain material. Under the assumption that it would be easier, they initially looked out for materials comprising of a single nodal loop and then determined the type of symmetry properties the crystal lattice of such a material should possess.
On the whole, there are 230 varied types of crystal symmetries in existance. These symmetries have proven to be highly responsible for the features of a material’s band structure.
Huge online databases (ICSD – Inorganic Crystal Structure Database) were then scoured by Soluyanov and his colleagues. Thousands of known solids have been listed together with their crystal structures in these databases. They eventually chanced upon one that not only had a nodal loop, but the more intricate nodal chain: iridium tetrafluoride.
“It was an unexpected surprise”, admits Quan Sheng Wu, a member of the ETH team.
A Possible Prototype
This solid is relatively unknown and isn't particularly useful, but it could be the prototype for a new type of material with potentially technologically interesting features. For example, the physicists in Zurich predict that that the electric conductivity of these solids should be influenced by magnetic fields in a characteristic manner. This phenomenon is also referred to as magneto-resistance and plays a vital role in modern data storage technologies.
The band structure of iridium tetrafluoride comprises of specific peculiarities that have been linked with higher-temperature superconductivity.
“All of that’s a long shot, of course”, Sigrist concedes. Experimental tests of the unique nodal chain metals are yet to be performed, and it is possible to obtain surprising results.