Strongly correlated materials are a subcategory of quantum materials and they are often referred to as this, the former name paints a good picture of what they are but doesn’t make them sound anywhere near as cool as the latter. When it comes down to defining strongly correlated materials, its all to do with how the electrons move. Most of our electronic devices are based on the movement of electrons, these electrons are not attached to specific atoms and are free to roam around with other electrons. These electrons have a negative charge so when we place a positive charge at one end, the electrons all move towards it, creating a current and powering our devices. Strongly correlated materials are a bit more complicated and show interesting results in these situations.

When doing calculations for electronic devices, we take into account the fact that there are millions of electrons moving and can average out all the properties. So one electron may be moving very fast but its balanced out by one electron moving very slowly. We call this the mean field approach, we take the average of all the properties and assume each electron has this averaged value. It works very well for a lot of materials and is what most of our electronic devices are based upon.

However, this method breaks down when dealing with strongly correlated materials. The electrons within these materials repel each other strongly and this needs to be taken into account wisely when doing calculations. When the electrons were only interacting weakly, the mean field approach was sufficient. In order to solve problems with strongly interacting electrons we need to solve something called Schrodinger’s equation, but unfortunately this is very difficult when there are so many electrons. We can only actually solve Schrodinger’s equation for a few very simple problems and none of them involve more than one electron. It’s quite difficult to believe that after all this time and all these technological advancements, we still cannot solve a problem with more than one electron precisely, but its true. Luckily, the mean field approach works very well and we haven’t needed to up until now.

The only way round this problem is to use some sort of model. A commonly used model is called the Hubbard model and was created by John Hubbard in 1963. It is the simplest model for interacting electrons but is very effective and is still used to this day. With the help of this model we can calculate an approximate result for Schrodinger’s equation and look at how the interaction between electrons has an impact on the material.

So now we know what strongly correlated materials are and how to go about solving Schrodinger’s equation for them, why are strongly correlated materials interesting? Well, most of these materials show some unique properties. When I was speaking about electronic devices before, I was referring to metals, they allow the electrons to roam free and this means they can conduct electricity well. Electrons have charge but also have a property called spin that can either be up or down, the details of this is not too important you just need to know there are only two possible states. Some strongly correlated materials are what we call half-metals, half-metals are materials that conduct electricity but only for electrons with spin up. This gives us an extra degree of freedom that can be used to our advantage. This property isn’t currently used in technology but is thought to become useful within spintronics (spin electronics) in the future. Other strongly correlated materials exhibit something called spin-charge separation, this means that instead of treating the electron as having the properties of spin and charge, you can treat the electrons spin and charge as two separate particles. They also produce interesting magnetic properties such as ferromagnetism and antiferromagnetism. Ferromagnetism is when all of the electrons in the material have spin pointing in one direction and antiferromagnetism is when all the spins are aligned antiparallel.

Half-metallicity and spin-charge separation are unique properties that occur in strongly correlated materials. There needs to be a lot more research done on these materials and how they can be used, but these properties could come into play in lots of different areas of science and technology. For example, in order to advance quantum computers we need to find a more reliable material to store qubits and they could become useful for this.

SUMMARY

• Strongly correlated materials have electrons that interact too strongly to be thought of as a sea of electrons moving at the same pace.
• Calculating interactions between electrons are still a difficult problem and cannot be solved exactly but models can be sufficient in some cases.
• Strongly correlated materials show interesting properties such as half-metallicity, spin-charge separation and well ordered spin alignments.