Visualizing and Simulating Quantum Materials

Intro:
Long story short. So this article is spawned out of some cool admiration for a family friend. He is one of Canada’s quantum material scientists. He has a very interesting life, and is often very quiet about his work. I don’t know if that’s because of the extreme NDAs he has to work under, or just because he’s a super humble person. But this is for you man.
What are Quantum Materials?
So what the heck is a quantum material? Quantum materials is an umbrella term that describes all materials that have properties that cannot be described through atomic level particles or through low-level quantum mechanics. This term is commonly used in condensed matter physics.

These materials have electronic correlations that can emit superconducting and/or magnetic properties. Or electronic properties linked to complex quantum effects. This can include insulating types of effects.

Quantum materials can be very puzzling, as one of their features is the ability to have no counterpart material that exhibits the same factors. This can include: quantum entanglement, quantum fluctuations, and boundary states dependent on the topology of the materials' bulk wave functions.

Some quantum materials contain Dirac electron systems. These are electrons that follow the Dirac equation. These are systems that are controlled by relativistic wave equations. These are equations that predict the behavior of particles at high energies and velocities. The Driac equation describes the Spin-½ that is seen in electrons and quarks. It’s an important equation in quantum mechanics because it helped predict the existence of antimatter.

Long story short, without diving into too many confusing topics. This equation describes quantum fields corresponding to spin-1⁄2 particles.

Dirac electron systems are controlled by quantum behavior. Other particles that are controlled by this are ultra-cold atoms, cold excitons, and polaritons.

The most important concept when dealing with particles in a quantum state, is understanding their four fundamental degrees of freedom. This is charge, spin, orbit, and lattices.

Solid state materials that we use in our everyday lives are now classified through lens topology or lens space. Lens space describes topological space that works with 3-manifold geometry. In chemistry, quantum materials are defined through this topology concept. This can help scientists look for new topology traits in materials including: responses to external stimuli, such as field (electric and magnetic), to waves (from light to acoustic waves), and to temperature, pressure, and strain forces.

Research into topological traits in condensed matter physics is an ongoing topic. It is leading new discoveries into how the behavior of quantum materials can be predicted and noticed. It can showcase a material’s small thermal and hydrodynamic electric conductivities, large chiral photocurrents, magnetoresistance, and Nernst effects. These attributes can sometimes go against the classical laws of physics.

Most solid state materials can be classified into two categories. The first group is considered conductors. Metals conduct electricity. The second group is insulators. Insulators do not conduct electricity. These states are differentiated by their valence and conduction bands. If the valence band is filled and separated completely from the conduction band, then it is considered an insulator. The gap between them is called an energy gap. Depending on the distance, the matter can also be considered a semiconductor. Vice versa if it is a conductor.

For example, diamonds are considered insulators. This is because the energy gap is so wide that any temperature cannot excite it’s internal electrons.

Semiconductors are fairly interesting too. For example, silicon is considered a semiconductor because at absolute zero the material behaves as an insulator. But they have small band gaps that allow heat to excite the electrons.

Conductor wise, the valence and conduction bands overlap, and in turn have now energy gap. Because of this, even at absolute zero and below these materials can conduct energy.

Exotic materials(such as quantum), on the other hand, cannot fit into these traditional classes. They still contain valence and conduction bands, however these bands are connected by metallic states. These metallic states are known as topological surface states. These surface bands cross each other to form Dirac cones in the material. This causes the spin and the momentum of the electrons to be locked perpendicular to each other. This is a common trait in exotic materials.

One compound material that helps identify new topological insulators is Heusler compounds. These compounds are magnetic intermetallics, and they are also considered quantum materials. Intermetallics are metallic alloys that form an ordered solid-state compound between two or more metallic elements. These compounds contain cubic crystalline structures that use a composition of attributes classified under the units X, Y, and Z. X and Y represent the transition metals and Z represents the p-block on the periodic table of elements. Its structure can be easily modified as well as it;s electronic properties.

Heusler compounds can also help discover topological insulators in organic solids.

Quantum materials are used in many different places and objects. Most famously MRIs, which use superconductors for medical imaging. They are also used in hard disk drives, which have magnetoresistance sensors in them. Currently the U.S Department of Energy is looking into using them for energy technologies. They are looking into them at their many Energy Frontier Research Centers (EFRCs). Other quantum material scientists are looking to add them into solar energy products so more energy can be easily made.
Other Uses For Quantum Materials
There are many other uses for quantum materials,so let’s talk about them.As well as breakdown how they are integrated. Also I just want a chance to talk about the James Webb Telescope. So, stick with me on this one.

Briefly before we get started. Keep in mind that most particles, especially electrons have something called spin. This spin can be classified as either up or down. This spin makes materials magnetic if they are metals. This spin follows certain rules, and it can also be used to classify certain quantum materials. So let’s cover some.

Spin Liquids: This is one of four states of matter that is a liquid. This liquid is unique because it can be formed by the spins of certain magnetic materials. The magnetic order of them is all over the place, and is not unified. They can be easily quantum entangled, and weakly attracted to magnetic fields. Their behavior can be compared to ferromagnetic fluids. They are being looked into as a possible data storage method, and for computer memory applications.

Spin Glass: The name of this material is a bit misleading as it is less of a material, and more of a state of being. It refers to a magnetic state where the spins of the particles are affected randomly by magnetic fields. The spins will act disordered in the field, and the material itself will be considered metastable. This means that the particles are in stable configurations that are not in their lowest possible energy state. They are one of the most difficult materials to study in simulations and in practical experiments. However, they are finding uses in AI neural networks, and other quantum material research.

Spin Ice: This is a magnetic material that does not have a minimal energy state. A minimal energy state is also considered a ground state. This state refers to when the system has zero energy in it. Therefore, a spin ice always has energy in its system. It has magnetic strength that allows it to form complex structures in any direction. They commonly have low-energy properties, and its spin has a configuration that is commonly seen in water based ice.

Most quantum materials have strange electronic properties that change our idea of how the spin on unpaired electrons work. This feeds the concept of something called Frustration.(An accurate description for a confused scientist in this field) Frustration happens when the geometry of the structure should now allow for all the spins to align with each other. But they do.

Frustration allows scientists to build a large amount of energy states in quantum materials. This allows for complicated spin structures to form, which in turn creates entanglements in the material.

Before we go any farther we should talk about quantum entanglement, as entanglement and quantum entanglement plays a huge factor in what we are talking about.

- Quantum Entanglement happens when particles are generated, interact, or are so close together that each particle’s state cannot be defined from one another. This is the core concept that separates classical and quantum physics.

Entangled particles become so linked that scientists can’t even distinguish the spin from each individual particle. Einstein first called this effect the “spooky action at a distance”. Materials that showcase this entangled effect can be useful for data storage and memory because the data can exist in the same place at the same time.

Chemistry is a huge part of building quantum materials because in order to develop them you have to create quantum states out of the different elements on the periodic table. Materials that scientists are particularly interested in are soft materials. These materials can have different magnetic properties than solid ones based on their elemental makeup. Magnetic atoms such as manganese or iron, or the size of the atom can move electrons to different orbitals. During this process, the atom can also change sizes. This in turn can affect the lattice structure of the material. This is often seen in solids. In organic or soft materials, this process usually doesn't happen. This can allow for a smoother spin crossover to happen, and for a better energy transfer to occur.

Application wise, this means faster computers, less power needed, and more efficiency.

Now let’s dive into 2D and 3D quantum materials.

2D quantum materials are starting to be pursued as a possible way to make the application of these materials more efficient. The 2D version of these states exhibit the same properties, but are very thin and plate-like. They also have very unique characteristics.

2D quantum materials are used to create tunable quantum states. They are described as being “all interface”. They are very easily synthesized, and because they are so thin they can concentrate energy in one particular place. This can make light and matter interactions more visible.

Combining these concepts together can help us to build Metal-free, biocompatible silicon quantum dots, silicon-based nanomaterials and semiconductor photolithography instruments. Which we can use in a variety of tools. As well as developments in nanoelectronics.

Now to something I think we’ve all been waiting to talk about for over ten years. The James Webb Telescope. Or the 10 Billion Dollar Camera that likes to keep it: Coors Light cold.

So as you might have heard or guessed, this is the most expensive telescope in the world, and it needs to complete a bucket full of missions while operating in temperatures well below minus 455 degrees Fahrenheit. As well as helping us further bridge the gap between classical and quantum physics.

As we covered above, certain quantum materials can operate and carry energy below zero. So let's take a look at what James Webb has on board.

In order to detect most things in the Universe, it needs a mirror that has to be over 6.5 meters across to refract light. As well as processing images in extreme cold in a vacuum.

Webb engineers built 18 mirrors that act together as one big mirror when packaged into three different sections. Each mirror is made of beryllium, and weighs 20 kilos.

- Beryllium ions are currently being used to try and detect dark matter particles, so this element has a huge amount of uses when it comes to uses in astrophysics.

Beryllium is known for holding its shape at cryogenic temperatures. It is also very strong and is an excellent conductor of electricity, heat, and is not magnetic. However, it is also very toxic if inhaled. For James Webb, they tested these pieces of beryllium multiple times under conditions that matched outer space.

After creating these mirrors, the engineers then added a layer of gold. This thin layer of gold improves the mirror’s reflection with infrared light. The gold is only about 100 nanometers thick, and was applied to the telescope using a vacuum chamber.

There are many technologies that the James Webb Telescope has already helped us with even before it’s launched. This is because of all the challenges that needed to be tackled to make sure the tools we wanted to send up would make it there safely.

The first piece of technology it has helped us develop is assistance to human eyesight. The wavefront technology NASA used to measure the mirrors of the spacecraft have helped us to accurately measure the human eye, diagnosing ocular diseases and improve eye surgery.

Webb has also helped save the Hubble Space Telescope. So if you needed a better example of the greatest spacecraft bro-ship of all time: here it is. Webb’s application-specific integrated units (ASICs) have been decided to make an entire circuit board of electronics fit easily into small confined spaces. ASICs are programmable for different applications, and in one of the last Hubble missions, astronauts were able to install one of these devices into the telescope. This was able to fix Hubble’s Advanced Camera for Surveys.
The infrared sensors developed for Webb are now also used for other spacecraft missions. These sensors pick up weak light emitted from galaxies, planets, and stars. Hubble, and countless observatories around the world now use these sensors.
Research and Development
Furthering the development of quantum materials, is the study of their topological structure when it comes to electrons. Electrons exist as both a particle and a wave in quantum mechanics. When they exist as a wave, this can cause some interesting behavior in the topological structure, as waves from surrounding electrons can affect each other. Waves affecting each other can create smaller secondary waves. This in turn creates other electrical properties.

Topology in a greater sense just describes how you can deform something without cutting it apart. Different topologies affect and carry electric currents differently. However, in general, these electron wavefunctions will then deform around the topology. Right now there is a push inside the scientific community to develop better materials so that their topology has less wear and tear to conducting electrons. One of the most promising ways to do this is by looking to develop axion insulators. In most materials, if they are considered a conductor or an insulator, they will remain as a conductor or an insulator despite any changes to their shape.

Axiom insulators are a bit different. For these insulators, the electrons will travel over their surfaces in relation to their spin. These insulators are also magnetic, so they can also showcase strong magnetoelectric currents. This means it can conduct electrons on its surface, and also work as an insulator internally. This makes axiom insulators incredibly interesting when it comes to the development of new technology, as you can now tell electrons to avoid certain places on a circuit board,sensor research, switches, computer, and memory storage.

This all leads into something called spintronic materials. These are materials that can be manipulated by their electrons spin. Depending on the direction the electron is traveling, this is the direction the magnetic field will face. Axiom insulators can be considered as spintronic materials.

Another spintronic material scientists are looking into are spin batteries. These are a lot more hypothetical than axiom insulators. A spin battery is a battery that can be charged by magnetic fields to a device that uses nanotechnology. A few examples of them have been developed in Japan. However, none of them to my knowledge yet have been considered practical.

Onto semimetals. These play an important role in quantum technologies as they have no energy gap. But they also have fewer charge carriers than regular metals. Two very interesting ones are Dirac and Weyl semimetals. Both of these semimetals have 2D and 3D states. Dirac semimetals are condensed matter systems that follow the Dirac equation. However, they have an unusually high electron mobility even though they have a topology that resembles an insulator. Weyl semimetals are a bit different. They are considered massless fermions that prove the existence of a Weyl spinor. This is a wave equation that clarifies how fermions can exist in a manifold, and how spin can be defined in general relativity.

Dirac semimetals can be used to form weyl semimetals. Electrons behave like photons in light when they are conducted through a dirac semimetal. If you apply a magnetic field to it, the dirac points inside of it will split to form mirror opposites of each other. This mathematically forms a weyl semimetal.
Simulations and Visualization
So you might be wondering how you can simulate a material, when most of the science behind it is theoretical, or very very small. So let's cover some of the simulators scientists are using.

QMAS, also known as The Quantum Materials Simulator, is a computational code package for quantum materials. It also has a website you can check out here: http://qmas.jp/about/index.html

It is based on a projector augmented wave system(PAW), and has three subprograms that you can use to simulate quantum materials. The main objectives of QMAS is to increase the development of PAW based codes, share knowledge about computational physics, and find applications to problems involving solid state physics and material science. It is mainly an open source project, so a lot of the information about it is publicly available.

Then there are the quantum simulations scientists are doing on quantum computers. Quantum computers are the key to improving simulation time, and creating efficient ones. Right now when it comes to simulating molecules and materials, we can only simulate a few atoms together on a regular computer. Quantum computers can allow for larger simulations and greater theoretical accuracy when it comes to simulating electronic states of active regions. Currently, this would be the preferred method of simulating and developing quantum materials in a 3D space, however quantum computers are expensive, and we have yet to design commercial versions of them.
Now onto something more or less that I think would be fun to explore from a Houdini perspective. Lately, I've been hard at work developing and visualizing proteins associated with diabetes in Houdini. Maybe for a future presentation….shuuuussshh. But this process has genuinely proven to me that we can visualize atomic structures with scientific ease in the software. As well as animate them. Now biology wise we have the ease of using the Protein Data Bank to pull accurate point clouds from. However, we don’t really have one for atomic structures or quantum data. So if anyone would like to look into that, that would be great.

Unfortunately, there doesn’t seem to be many confirmed examples of people using 3D softwares we use in the film industry for quantum visualization. There are a few cinematic examples, however these don’t incorporate the science very correctly. BUT there is an example that I found for a Mardi submission that is fairly interesting. The file used to be available in this thread here: https://www.sidefx.com/forum/topic/74515/ , However the end result is visualized here: https://vimeo.com/435463922

This quantum material electron wave in the software was done by Adam Katz. On the surface level it doesn’t look like much, however after downloading the file it seems to be super thought out. The goal of this project was to create a Quantum mechanics wave solution for the electron. Adam succeeded.
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