The band structure of certain crystals defines a class of materials known as topological. Visualizing a material's energy band structure can immediately reveal something about that material's properties. The interactions between these atoms and electrons cause the allowed discrete energy values to spread out and smear into allowed ranges of energy called bands. But a chunk of solid crystal the size of a grape typically contains more atoms (around 10 23) than there are grains of sand on Earth. Different states have separate and distinct-discrete-energy values. All other amounts of energy are forbidden. In a solid crystal these limits restrict a single electron on a single atom to only one value of energy for each possible movement pattern (called a quantum state). After all, although electrons in a crystal have mass, they are both particles and waves (the same is true for our ultracold atoms). The crystal phenomena we investigate result from the way quantum mechanics limits the motion of wavelike particles. Our experiments revealed special properties of our synthetic material that are directly related to the bizarre physics manifesting in graphene. We can even study lattice physics in ways that are impossible in solid-state crystals. Our system is not a perfect emulation of graphene, but for understanding the phenomena we're interested in, it's just as good. With cold atoms in an optical lattice, we can magnify the system and slow down the hopping process enough to actually see the particles jumping around and make measurements of the process. In our system, we make cold atoms hop around a lattice of bright and dim light just as electrons hop around the carbon atoms in graphene. In a recent experiment, for instance, my team and I made an optical version of graphene with the same honeycomb lattice structure as the standard carbon one. Our optical lattice has the exact same geometry as the atomic lattice. In place of the atomic lattice, we use light waves to create what we call an optical lattice. We've found a clever way to get around this limitation, however, by making matter out of light. Electrons move too fast for us to capture the details we want to see. I and other physicists would like to understand what's going on inside graphene on an atomic level, but it's difficult to observe action at this scale with current technology. Brown II (right) uses optical lattices to probe exotic physics. Credit: Spencer Lowell (left), Wayne Lawrence (right) Notes on a wall (left) offer reminders for alignment of optical lattice laser beams and other methods. These kinds of properties make graphene intrinsically interesting as well as potentially useful in applications ranging from better electronics and energy storage to improved biomedical devices. Graphene also exhibits a phenomenon called the quantum Hall effect: the amount of electricity it conducts increases in specific steps whose size depends on two fundamental constants of the universe. The way electrons move inside graphene-a crystal made of carbon atoms arranged in a hexagonal lattice-produces an extreme version of a quantum effect called tunneling, whereby particles can plow through energy barriers that classical physics says should block them. In certain crystals the behavior of electrons can create properties that are much more exotic. For example, metals are shiny because they contain lots of free electrons that can absorb light and then reemit most of it, making their surfaces gleam. How electrons move through a lattice, hopping from atom to atom, determines many of a solid's properties, such as its color, transparency, and ability to conduct heat and electricity. These materials are crystals, which in physics means they are made of highly ordered repeating patterns of regularly spaced atoms called atomic lattices. Many seemingly mundane materials, such as the stainless steel on refrigerators or the quartz in a countertop, harbor fascinating physics inside them.
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