Nav: Home

Solid-state physics: Probing the geometry of energy bands

June 01, 2016

Scientists at Ludwig-Maximilians-Universitaet (LMU) in Munich and the Max Planck Institute for Quantum Optics (MPQ) have devised a new interferometer to probe the geometry of band structures.

The geometry and topology of electronic states in solids play a central role in a wide range of modern condensed-matter systems, including graphene and topological insulators. However, experimentally accessing this information has proven to be challenging, especially when the bands are not well isolated from one another. As reported by Tracy Li et al. in last week's issue of Science (Science, May 27, 2016, DOI: 10.1126/science.aad5812), an international team of researchers led by Professor Immanuel Bloch and Dr. Ulrich Schneider at LMU Munich and the Max Planck Institute of Quantum Optics has devised a straightforward method with which to probe band geometry using ultracold atoms in an optical lattice. Their method, which combines the controlled transport of atoms through the energy bands with atom interferometry, is an important step in the endeavor to investigate geometric and topological phenomena in synthetic band structures.

A wide array of fundamental issues in condensed-matter physics, such as why some materials are insulators while others are metals, can be understood simply by examining the energies of the material's constituent electrons. Indeed, band theory, which describes these electron energies, was one of the earliest triumphs of quantum mechanics, and has driven many of the technological advances of our time, from the computer chips in our laptops to the liquid-crystal displays on our smartphones. We now know, however, that traditional band theory is incomplete.

Among the most surprising and fruitful developments in modern condensed-matter physics was the realization that band structure involves more than the just the electron energies - the geometric form of the bands also plays an important role. Indeed, this geometric contribution is responsible for much of the exotic physics in newly discovered materials such as graphene or topological insulators, and underlies a variety of exciting technological possibilities from spintronics to topological quantum computing. It is, however, notoriously difficult to access this information experimentally.

Now, an international team of researchers led by Immanuel Bloch (Professor of Experimental Physics at LMU Munich and a Director of the Max Planck Institute of Quantum Optics (MPQ)) has devised a straightforward method to probe band geometry using ultracold atoms in an optical lattice, a synthetic crystal formed from standing waves of light. Their method relies on creating a system that can be described by a quantity known as the Wilson line, and the experimental tests performed at LMU and the MPQ have verified that the technique allows one to explore the geometry of band structure.

Although originally formulated in the context of quantum chromodynamics, it turns out that Wilson lines also describe the evolution of degenerate quantum states, i.e., quantum states with the same energy. Applied to condensed-matter systems, the elements of the Wilson line directly encode the geometric structure of the bands. Therefore, to access the band geometry, the researchers need only to access the Wilson line elements.

The problem, however, is that the bands of a solid are generally not degenerate. However, the researchers realized that there was a way to get around this: When moved fast enough in momentum space, the atoms no longer feel the effect of the energy bands and their behavior is influenced only by the essential geometric information. In this regime, two bands with different energies behave like two bands with the same energy.

In their work, the researchers first cooled atoms to quantum degeneracy. The atoms were then placed into an optical lattice formed by laser beams to realize a system that mimics the behavior of electrons in a solid, but without the added complexities of real materials. In addition to being exceptionally clean, optical lattices are highly tunable -- different types of lattice structures can be created by changing the intensity or polarization of the light. In their experiment, the researchers interfered three laser beams to form a graphene-like honeycomb lattice.

Although spread out over all lattice sites the quantum degenerate atoms carry a well-defined momentum in the light crystal. The researchers then rapidly accelerated the atoms to a different momentum and measured the magnitude of the excitations they created. When the acceleration is fast enough, such that the system is described by the Wilson line, this straightforward measurement reveals how the electronic wave function at the higher momentum differs from the wave function at the initial momentum. Repeating the same experiment at many different crystal momenta would yield a complete map of how the wave functions change over the entire momentum space of the artificial solid.

The researchers not only confirmed that it was possible to move the atoms in such a fashion that the dynamics were described by two-band Wilson lines, the measurements at different momenta also revealed both the local, geometric properties and the global, topological structure of the bands. While the lowest two bands of the honeycomb lattice are known not to be topological, the results demonstrate that Wilson lines can indeed be experimentally used to probe and uncover the band geometry and topology in these novel synthetic settings.
-end-


Ludwig-Maximilians-Universität München

Related Topological Insulators Articles:

Bridging the gap between the magnetic and electronic properties of topological insulators
Scientists at Tokyo Institute of Technology shed light on the relationship between the magnetic properties of topological insulators and their electronic band structure.
Topological superconducting phase protected by 1D local magnetic symmetries
Scientists from China and USA classified 1D gapped topological superconducting quantum wires with local magnetic symmetries (LMSs), in which the time-reversal symmetry is broken but its combinations with certain crystalline symmetries, such as MxT, C2zT, C4zT, and C6zT, are preserved.
Octupole corner state in a three-dimensional topological circuit
Higher-order topological insulators featuring quantized bulk polarizations and zero-dimensional corner states are attracting increasing interest due to their strong mode confinement.
Quantum simulation for 3D chiral topological phase
Professor Liu at PKU, Professor Du and Professor Wang at USTC build up a quantum simulator using nitrogen-vacancy center to investigate a three-dimensional (3D) chiral topological insulator which was not realized in solid state system, and demonstrate a complete study of both the bulk and surface topological physics by quantum quenches.
Photonic amorphous topological insulator
The current understanding of topological insulators and their classical wave analogues, such as photonic topological insulators, is mainly based on topological band theory.
Recent advances in 2D, 3D and higher-order topological photonics
A research team from South Korea and the USA has provided a comprehensive review covering the recent progress in topological photonics, a recently emerging branch of photonics.
Synthetic dimensions enable a new way to construct higher-order topological insulators
Higher-order topological insulators (HOTIs) are a new phase of matter predicted in 2017, involving complicated high-dimensional structures which show signature physical effects called ''corner modes.'' Now, scientists have proposed a recipe to construct such HOTIs and observe corner modes for photons in simpler, lower-dimensional structures by harnessing an emerging concept called ''synthetic dimensions.'' This construction allows flexible tuning of the topological behavior and opens avenues for even more exotic phases of photons in very high dimensions.
Topological photonics in fractal lattices
Photonic topological insulators are currently a subject of great interest because of the features: insulating bulk and topological edge states.
Low-threshold topological nanolasers based on the second-order corner state
Topological lasers are immune to imperfections and disorder, which are mostly at microscale.
Quantum physics: Realization of an anomalous Floquet topological system
An international team led by physicists from the Ludwig-Maximilians Universitaet (LMU) in Munich realized a novel genuine time-dependent topological system with ultracold atoms in periodically-driven optical honeycomb lattices.
More Topological Insulators News and Topological Insulators Current Events

Trending Science News

Current Coronavirus (COVID-19) News

Top Science Podcasts

We have hand picked the top science podcasts of 2020.
Now Playing: TED Radio Hour

Listen Again: The Power Of Spaces
How do spaces shape the human experience? In what ways do our rooms, homes, and buildings give us meaning and purpose? This hour, TED speakers explore the power of the spaces we make and inhabit. Guests include architect Michael Murphy, musician David Byrne, artist Es Devlin, and architect Siamak Hariri.
Now Playing: Science for the People

#576 Science Communication in Creative Places
When you think of science communication, you might think of TED talks or museum talks or video talks, or... people giving lectures. It's a lot of people talking. But there's more to sci comm than that. This week host Bethany Brookshire talks to three people who have looked at science communication in places you might not expect it. We'll speak with Mauna Dasari, a graduate student at Notre Dame, about making mammals into a March Madness match. We'll talk with Sarah Garner, director of the Pathologists Assistant Program at Tulane University School of Medicine, who takes pathology instruction out of...
Now Playing: Radiolab

What If?
There's plenty of speculation about what Donald Trump might do in the wake of the election. Would he dispute the results if he loses? Would he simply refuse to leave office, or even try to use the military to maintain control? Last summer, Rosa Brooks got together a team of experts and political operatives from both sides of the aisle to ask a slightly different question. Rather than arguing about whether he'd do those things, they dug into what exactly would happen if he did. Part war game part choose your own adventure, Rosa's Transition Integrity Project doesn't give us any predictions, and it isn't a referendum on Trump. Instead, it's a deeply illuminating stress test on our laws, our institutions, and on the commitment to democracy written into the constitution. This episode was reported by Bethel Habte, with help from Tracie Hunte, and produced by Bethel Habte. Jeremy Bloom provided original music. Support Radiolab by becoming a member today at Radiolab.org/donate.     You can read The Transition Integrity Project's report here.