‘Magic’ angle graphs and the emergence of unexpected topological quantum states

Electrons live in a strange and upside-down world. These infinitesimal particles have never ceased to amaze and mystify, despite the more than a century that scientists have studied them. Now, in an even more astonishing twist, physicists have discovered that, under certain conditions, interacting electrons can create so-called “topological quantum states.” This finding, which was recently published in the journal Nature, affects many technological fields of study, especially information technology.

Topological states of matter are especially intriguing classes of quantum phenomena. Their study combines quantum physics with topology, the branch of theoretical mathematics that studies geometric properties that can be distorted but not intrinsically altered. Topological quantum states first came to the public’s attention in 2016 when three scientists – Princetons Duncan Haldane, Princetons Thomas D. Jones Professor of Mathematical Physics and Sherman Fairchild University Professor of Physics, along with David Thouless and Michael Kosterlitz – won the Nobel Prize for Nobel got. Prize for their work in uncovering the role of topology in electronic materials.

“The last decade has seen quite a bit of excitement about new topological quantum states of electrons,” said Ali Yazdani, the 1909 class of physics professor at Princeton and the study’s senior author. “Most of what we’ve discovered over the past decade has focused on how electrons acquire these topological properties without thinking about how they interact with each other.”

But by using a material known as the magic angle turned bilayer grapheneYazdani and his team were able to investigate how interacting electrons can give rise to surprising phases of matter.

Graphene’s remarkable properties were discovered two years ago when Pablo Jarillo-Herrero and his team at the Massachusetts Institute of Technology (MIT) used it to induce superconductivity – a state where electrons flow freely without any resistance. The discovery was immediately recognized as a new material platform for exploring unusual quantum phenomena.

Yazdani and his fellow researchers were intrigued by this discovery and set out to explore the intricacies of superconductivity.

But what they discovered led them on a different and untrodden path.

“This was a wonderful detour that came out of nowhere,” said Kevin Nuckolls, the paper’s lead author and a graduate physics student. “It was totally unexpected, and something we felt was going to be important.”

Following Jarillo-Herrero and his team, Yazdani, Nuckolls and the other researchers focused their research on twisted bilayer graphene.

“It is truly a miracle material,” said Nuckolls. “It’s a two-dimensional lattice of carbon atoms that is a great electrical conductor and one of the strongest crystals we know.”

Graphene is produced in a deceptively simple yet painstaking way: a bulk crystal of graphite, the same pure graphite in pencils, is exfoliated with masking tape to remove the top layers until it finally reaches a single layer.atom-Thin low carbon, with atoms arranged in a flat honeycomb pattern.

To get the desired quantum effect, following the work of Jarillo-Herrero, the Princeton researchers placed two sheets of graphene on top of each other with the top layer slightly angled. This rotation creates a moiré pattern, which resembles and is named after a commonly used French textile design. The most important point, however, is the angle at which the top layer of graphene is positioned: exactly 1.1 degrees, the ‘magic’ angle that produces the quantum effect.

“It’s such a weird disturbance in nature,” said Nuckolls, “that it’s exactly this angle that needs to be reached.” For example, if the top layer of graphene is placed at an angle of 1.2 degrees, this will have no effect.

The researchers generated extremely low temperatures and created a light magnetic field. Then they used a machine called a scanning tunneling microscope, which relies on a technique called “quantum tunneling” instead of light to view the atomic and subatomic world. They aimed the conductive metal tip of the microscope at the surface of the magically angled graphene and were able to detect the energy levels of the electrons.

They found that the magic angle graphene changed the way electrons moved on the graphene sheet. “It creates a state that forces the electrons to be on the same energy,” said Yazdani. “We call this a ‘flat tire’.”

When electrons have the same energy – they are in a flat band material – they interact very strongly with each other. “This interplay allows electrons to do many exotic things,” said Yazdani.

One of these “exotic” things, the researchers found, was the emergence of unexpected and spontaneous topological states.

“This twisting of the graphene creates the right conditions to create a very strong interaction between electrons,” explains Yazdani. “And this interaction unexpectedly encourages electrons to organize themselves in a series of topological quantum states.”

In concrete terms, they discovered that the interaction between electrons provides so-called topological insulators. These are unique devices that act as insulators in their interiors, meaning that the electrons inside cannot move freely and therefore do not conduct electricity. However, the electrons on the edges can move freely, which means they are conductive. Moreover, due to the special properties of the topology, the electrons flowing along the edges are not hindered by defects or distortions. They flow continuously and effectively circumvent the limitations – such as small imperfections in the surface of a material – that typically hinder the movement of electrons.

During the work, Yazdani’s experimental group brought together two other Princetonians – Andrei Bernevig, a physics professor, and Biao Lian, an assistant professor of physics – to understand the underlying physical mechanism of their findings.

“Our theory shows that two key ingredients – interactions and topology – that usually appear unrelated in nature, are combined in this system,” said Bernevig. This coupling creates the topological isolation states observed experimentally.

Although the field of quantum topology is relatively new, it holds great potential for a revolution in electrical engineering, materials science, and especially computer science.

“People talk a lot about its relevance for quantum computers, where you can use these topological quantum states to make better kinds of quantum bits, ”said Yazdani. “The motivation for what we are trying to do is to understand how quantum information can be encoded in a topological phase. Research in this field is yielding exciting new science and has a potential impact on advancing quantum information technologies. “

Yazdani and his team will continue their research to understand how the interactions of electrons give rise to different topological states.

“The interplay between the topology and superconductivity in this material system is quite fascinating and is something we’ll try to understand next,” said Yazdani.

In addition to Yazdani, Nuckolls, Bernevig, and Lian, the study contributors included co-first authors Myungchul Oh and Dillon Wong, postdoctoral fellows, as well as Kenji Watanabe and Takashi Taniguchi from the National Institute for Material Science in Japan.

Reference: “Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene” by Kevin P. Nuckolls, Myungchul Oh, Dillon Wong, Biao Lian, Kenji Watanabe, Takashi Taniguchi, B. Andrei Bernevig and Ali Yazdani, December 14, 2020, Nature.
DOI: 10.1038 / s41586-020-3028-8

This work was mainly supported by the EPiQS initiative of the Gordon and Betty Moore Foundation (GBMF4530, GBMF9469) and the Department of Energy (DE-FG02-07ER46419 and DE-SC0016239). Other support for the experimental work was provided by the National Science Foundation (Materials Research Science and Engineering Centers through the Princeton Center for Complex Materials (NSF-DMR-1420541, NSF-DMR-1904442) and EAGER DMR-1643312), ExxonMobil through the Andlinger Center for Energy and the Environment in Princeton, the Princeton Catalysis Initiative, the Elemental Strategy Initiative implemented by the Japanese Ministry of Education, Culture, Sports, Science and Technology (JPMXP0112101001, JSPS KAKENHI grant JP20H0035 and CREST JPMJCR15F3), the Princeton Center for Theoretical Science at Princeton University, the Simons Foundation, the Packard Foundation, the Schmidt Fund for Innovative Research, BSF Israel US foundation (2018226), the Office of Naval Research (N00014-20-1-2303) and the Princeton Global Network Funds.