A
Princeton-led team of physicists have discovered that, under certain
conditions, interacting electrons can create what are called “topological
quantum states,†which, has implications for many technological fields of
study, especially information technology. This diagram of a scanning tunneling
microscope shows the magic-angle twisted bilayer graphene.
Credit: Kevin
Nuckolls, Department of Physics, Princeton University
Electrons
inhabit a strange and topsy-turvy world. These infinitesimally small particles
have never ceased to amaze and mystify despite the more than a century that
scientists have studied them. Now, in an even more amazing twist, physicists
have discovered that, under certain conditions, interacting electrons can
create what are called “topological quantum states.†This finding, which was
recently published in the journal Nature, has implications for many
technological fields of study, especially information technology.
Topological
states of matter are particularly intriguing classes of quantum phenomena.
Their study combines quantum physics with topology, which is the branch of
theoretical mathematics that studies geometric properties that can be deformed
but not intrinsically changed. Topological quantum states first came to the public’s
attention in 2016 when three scientists — Princeton’s Duncan Haldane, who is
Princeton’s Thomas D. Jones Professor of Mathematical Physics and Sherman
Fairchild University Professor of Physics, together with David Thouless and
Michael Kosterlitz — were awarded the Nobel Prize for their work in uncovering
the role of topology in electronic materials.
“The last
decade has seen quite a lot of excitement about new topological quantum states
of electrons,†said Ali Yazdani, the Class of 1909 Professor of Physics at
Princeton and the senior author of the study. “Most of what we have uncovered
in the last decade has been focused on how electrons get these topological
properties, without thinking about them interacting with one another.â€
But by using a material known as magic-angle twisted bilayer graphene, Yazdani and his team were able to explore how interacting electrons can give rise to rise to surprising phases of matter.
A
Princeton-led team of physicists have discovered that, under certain
conditions, interacting electrons can create what are called “topological
quantum states,†which, has implications for many technological fields of
study, especially information technology. This diagram depicts different
insulating states, each characterized by an integer called its “Chern number,â€
which distinguishes between different topological phases. Courtesy: Kevin
Nuckolls, Department of Physics, Princeton University.
The
remarkable properties of graphene 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 in which 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
further explore the intricacies of superconductivity.
But what
they discovered led them down a different and untrodden path.
“This was
a wonderful detour that came out of nowhere,†said Kevin Nuckolls, the lead
author of the paper and a graduate student in physics. “It was totally
unexpected, and something we noticed that was going to be important.â€
Following
the example of Jarillo-Herrero and his team, Yazdani, Nuckolls and the other
researchers focused their investigation on twisted bilayer graphene.
“It’s
really a miracle material,†Nuckolls said. “It’s a two-dimensional lattice of
carbon atoms that’s a great electrical conductor and is one of the strongest
crystals known.â€
Graphene
is produced in a deceptively simple but painstaking manner: a bulk crystal of
graphite, the same pure graphite in pencils, is exfoliated using sticky tape to
remove the top layers until finally reaching a single-atom-thin layer of
carbon, with atoms arranged in a flat honeycomb lattice pattern.
To get the
desired quantum effect, the Princeton researchers, following the work of Jarillo-Herrero,
placed two sheets of graphene on top of each other with the top layer angled
slightly. This twisting creates a moiré pattern, which resembles and is named
after a common French textile design. The important point, however, is the
angle at which the top layer of graphene is positioned: precisely 1.1 degrees,
the “magic†angle that produces the quantum effect.
“It’s such
a weird glitch in nature,†Nuckolls said, “that it is exactly this one angle
that needs to be achieved.†Angling the top layer of graphene at 1.2 degrees,
for example, produces no effect.
The
researchers generated extremely low temperatures and created a slight magnetic
field. They then used a machine called a scanning tunneling microscope, which
relies on a technique called “quantum tunneling†rather than light to view the
atomic and subatomic world. They directed the microscope’s conductive metal tip
on the surface of the magic-angle twisted graphene and were able to detect the
energy levels of the electrons.
They found
that the magic-angle graphene changed how electrons moved on the graphene
sheet. “It creates a condition which forces the electrons to be at the same
energy,†said Yazdani. “We call this a ‘flat band.'â€
When
electrons have the same energy — are in a flat band material — they interact
with each other very strongly. “This interplay can make electrons do many
exotic things,†Yazdani said.
One of
these “exotic†things, the researchers discovered, was the creation of
unexpected and spontaneous topological states.
“This
twisting of the graphene creates the right conditions to create a very strong
interaction between electrons,†Yazdani explained. “And this interaction
unexpectedly favors electrons to organize themselves into a series of
topological quantum states.â€
Specifically,
they discovered that the interaction between electrons creates what are called
topological insulators. These are unique devices that act as insulators in
their interiors, which means that the electrons inside are not free to move
around and therefore do not conduct electricity. However, the electrons on the
edges are free to move around, meaning they are conductive. Moreover, because
of the special properties of topology, the electrons flowing along the edges
are not hampered by any defects or deformations. They flow continuously and
effectively circumvent the constraints — such as minute imperfections in a
material’s surface — that typically impede the movement of electrons.
During the
course of the work, Yazdani’s experimental group teamed up two other
Princetonians — Andrei Bernevig, professor of physics, and Biao Lian, assistant
professor of physics — to understand the underlying physical mechanism for
their findings.
“Our
theory shows that two important ingredients — interactions and topology — which
in nature mostly appear decoupled from each other, combine in this system,â€
Bernevig said. This coupling creates the topological insulator states that were
observed experimentally.
Although
the field of quantum topology is relatively new, it holds great potential for
revolutionizing the areas of electrical engineering, materials science and
especially computer science.
“People
talk a lot about its relevance to quantum computing, where you can use these
topological quantum states to make better types of quantum bits,†Yazdani said.
“The motivation for what we’re trying to do is to understand how quantum
information can be encoded inside a topological phase. Research in this area is
producing exciting new science and can have potential impact in advancing
quantum information technologies.â€
Yazdani
and his team will continue their research into understanding 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 will try to understand next,†Yazdani
said.
In
addition to Yazdani, Nuckolls, Bernevig and Lian, contributors to the study included
co-first authors Myungchul Oh and Dillon Wong, postdoctoral research
associates, as well as Kenji Watanabe and Takashi Taniguchi of the National
Institute for Material Science in Japan.