Non-Abelian Anyon Observed in Bilayer Graphene

A research group headed by Assistant Professor of Physics Cory Dean from Columbia University and Wang Fong-Jen Professor of Mechanical Engineering James Hone from Columbia Engineering has for sure noticed an ever more analyzed anomaly in the field of condensed matter physics, that is, the even-denominator fractional quantum Hall (FQH) state, by adopting transport measurement in bilayer graphene. The research has been reported in the journal Science on October 6th, 2017.

The so-called 5/2 state has confounded scientists for several decades. While all known particles in the universe are classified as either Bosons or Fermions, the 5/2 state, which emerges only in a 2D electron gas under large magnetic fields, is thought to be an exotic new type of particle that doesn’t fit either description. Previously this state has been observed only in the highest mobility semiconductor heterostructures when cooled to milli-Kelvin temperatures, making it challenging to confirm its expected properties. Recently however, researchers at Columbia found evidence of an equivalent state in bilayer graphene, appearing at temperatures more than 10 times larger than in conventional systems. CREDIT: Cory Dean/Columbia Engineering

Observing the 5/2 state in any system is a remarkable scientific opportunity, since it encompasses some of the most perplexing concepts in modern condensed matter physics, such as emergence, quasi-particle formation, quantization, and even superconductivity. Our observation that, in bilayer graphene, the 5/2 state survives to much higher temperatures than previously thought possible not only allows us to study this phenomenon in new ways, but also shifts our view of the FQH state from being largely a scientific curiosity to now having great potential for real-world applications, particularly in quantum computing.

Cory Dean, Assistant Professor of Physics, Columbia University

The 5/2 fractional quantum hall state was first observed in gallium arsenide (GaAs) heterostructures in the 1980s and prevails to be the sole anomaly in the otherwise strict law which states that fractional quantum hall states can occur only with odd denominators. Following the finding, theoretical studies have proposed that this state might characterize an exceptional kind of superconductor which is remarkable to a certain extent due to the probability that this phase might enable a basically innovative perspective toward quantum computation.

Yet, verification of such theories has been difficult mainly because of the frail nature of the state. In GaAs, this state can be observed only in samples of exceptional quality and hitherto they appear only at milli-Kelvin temperatures, that is, temperatures nearly 10,000 times colder than the freezing point of water.

The Columbia Researchers have now noticed the same state to appear in bilayer graphene at considerably higher temperatures, nearing several Kelvin.

While it’s still 100 times colder than the freezing point of water, seeing the even-denominator state at these temperatures opens the door to a whole new suite of experimental tools that previously were unthinkable. After several decades of effort by researchers all over the world, we may finally be close to solving the mystery of the 5/2.

Cory Dean, Assistant Professor of Physics, Columbia University

A major challenge in modern condensed matter physics is gaining in-depth knowledge of the phenomenon of “emergence,” which occurs when a large number of quantum particles behave in collaboration as a result of interactions between the particles and consequently lead to innovative properties that are not characteristic of the individual particles.

For example, in the case of superconductors, a collection of electrons falls into a single quantum state, which consequently travels through a metal with no loss in energy. The fractional quantum Hall effect is another such state where electrons collaborate with each other under a magnetic field, thereby culminating in the formation of quasiparticles that have prospectively exceptional quantum characteristics.

As it cannot be easily predicted theoretically, the phenomenon of emergence often confronts our basic knowledge of the behavior of particles. For instance, due to the fact that two electrons have the same charge, we perceive electrons as particles that repel each other. On the contrary, in the case of a superconducting metal, electrons unusually get coupled with each other, culminating in an innovative particle called the cooper pair. When individual electrons travel through a metal, they get scattered, thereby producing resistance. In contrast, automatically formed cooper pairs act collectively and travel through the material without any resistance.

Think of trying to make your way through a crowd at a rock concert where everyone is dancing with a lot of energy and constantly bumping into you, compared to a ballroom dance floor where pairs of dancers are all moving in the same, carefully choreographed way, and it is easy to avoid each other,” stated Dean. “One of the reasons that makes the even-denominator fractional quantum Hall effect so fascinating is that its origin is believed to be very similar to that of a superconductor, but, instead of simply forming cooper pairs, an entirely new kind of quantum particle emerges.”

In quantum mechanical terms, elementary particles can be classified into two categories, namely, Bosons and Fermions, which have completely contrasting behaviors. As two Fermions (e.g. electrons) cannot fall into the same state, the electrons inside an atom occupy successive orbitals. Bosons (e.g. photons), or light particles, can fall into the same state, enabling them to behave coherently (e.g. emission of light from a laser). Interchanging of two identical particles leads to multiplication of the quantum mechanical wave-function representing their combined state by a phase factor of 1 in the case of Bosons, and -1 in the case of Fermions.

Following the finding of the fractional quantum Hall effect, Researchers theoretically stated that the quasiparticles related to this state do not behave like Fermions or Bosons. Rather, they behave like the so-called anyon—interchanging of anyon quasiparticles results in a phase factor of neither 1 nor -1 but a fractional one.

Although many decades of research has gone into analyzing this, these quasiparticles could not be proved to be anyons. The 5/2 state, or a non-abelian anyon, is perceived to be highly exceptional. Theoretically speaking, non-abelian anyons behave in accordance with anyonic statistics, similar to other fractional quantum Hall states; however, they have a distinctive characteristic that this phase cannot be simply reversed by reversing the process.

Such a lack in ability to easily reverse the phase will render any information stored in the system to be distinctively stable. That is the reason many Researchers consider the 5/2 state to be an exceptional state for quantum computation.

Demonstration of the predicted 5/2 statistics would represent a tremendous achievement. In many regards, this would confirm that, by fabricating a material system with just the right thickness and just the right number of electrons, and then applying just the right magnetic fields, we could effectively engineer fundamentally new classes of particles, with properties that do not otherwise exist among known particles naturally found in the universe. We still have no conclusive evidence that the 5/2 state exhibits non-abelian properties, but our discovery of this state in bilayer graphene opens up exciting new opportunities to test these theories.

Cory Dean, Assistant Professor of Physics, Columbia University

Until now, it has been mandatory that all such conditions be not just correct but also exceptional. In the case of traditional semi-conductors, it is highly challenging to isolate even-denominator states, and such states occur just for ultra-pure materials, at higher magnetic fields and exceptionally lower temperatures. Although specific characteristics of the state could be observed, coming up with experiments for analyzing the state without destructing it has been very difficult.

We needed a new platform,” stated Hone. “With the successful isolation of graphene, these atomically thin layers of carbon atoms emerged as a promising platform for the study of electrons in 2D in general. One of the keys is that electrons in graphene interact even more strongly than in conventional 2D electron systems, theoretically making effects such as the even-denominator state even more robust. But while there have been predictions that bilayer graphene could host the long-sought even-denominator states, at higher temperatures than seen before, these predictions have not been realized due mostly the difficulty of making graphene clean enough.”

The Columbia Researchers developed on multiple years of groundbreaking research to enhance the quality of graphene devices, thereby developing ultra-clean devices by wholly using atomically flat 2D materials— conducting channel made of bilayer graphene, protective insulator formed of hexagonal boron nitride, and electrical connections made of graphite, which was used as a conductive gate to modify the charge carrier density in the channel.

An important component of the study was having obtaining access to the high magnetic fields tools from the National High Magnetic Field Laboratory in Tallahassee, Florida, which is a nationally funded user facility where Hone and Dean have had large-scale collaborations. They analyzed the electrical conduction by using their devices under magnetic fields of nearly 34 Tesla, and were successful clearly observing the even-denominator states.

By tilting the sample with respect to the magnetic field, we were able to provide new confirmation that this FQH state has many of the properties predicted by theory, such as being spin-polarized,” stated Jia Li, Lead Author of the paper and a Post-doctoral Researcher collaborating with Dean and Hone. “We also discovered that in bilayer graphene, this state can be manipulated in ways that are not possible in conventional materials.”

The findings of Columbia Researchers demonstrating the measurement in transport (i.e. the flow of electrons in the system) is an important step toward corroborating the probable exceptional origin of the even denominator state. The outcomes of the study have been reported simultaneously with an identical report by a research team from University of California, Santa Barbara (UCSB). The UCSB research adopted capacitance measurement to observe the even denominator state, which involves probing the occurrence of an electrical gap intrinsic to the onset of the state.

The Researchers anticipate that the potent measurements observed by them at present in bilayer graphene will open the door for innovative experiments that can convincingly prove its non-abelian nature. Upon established this, the Researchers aspire to start exhibiting computation by adopting the even denominator state.

For many decades now it has been thought that if the 5/2 state does indeed represent a non-abelian anyon, it could theoretically revolutionize efforts to build a quantum computer,” noted Dean. “In the past, however, the extreme conditions necessary to see the state at all, let alone use it for computation, were always a major concern of practicality. Our results in bilayer graphene suggest that this dream may now not actually be so far from reality.”

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