A research story: advancing mesoscopic physics

As previously reported on 16 November, a group of researchers led by Sir Andre Geim and Dr Alexey Berdyugin at The University of Manchester have discovered and characterised a new family of quasiparticles named ‘Brown-Zak fermions’ in graphene-based superlattices.

How did this particular line of research come about?

It started in 2013, long before I started my PhD in the group. At the time, Leonid Ponomarenko and coworkers published the first experimental observation of the Hofstadter’s butterfly, simultaneously with groups at Columbia and MIT. Developments then continued on the butterfly spectrum until 2017 when Roshan Krishna Kumar reported ‘Brown-Zak oscillations’ in a paper published in the journal Science, that were high conductivity oscillations appearing when the magnetic length (the characteristic length of electrons exposed to a magnetic field) is commensurate with the size of the superlattice. Local conductivity maxima were observed at temperatures around 200K (-80°C) suggesting a high mobility when decreasing the temperatures, however this was not observed at the time.

When I started my PhD in 2018, Piranavan Kumaravadivel was working with Roshan on extra-large graphene devices to observe magnetophonons. Through discussions we had the idea to use one of these devices to study the mobility of the states. Alexey Berdyugin (who is corresponding author on this paper) suggested that studying this device could be part of my training in the lab. I measured this at lower temperatures than had been done previously (20mK) and we observed an incredibly well-defined Hofstadter’s butterfly. We later reproduced it on other devices. What is particularly important is that, thanks to the high mobility of the Brown-Zak fermions, we were able to see Landau quantisation that should not exist within the single-particle Hofstadter’s model. The overall picture and understanding came later however and I’m delighted that what started as simple training turned into this unexpected result.

Why is this particular line of enquiry is important?

I think the most important result here is the high mobility for Brown-Zak fermions.

For usual electronic systems the mobility characterises how much you can accelerate charge carriers when you apply one volt, for example, along a material. At low temperatures, the mobility is only limited by impurities and defects, so it has been a metric for the quality of an electron system. If you look at applications, there have been fundamental advances allowed by higher electron mobility, but I’d like to focus on fundamental progress in mesoscopic physics.

When 2D electron systems were invented, high mobility was considered the Holy Grail in this field of physics, because it allowed for the observation of various electronic effects. For example, in the late seventies, the highest mobilities achieved were on the order of 10 thousand (in units of cm²/V/s), and von Klitzing observed the quantum Hall effect for the first time, for which he was awarded the Nobel prize. A few years later, with mobilities of 100 thousand, Tsui and Stormer observed the odd-denominator fractional quantum Hall effect for which they too were awarded the Nobel prize. This was followed by another Nobel Prize achievement by Stormer, along with his graduate student Willet, a few years later on a device with a mobility of 1.5 million that showed the even-denominator quantum Hall effect. These are but a few examples of fundamental research allowed by high quality devices characterised by their mobility. 

What is important in our paper is that not only are we able to observe mobilities as high as 10 million in a graphene device, we also observed the Brown-Zak fermions with high mobility. In any device, an electron under a magnetic field would be subject to a Lorentz force that drives it to rotate in circular orbits and therefore prevents it from contributing to the current propagation. We found that at specific fields we form new quasiparticles that have straight trajectories and are able to propagate a current. This was highly unexpected. We called these new quasiparticles Brown-Zak fermions and were able to determine their key properties at low temperatures. Even more unexpected was the really high mobility of these fermions, comparable to the best mobilities achieved in graphene devices for normal electrons at zero field. From a fundamental point of view, this is fascinating.

What kind of “new electronic devices” do you predict could benefit from these results?

The main device we made for the paper is a transistor made out of graphene and boron nitride with high electron mobility. Such transistors would be able to operate at high frequency, possibly up to millimeter wave frequencies (e.g. 5G). There are many applications for high mobility devices, such as high-speed calculators, smartphones, and satellite television receivers.

You mention that this could improve processor speeds. Is this the next significant step In ‘Moore’s Law’?

Unfortunately, no. Moore's law tells us that every other year, the number of transistors on a processor doubles. In reality, this means that transistors have to be increasingly small in order to fit on the chips. As we approach atomic limits, many assume that we will find a limit to that law, however Apple is now able to make 5nm transistors. Conversely, our devices are 40,000 times larger. This is because we are better able to observe Brown-Zak fermions with a greater number of Moiré unit cells. There may be potential in the future for smaller devices.

“Brown-Zak fermions define new metallic states” – please expand on this statement lifted from the original news story. What does it imply? What might this mean for other 2D material functionality?

The Brown-Zak fermions are the new set of quasiparticles that evolve in superlattices exposed to high magnetic fields. We usually define a phase diagram for the 2D material used in our devices, where we can vary some parameters, such as doping, temperature, magnetic field, etc. The different states on this phase diagram can be a metal, an insulator, or a series of exotic phases (superconducting, mott insulator, etc.). A typical phase diagram would show a metal phase at low fields, and as we increase the field, it develops into insulating phases. It is very unlikely that a metal appears at high magnetic fields.

However, since we are talking about Brown-Zak fermions and not electrons, they evolve under a zero effective field despite the externally applied magnetic fields. Under these zero fields, the Brown-Zak fermions behave like a new metal, and these fermions have all the properties of electrons in a metal (like copper or gold exposed to no magnetic field).

As Brown-Zak fermions are a general family of quasiparticles that will appear in any 2D material assembled in a Moiré structure, you define a new conductor with its own set of properties depending on the characteristics of the 2D materials you assemble. 

Refering back to your final comment in the orignal news article, "The high mobilities of Brown-Zak fermions at high magnetic fields open a new perspective for electronic devices operating under extreme conditions," which extreme conditions do you refer to?”

The magnetic fields at which Brown-Zak fermions are created are very high (500,000 times the Earth’s magnetic field). The fact that our devices retain a high mobility under these conditions is surprising, and might allow us to use transistors when a very high magnetic field is applied. That is in itself an extreme condition.

What is the next step in your research?

We are trying a variety of electrical measurement techniques with different 2D materials and structures. There are still some questions around Brown-Zak fermions, but I don’t think we can explain the full range of characteristics with the current background. For example, we reported an anomalous behaviour in the hole-doped region of the butterfly, where the Landau levels originating from the Brown-Zak fermions bend. This cannot be explained by the usual theories. Understanding such features will be important to decipher all the parameters of this family of quasiparticles.

What’s it like working as a team at Manchester University?

It is inspiring. I am surrounded by very talented people with diverse backgrounds, and incredible equipment - what else can a student ask for? I particularly enjoy discussing and collaborating with my colleagues, all of whom are incredibly passionate about their chosen fields. This is highly motivating.

What’s it like working with a Nobel Prize winner [Sir Andre Geim]?

He seems to attract very intelligent people. I feel very lucky to have this unique experience at such a young age. Unfortunately due to the COVID-19 pandemic our team doesn't have many opportunities to meet physically. This limits spontaneous interactions and therefore curbs bursts of creativity.

What’s it like working in an emerging field like graphene technology?

It’s very stimulating because there is always something new. Simultaneously, the pace of developments can prove difficult to keep track of. Still, I’m glad that 16 years after the first isolation of graphene, there continues to be fascinating physics to discover in these devices.

How close is graphene research to becoming truly integral in the commercial world?

I’ve seen many companies attempt to integrate graphene in materials for its mechanical or chemical properties. That is something that the Graphene Engineering and Innovation Center at Manchester is working on. In my opinion, the biggest hurdle to commercialisation is the method by which graphene is fabricated. The electronic properties of graphene devices have improved over the past decade and I believe the next decade will see huge improvements in the fabrication techniques.

Increase your Impact! If you have a research story to share, do please get in touch with the editor at: sarah.lawton@synthesismedia.co.uk