Space & Physics
The various avatars of the Hall effect
In this second article of Ed Publica’s series on the Hall effect, Dr. Saraubh Basu examines the physics of the Hall effect variants discovered over the course of the past century.
This is the second article of Ed Publica’s series on the Hall effect, which covers the various manifestations of the Hall effect. You can read the first article here.
The ‘anomalous’ Hall effect
In 1881, just two years after Edwin Hall discovered the eponymous Hall effect, he spotted an anomaly when replicating the effect with ferromagnets.
He had observed a tenfold deflection of electric charges this time around, compared to non-magnetic conductors.
Suspecting the magnetic properties played a role, this avatar of the Hall effect is dubbed the anomalous Hall effect. The word ‘anomalous’ is used owing to the fact that external magnetic field no longer remains as a stringent requirement for the Hall effect; instead, the intrinsic magnetization (for instance, the ferromagnet in the above example) fulfils that criterion.
The physicist Edwin Hall. Credit: Wikimedia
The Hall resistivity in ferromagnets increase steeply under the presence of very weak magnetic fields. However, in stronger magnetic fields, the Hall resistivity doesn’t increase further very much. This saturation is rather strange, for it is in contrast to the classical Hall effect where the Hall resistivity maintains its steady growth.
There are several other effects that play a crucial role in determining the anomalous Hall resistivity, thus making it a complicated phenomenon that physicists lack comprehensive understanding about, in comparison to the various other avatars of the Hall effect.
Quantum avatar(s)
The fact that a simple lab experiment showed how the Hall resistivity can be expressed as an equation that contains merely constants, opened up a a plethora of research to understand the cause of this ‘universality’. For it hinted to the involvement of a very fundamental phenomenon.
In 1980, Klaus von Klitzing discovered the quantum avatar of the Hall effect was detected. He was amidst research at a magnetic facility in Grenoble, France, working to improve electron mobility in metal oxide semiconductor field effect transistors (MOSFET). These are transistors that typically operate at extremely low temperatures and under intense magnetic fields.
von Klitzing observed his sample’s Hall resistivity assuming discretized values. This means the resistivity jumps in steps, by a fixed amount that can be scaled as multiples of an integer number (includes 0 along with whole numbers such as 1,2,3, and so on). This discretization reveals the underlying quantum mechanical behavior that has been unraveled at long last – thus bearing its name – the integer quantum Hall effect. von Klitzing later won the Nobel Prize in Physics for 1985 for this work.
The plot here depicts the transverse and longitudinal Hall resistivity (y-axis) increasing in integer steps as the magnetic field (x-axis) increases. This is due to the integer quantum Hall effect. Credit: Wikimedia
But the quantization isn’t limited to integer multiples. In fact, two years later, the fractional quantum Hall effect was observed in experiments. It was shown there were about 100 fractions, including those that aren’t whole numbers that were now in the formula.
Robert Laughlin, who would later win a share of the 1998 Nobel Prize in Physics, proposed a theory to explain the observations. It boils down to the interaction among electrons, either due to the Coulombic repulsion force or the Pauli exclusion principle.
These interacts would eventually split the degeneracy of these enormously degenerate Landau energy levels. These are quantum states occupied by electrons that complete circular revolutions under the influence of an external magnetic field. Splitting these degeneracies, lead to the opening of an energy gap, for the fractional quantum Hall effect to be observed.
‘Spin’ avatar(s)
Just as there are electric charges in nature, so are there spin currents found in nature. ‘Spin’ is a key property found in quantum particles. Unlike what the name suggests, these quantum particles don’t spin or rotate about any axis passing through them. However, these particles carry an angular momentum as though it does spin.
In 1971, before von Klitzing observed the quantum Hall effect, Mikhail Dyakonov and Vladimir Perel hypothesized the spin Hall effect.
In this avatar of the Hall effect, quantum spins of opposite kinds accumulate at the edges of the sample, orthogonal to the direction in which the charge current passes.
The spin selection can be facilitated by the spin-orbit coupling. This refers to the modified energy levels in an atom when the electron’s motion is under the influence on the magnetic field generated by the nucleus. Strong coupling may be intrinsic to doped semiconductors. The proposal has triggered intense investigation of the phenomenon, with first experimental observations of the spin Hall effect seen in n-doped semiconductors and two-dimensional hole gases.
Quantum spins don’t really look like the depiction above, which is meant to showcase a fact that particles like electrons do have an intrinsic angular momentum nonetheless. Credit: Karthik / Ed Publica
For more than a decade, studies concerning the spin current and its application to novel spintronics (or spin electronics) have received plethora of attention. This is with regard to efficiently generating, manipulating and detecting spin accumulation in a sample material. Some progress has also occurred from the device fabrication perspective via techniques such as spin injection, among others.
A major advantage in dealing with the spin current lies in the non-dissipative (or very less dissipation) nature which arises owing to the time reversal invariance of the spin current. This presents a non-dissipative scenario (unlike the dissipative effects seen with charged currents), thus making it quite advantageous for spin transport phenomena.
Furthermore, a quantized version of the spin Hall effect exists, with mercury telluride and cadmium telluride quantum well superlattices, showcasing this effect. In 2005, a quantum treatment was proposed by Charles Kane and Eugene Mele, in the form of a tight binding toy model of electrons operating in a two-dimensional honeycomb lattice.
In fact, the ‘wonder material’ graphene, which is a two-dimensional honeycomb lattice constituting carbon atoms, does satisfy some key requirements for the quantum spin Hall effect. However, it lacks a large spin-orbit coupling among other requirements.
Nonetheless, graphene’s ability to entertain the quantum spin Hall effect, makes it a prospective candidate to find applications in next-generation spintronic devices.
Space & Physics
MIT Physicists uncover key Mechanism behind fractional charge in Graphene
In the decades-long history of studying these phenomena, no one has observed a system that naturally leads to such fractional electron effects, according to the researchers.
MIT physicists have made a significant breakthrough in understanding the phenomenon where electrons split into fractions of their usual charge, offering new insights into the behaviour of exotic electronic states in graphene and other two-dimensional materials.
This latest research builds on a discovery earlier this year, when a team led by Assistant Professor Long Ju at MIT reported that electrons in pentalayer graphene—a structure composed of five graphene layers stacked on top of boron nitride—exhibited fractional charge. Remarkably, this behaviour was observed without the application of a magnetic field, challenging prior assumptions.
Previously, scientists knew that under a strong magnetic field, electrons could split into fractions as part of the fractional quantum Hall effect. However, Ju’s findings marked the first time such fractional behaviour occurred in graphene without any magnetic influence, which led to the coining of the “fractional quantum anomalous Hall effect.” Since then, researchers have been eager to uncover how fractional charge could emerge in this unusual system.
MIT professor Senthil Todadri, who led the new study published in Physical Review Letters, offers a critical piece of the puzzle. Through detailed quantum mechanical calculations, Todadri and his team discovered that the electrons in pentalayer graphene form a crystal-like structure, which provides the ideal conditions for fractional electron behavior.
“This is a completely new mechanism,” said Todadri. “In the decades-long history of studying these phenomena, no one has observed a system that naturally leads to such fractional electron effects. It opens the door to all kinds of new experimental possibilities.”
The study, which includes contributions from Zhihuan Dong and former postdoc Adarsh Patri, is part of a wider body of research. Two other teams—one from Johns Hopkins University and another from Harvard University, UC Berkeley, and Lawrence Berkeley National Laboratory—have also reported similar findings in the same journal issue.
Building on “Twistronics” and the Magic-Angle Graphene Discovery
This research builds upon the work of MIT physicist Pablo Jarillo-Herrero and his team, who in 2018 were the first to demonstrate that twisting two sheets of graphene could give rise to novel electronic behaviors. This discovery of “magic-angle graphene” spurred a new field known as “twistronics,” focused on understanding how the interactions between twisted two-dimensional materials could lead to unusual quantum phenomena, such as superconductivity and insulating behavior.
“We quickly realized that these twisted systems could provide the right conditions for fractional electron phenomena to emerge,” said Todadri, who collaborated with Jarillo-Herrero on a 2018 study that theorized such systems might exhibit fractional charge without a magnetic field. “We saw these systems as ideal platforms to study these fractional effects.”
A Surprising Discovery and the New Crystal Model
In September 2023, Todadri received an unexpected call from Ju, who was eager to share data showing fractional charge behavior in pentalayer graphene. This discovery caught Todadri by surprise, as it did not align with his earlier predictions. In his 2018 paper, Todadri had theorized that fractional charge would emerge from a specific twisting of the electron wavefunction, and that this twisting would intensify as more graphene layers were added.
“Initially, we expected the wavefunction to wind five times in pentalayer graphene,” Todadri explained. “But Ju’s experiments showed that it only wound once. This raised a big question—how do we explain what we’re seeing?”
Uncovering the Electron “Crystal”
Todadri and his team revisited their hypothesis and discovered they had overlooked an important factor. The conventional approach in the field had been to treat electrons as independent entities and analyze their quantum properties. However, in the confined, two-dimensional space of pentalayer graphene, electrons are forced to interact with each other, behaving according to their quantum correlations in addition to their natural repulsion.
By incorporating these interelectron interactions into their model, the team was able to match their predictions with the experimental data Ju had obtained. This led them to a crucial realization: the moiré pattern formed by the stacked graphene layers induces a weak electrical potential that forces the electrons to interact and form a crystal-like structure. This electron “crystal” creates a complex pattern of quantum correlations, allowing for the formation of fractional charge.
“The crystal has a whole set of unique properties that differentiate it from ordinary crystals,” said Todadri. “This opens up many exciting avenues for future research. In the short term, our work provides a theoretical foundation for understanding the fractional electron observations in pentalayer graphene and predicting similar phenomena in other systems.”
This new insight paves the way for further exploration into how graphene and other two-dimensional materials might be used to engineer new electronic states, with potential applications in quantum computing and other advanced technologies.
Space & Physics
How Shyam Gollakota is revolutionizing mobile systems and healthcare with technology
His research is already opening up new possibilities for battery-free networks, including underwater Wi-Fi, powerline communication, and even wireless cameras
Prof. Shyam Gollakota, Washington Research Foundation and Thomas J. Cable Endowed Professor at the Paul G. Allen School of Computer Science and Engineering at the University of Washington, has been honored with the Infosys Prize 2024 in Engineering and Computer Science for his groundbreaking contributions to mobile systems and healthcare. His research, which spans multiple engineering domains, has had a profound societal impact, particularly in areas like smartphone-based healthcare tools, battery-free communication, and the augmentation of human auditory perception with artificial intelligence.
Prof. Gollakota’s innovations have not only advanced the field of mobile systems but have also provided scalable, affordable solutions to some of the world’s most pressing challenges. His work is reshaping how we think about the intersection of technology and healthcare, and his pioneering research promises to improve the lives of millions globally, especially in low- and middle-income countries.
At the heart of Prof. Gollakota’s innovations is his ability to repurpose existing technologies to address real-world challenges
“His work on mobile and wireless communications is game-changing. Particularly impressive is his work on active sonar systems for physiological sensing, battery-free communications, and the use of AI to selectively tailor acoustic landscapes. These innovations will continue to benefit humanity for years to come,” stated Jury Chair, Infosys Prize 2024.
Transforming Mobile Devices into Healthcare Tools
At the heart of Prof. Gollakota’s innovations is his ability to repurpose existing technologies to address real-world challenges. One of his most remarkable contributions is his development of contactless physiological sensing using smartphones. By transforming mobile devices into active sonar systems, Gollakota’s research leverages the microphones and speakers in smartphones—components that are ubiquitous in today’s devices—to detect subtle physiological movements such as breathing.
This novel approach has significant implications for mobile health, particularly in resource-constrained areas where access to traditional medical equipment is limited. According to him, the ability to perform contactless physiological sensing with just a smartphone has the potential to revolutionize medical diagnostics, and make healthcare more accessible to billions of people around the world.
Battery-Free Communication: A Leap Forward in Sustainability
In a world increasingly concerned with energy efficiency and sustainability, Prof. Gollakota’s work on battery-free communication stands out as a pioneering achievement. He developed a technique called ambient backscatter, where wireless devices communicate by reflecting existing radio signals, rather than generating their own. This method drastically reduces energy consumption, allowing devices to communicate without the need for batteries.
This research is already opening up new possibilities for battery-free networks, including underwater Wi-Fi, powerline communication, and even wireless cameras. Battery-free devices could transform industries ranging from environmental monitoring to the Internet of Things (IoT). As per his visions, we are creating a future where energy-efficient, sustainable communication systems will be a part of our everyday lives.
Augmenting Human Auditory Perception with AI
In a truly visionary move, Prof. Gollakota’s research also explores how artificial intelligence (AI) can be used to augment human auditory perception. His work in this field enables people to program their acoustic environments, allowing them to focus on specific sounds or filter out others based on semantic descriptions. This breakthrough could have significant applications in hearing aids, earbuds, and assistive listening devices, where users can customize their listening experiences.
Battery-free devices could transform industries ranging from environmental monitoring to the Internet of Things (IoT)
By using AI to isolate and manipulate soundscapes in real time, Prof. Gollakota’s research is poised to improve quality of life for millions, offering individuals greater control over their auditory experiences. This technology will soon be commonplace in consumer electronics, giving people a level of control over their hearing that was once thought impossible.
A Thought Leader and Innovator
Prof. Shyam Gollakota’s career trajectory has been exceptional. A graduate of IIT Madras and MIT, where he received his Ph.D., Gollakota has quickly risen to prominence as a thought leader in mobile systems, machine learning, and human-computer interaction. He has received numerous accolades, including the National Science Foundation CAREER Award, the Alfred P. Sloan Fellowship, and the ACM Grace Murray Hopper Award. His recognition on MIT Technology Review’s 35 Innovators Under 35 list and twice on Forbes’ 30 Under 30 further cements his status as one of the brightest minds in his field.
As the director of the Mobile Intelligence Lab at the University of Washington, Gollakota is at the forefront of cutting-edge research in mobile health, networking, and battery-free computing. His work has already led to the creation of novel technologies that push the boundaries of what mobile systems can achieve, all with the potential to address key societal challenges.
The Future of Computing
Looking to the future, Prof. Gollakota’s research will continue to revolutionize mobile systems and human-computer interaction. His work in programmable sound, battery-free communication, and contactless diagnostics lays the foundation for the next generation of computing technologies. These innovations promise to reshape industries, improve global health, and enhance human capabilities.
With his visionary ideas and transformative research, Prof. Shyam Gollakota’s work will undoubtedly continue to have a profound impact on both the world of technology and the lives of people worldwide.
Space & Physics
Chandrayaan-3: The moon may have had a fiery past
A magma ocean might’ve wrapped the ancient moon, suggests findings from India’s robotic lunar mission, Chandrayaan-3.
On 23rd August last year, India’s Chandrayaan-3 made history being the first to soft-land on the moon’s south polar region. The landing marked the end of the high-octane phase of the mission. But its next phase was a slow-burner.
Pragyan, the suitcase-sized rover, that hitched a ride to the moon aboard the lander, Vikram, rolled off a ramp onto the lunar surface. It traversed along the dusty lunar surface slowly, at a pace even a snail could beat. Handlers at the Indian Space Research Organization (ISRO) didn’t want the suitcase-sized rover to risk stumbling over a rock or near a ridge, and jeopardize the mission.
The whitish spots are material excavated from the moon’s interior.
Nevertheless, the rover had a busy schedule to stick to. It was to probe the lunar soil, and relay that scientific data back to earth. Pragyan covered 100 meters in two weeks, before it stopped to take a nap ahead of a long lunar night. At the time, the rover’s battery pack was fully charged, thanks to the on-board solar panels soaking up sunlight during the day.
But lunar weather is harsh, especially at the south pole, where Pragyan napped, temperatures can reach as low as -250 degrees centigrade during the night. Added to that, a lunar night lasts two weeks. ISRO deemed Pragyan had only a 1% chance to survive.
Later, the expected happened, when the rover went unresponsive to ISRO’s pings to wake up.
But ISRO said the rover achieved what it was tasked to do. It relayed data all along for two weeks, examining soil from some 23 locations around the mission’s landing point, Statio Shiv Shakti. As months passed by, a slew of discoveries were made. Sulphur was discovered at the south pole, early on while the mission was ongoing. And only a few months ago, Pragyan found evidence of past weathering activity at the south pole.
But since August this year, research teams from ISRO and the Physical Research Laboratory in Ahmedabad, India, reported Pragyan’s most important findings yet – one of which sheds light onto the moon’s origins.
Chandrayaan-3’s Vikram lander, seen from the Pragyan rover’s camera
Moon and the Early Earth
Chandrayaan-3 had carried a radioactive passenger to the moon’s surface – curium-244.
The radioactive curium helps lase the surface: firing alpha particles (which are helium nuclei) at the dusty terrain. Some of these alpha particles bounce off the dust, whereas others evict electrons from the lunar soil, thereby producing x-ray emissions. Keeping watch is the Alpha Particle X-ray Spectrometer (APXS) on-board the Pragyan rover. In August, PRL scientists published findings in the journal, Nature, based on APXS data, reporting discovery of ferroan anorthosite.
It wasn’t the first ever detection per se of ferroan anorthosite. In fact, Apollo 11 had brought back anorthosite rocks to earth, where they were identified as such. That was in 1969, and Apollo sampled them from the equator. Successive missions by the Soviet Union and most recently China affirmed likewise from mid-latitude – equatorial regions as well. But Pragyan’s detection of the rock type was the first ever from the polar region.
The Pragyan rover’s payload.
Anorthosites are common on earth. In fact, just a year after the Apollo 11 sampled the rock, scientists had evidence of the earth and the moon’s entangled history. The authors noted the similar composition between these rocks, that are geographically widespread. Furthermore, ferroan anorthosite is an igneous rock that forms on earth when hot lava produced in volcanic eruptions cools down.
And scientists had piled up evidence in support of a similar process that underwent on the moon. The anorthosite rocks on the moon are old, in fact, more than 4 billion years ago – a figure close to the earth’s inception with rest of the solar system – around 4.5 billion years. Scientific consensus has been that the moon was formed from remnants of a collision between the early earth and a rogue Mars-sized planetary body.
But the collision energy would have yielded a moon that was molten. A lava blanketing the surface – aka a global magma ocean. As this ocean cooled, minerals amongst which is plagioclase (a class of feldspar) crystallized and formed the anorthosite rocks on the moon. It’s commonly called the lunar magma ocean hypothesis.
When Pragyan treaded over the dusty lunar terrain, it didn’t register the anorthosite as a physical rock per se. Instead, it observed remnants of the rock, as fine powder.
Meteorites beat down rocks to fine powder, as they slam into the moon from space with regular impunity. On earth, the ground is saved by the presence of an atmosphere. But the moon virtually has no atmosphere. Nor does it have water to wear down the rocks. The surface is extremely hot during the lunar day – in fact, when Chandrayaan-3 landed on the moon, the surface temperature was some 50 degrees centigrade. Just a few months ago, Pragyan revealed possible signs of rock degradation from the rims of a crater.
Moon dust opens doors to the past
The fact the moon doesn’t (and can’t) sustain an atmosphere helps it make an attractive destination to learn more about our planet and the satellite’s shared origins. There’s no chemistry to remove traces of the moon’s early evolution from the lunar dust. As such, the dust opens doors to the past.
Space explorations missions soft-landing on the surface study this dust – or sample and shuttle them to earth for scientists to study them in detail.
In fact, Pragyan revealed a crater that’s amongst the oldest ever discovered on the moon. The findings were published in the journal, Icarus, in September. Hidden in plain sight, the rover’s navigation camera, NavCam, spotted subtle stretch marks on the surface, that were confirmed later with the Chandrayaan-2 orbiter (which has been orbiting the moon since 2019). In fact, this crater was found buried under nearby craters, most notably the South Pole-Aitkin basin located 350 km away. The basin is the largest impact crater in the entire solar system (some 2,500 km wide and 8 km deep) touted to have formed millions of years ago.
And this became subject to an earlier paper that PRL scientists authored, and was published in August. Pragyan identified material thought to have emerged from the moon’s interior. The APXS instrument picked up unusually high magnesium content in the vicinity. The authors speculate the meteorite that created the basin probably dug up magnesium from deep inside the moon’s upper mantle, and spewed them into Pragyan’s vicinity.
But some experts believe in an alternate explanation. They believe the magnesium might have come from surface rocks in the vicinity, and not from the upper mantle. In fact, the authors acknowledged this amongst other possible alternatives. Nonetheless, the Chandrayaan-3’s findings doesn’t dispute the lunar magma ocean hypothesis either, if not backing it outright. Saying that, the theory lives on to fight another day.
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