Playing with relativistic particles on the two dimensional flatland
I had written this article back in 2019, for the scientific writing competition AWSAR, a very promising initiative by DST, India.
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The modern world is always looking for new applications of available science and technology for the betterment of mankind. From medicine to economy science has greatly affected all possible aspects of human life. But with the rapid scientific developments one should not forget the story of the beginning of science, and the milestones we have crossed to reach here.
I am a physicist from department of physics, Indian institute of science, Bangalore. I work in the field of experimental condensed matter physics. When I looked at the previously selected articles in AWSAR, I found that most of them are from the field of interdisciplinary sciences and sub-fields of biology. Truly speaking, this reflects the urge of general public searching for the science that will help improving their life. Definitely, these fields have revolutionized many things those directly affect our life, specifically the healthcare, and deserve all possible appreciations. But, the role of fundamental physics in all these progresses should not be forgotten.
It was the beginning of science, when few men started asking why something is true, and they realized that something can be proved by observations and logical analysis; this was a milestone in our philosophical development. This concept may sound trivial in the current time, but if one goes back to the time when the rules and facts were those which the church says, at that time this was not trivial. The modern science started from the observations of astrological objects, wherein the realization that the earth revolves around the sun was a big achievement. Centuries passed and we realized the same law that governs the planetary motion governs the behavior of objects on earth, e.g. the falling of an apple from the tree. This was a dramatic revolution in understanding our world. At this specific point of time the Newton’s laws of motion were devised.
Again, few centuries passed, many scientific discoveries made, human just started flying for the first time; scientist started thinking that the fundamental physics is almost done and now we understand the basis of almost everything that surrounds us. To a surprise, in 1905 four classic papers appeared in the journal of Annalen der Physik, those questioned our basic understandings of the nature; the works were from a teaching assistant at the Patent office in Bern, a guy named Albert Einstein. These were the beginning of a new paradigm in physics. One of these works, which explained the photo electric effect, was the beginning of quantum physics. The previous way of understanding was then called classical physics. The quantum physics was further developed and shaped by Werner Heisenberg, Erwin Schrödinger, Max Born, Paul Dirac and many others. In another work among the four papers, Einstein put forward another amazing theory called special theory of relativity, which interlinked the concept of space and time in a way never imagined before. Around this period, in 1911, Heike Kamerlingh Onnes discovered an unusual property in solid Mercury at cryogenic temperature, an abrupt disappearance of resistance at 4.2K. The observation is well understood now, known as superconductivity, which is manifestation of a macroscopic quantum phenomenon.
When two different concepts of physics are combined, that gives rise to a new physics. Superconductivity and relativity are two such completely different phenomena, one observed at small scales and the other at astronomical scales. A natural question then appears, can these two be combined? This idea remained a fiction for decades. Now some these ideas are becoming real science after the discovery of graphene, which is a single layer of graphite. Graphene has a unique Dirac like dispersion, in which the carriers behave as relativistic particles. When graphene is coupled with a superconductor we have a platform for studying the interplay of superconductivity and relativistic dynamics on the two dimensional flatland.
I work in such junctions of graphene with different superconductors to understand the dynamics at their interface. Before going into the physics of these interesting hybrids one need to understand what happens in a conventional normal metal – superconductor (NS) junction, for example the junction of gold and Aluminum below the superconducting transition temperature of Aluminum. In metals the current is carried by electrons having charge e, whereas in a superconductor the current is carried by Cooper pairs having an effective charge of 2e. So, at NS interface an electron from the metal needs a partner to enter into the superconductor. In this process a specific electron from the metal takes another electron with it to transmit 2e charge into the superconductor, this means a vacancy is created in the metal, which is called a hole. This process, in which an incident electron from the normal metal at the NS interface enters into the superconductor by reflecting back a hole, is called Andreev reflection (AR). Like any other classical collision problem here also the energy and momentum conservation needs to be considered; only difference is that here the energy and momentum are quantum mechanical in nature and can be evaluated by solving the Schrodinger equation. When one does this exercise it can be shown that the Andreev reflected hole will retrace the incident electron path. This type of AR is called retro type AR as shown in Fig. (a).
Graphene has a unique Dirac like band structure at low energy, in which the Fermi energy can be electrostatically tuned. It’s electron like band and hole like band touch at the charge neutrality point known as the Dirac point. In graphene - superconductor junction a new kind of AR is theoretically predicted to happen near the Dirac point, which was attributed to the relativistic nature of the carriers. In this scenario, the Andreev reflected hole will traverse in a specular manner relative to the incident electron; this kind of AR is called specular type AR schematically shown in Fig. (b). When the Fermi energy is tuned far away from the Dirac point graphene acts like a normal metal and conventional retro type AR is expected. Studying these physics require ultra-low temperature (order of 1 Kelvin, which is close to -270°C) and very high quality device. In one of our work that got published in the journal Physical Review B, by conductance measurements we demonstrated the transition of retro type AR to non-retro type AR in graphene – superconductor junction, which is an intermediate phase between retro type to specular type AR as shown in Fig. (c). We could not observe any signature of specular type AR, which might be due to the disorder effect in graphene. Another group from Columbia University used bilayer graphene, where the disorder effect is smaller and observed signature of specular type AR.
Quantum Hall effect is another interesting quantum mechanical effect observed in two dimensional systems. Von Klitzing in 1980 discovered quantum Hall effect in silicon based MOSFET, for which he was awarded the 1985 Nobel Prize. As studied in undergraduate level physics, when a charged particle with velocity v enters into a magnetic field its trajectory changes and its motion become circular. Due to the quantum nature of the electron this circular trajectory restricts the energy to take specific quantum energies. These allowed energy levels are called Landau levels. These Landau levels bend at the physical edge due to confining potential. As a result when Fermi energy is tuned between the Landau levels transport happens through the ballistic edge states; the longitudinal resistance becomes zero and transverse resistance takes quantum of values h/ne2, where h is the Planck’s constant and n is an integer. This effect is called quantum Hall effect. Combining this to superconductivity is a long standing problem in experimental condensed matter physics, which has great potentials for future quantum computing. Graphene, which exhibits a unique half integer quantum Hall effect, has emerged as most suitable system to combine quantum Hall effect and superconductivity. We studied the transport properties of a graphene quantum Hall – superconductor junction and revealed a new kind of AR happening at their interface when the Fermi energy is tuned close to the Dirac point. The electrons from lowest electron like Landau level can make pairs with an electron from the highest hole like Landau level to transmit a Cooper pair into the superconductor. We observed signatures of such a process, called inter Landau level Andreev reflection, which is another beautiful consequence of unique relativistic nature of carriers in graphene.
The purpose of this article is to give the reader an essence of the experimental condensed matter physics by connecting the modern problems with the historic one. As a concluding remark I want to quote “Science in itself is a collection of beautiful stories, once you start reading it you will fall for it”.