How does an atom adsorb to a surface? From the viewpoint of quantum field theory, can we understand this phenomenon by including the effects of the surface phonons- the quanta of vibration of surface? Over the years, theoretical predictions as well as experimental endeavors have elucidated a significant role played by the surface phonons in mediating the process of adsorption. While most of the previous research work has been conducted on conventional three-dimensional materials, the discovery of graphene, a two-dimensional material, has led to a recent effort to understand this phenomenon with special focus on phonon dispersion, tunability of the atom-phonon interaction and possible mass-sensor based applications. Sanghita Sengupta, currently a postdoctoral fellow at the Institut quantique (IQ), aimed to understand the adsorption phenomenon in graphene with a special focus on the role of surface phonons.

During her PhD at the University of Vermont, she had stumbled upon an interesting ongoing debate in this field, which has been prevalent since 2011. While one group of theorists predicted that suspended graphene membranes are perfect reflectors of atoms at low temperatures, other predicted it to be perfect absorbers. The main point of the disagreement between the groups was the role of low-energy (infrared) surface phonons in mediating the process of adsorption. In 2019, as part of her first project as a postdoctoral fellow at the IQ, she investigated the role of low-energy surface phonons and resolved the debate with a mathematical method which showed that suspended graphene is indeed a good adsorber. She then published the results in a paper in which she is the sole author: Theory of Phonon-Assisted Absorption in Graphene: Many-Body Infrared Dynamics.

**AN ORIGINAL APPROACH BUILT ON ACOUSTIC PHONONS**

What distinguishes Sanghita’s approach from the existent methods is that she developed a mathematical technique that models the surface adsorption physics from the viewpoint of the coherence of the bath of thermal phonons. The advantage of this theory is that it investigates in detail the true dynamics of the phonon bath with respect to the effects of time-evolution, temperature and atom-phonon coupling. This sort of a formalism concentrating on the dynamics of the surface phonons was not employed by the other groups. Her theory discovers a characteristic time scale for the thermal phonon dynamics, which then serves as a crucial parameter for understanding the crux of the debate, whether suspended graphene reflects or absorbs atoms impinging on it.

Within such a theoretical technique, her original work has shown that the result of zero adsorption (implying reflection) for suspended graphene is only possible when one considers the contribution of phonon dynamics from a long time regime which is beyond a characteristic time-scale. In such a case, the contribution to the adsorption phenomenon due to the thermal phonons from the short-time scale is completely neglected and hence, the resulting adsorption rate turns out to be zero. These approximations were indeed the regime of study for the group which theoretically predicted suspended graphene to be a reflector. However, the phenomenon of adsorption at low temperatures requires the inclusion of the contribution of thermal phonons from all time regimes and not just the long-time scales. When such conditions are obeyed, the contribution of the thermal phonons from the short-time scales result in an adsorption rate that is finite, implying suspended graphene to be a good adsorber.

**AN INTERESTING SIMILARITY WITH OTHER BRANCHES OF QUANTUM FIELD THEORY**

While resolving the debate from the viewpoint of the dynamics of the thermal phonons, Sanghita also found an interesting similarity of the phonon-mediated adsorption phenomenon with other branches of quantum field theory. During the initial stages of the formulation of this theory of surface adsorption for suspended graphene membranes, she encountered a puzzling mathematical problem in which the adsorption rates calculated within conventional perturbation theory were seen to diverge and give infinite adsorption rates. On further investigation, she found that this problem is not exclusive only to the surface adsorption phenomenon in graphene, but is also found in other fields of fundamental physics like quantum electrodynamics (QED) and perturbative gravity. This problem has a special name, it is called the Infrared (IR) Problem and has its origin in the emission of infinitely many infrared quanta (acoustic phonons in the case of suspended graphene) from the long-range tail of the interactions (van der Waals interaction for the graphene surface physics). Thus a crucial ingredient required to study the surface adsorption problem is to devise mathematical techniques that would tame these infrared divergences, first. She devised three such numerical resummation techniques which are non-perturbative and are based on standard Green’s function formalism that sum infinite orders of Feynman diagrams, tame the IR divergences and give finite adsorption rates for suspended graphene. A surprising outcome of her project was the realization of a subtle similarity between the theories of QED, perturbative gravity and quantum acoustics in 2D Dirac materials. In the theories with low-energy photons in QED, gravitons in perturbative gravity, the procedure of IR-divergence cancellation in the transition rates is predicted by the Bloch-Nordsieck theorem which finally leads to finite transition rates. Interestingly, her work showed that the low-energy acoustic phonons in quantum acoustics in 2D surface physics also validate the Bloch-Nordsieck theorem leading to finite adsorption rates for suspended graphene.

**THE NEXT STEPS**

Sanghita aims to apply her theoretical formalism to another interesting problem involving magnetic surfaces. First discovered experimentally in biological systems, Chiral Induced Spin Selectivity (CISS) is a remarkable phenomenon which unravels the spin-selective transmission of electrons through helical chiral molecules. This phenomenon has intrigued the spintronics community with proposals of developing spin-valves based on the effect of CISS without the use of permanent magnets. However, there is a potential road-block to the implementation of these proposals. The theoretical origin of CISS is not yet understood. Sanghita wants to apply and extend her mathematical formalism used to study phonon-mediated adsorption physics to magnetic surfaces where she will investigate the role of phonons in the transition rates of electrons through the chiral molecules. If fruitful, she envisions this theory to be advantageous for developing CISS-based spintronic devices as well understanding some of the biological phenomena that use spin-selectivity.

Since she published this paper, Sanghita worked on another project with Professor Garate, in which they found that it is possible to hear the sound of topological electrons in Weyl semimetals.