STRONGLY CORRELATED PHASES IN QUANTUM HALL SYSTEMS

Quantum Hall systems have a one-body energy spectrum consisting of dispersion-less Landau levels. Electron-electron interactions thus dominate in partially filled Landau levels, which exhibit a myriad of strongly correlated phases such as quantum hall ferromagnets and fractional quantum Hall phases. We study two examples of these phenomena. In the first project, we explore the ground state of a system with an interface between two semi-infinite regions with fillings ν= 4 and ν= 3 respectively. The width of the interface can be controlled by varying the background potential, which provides an additional tuning parameter. For a certain range of interaction strengths, the ν= 4 bulk is unpolarized whereas the ν= 3 bulk is fully polarized. In the parameter space spanned by the interaction strength and width of the interface, we find two phases at the interface. Phase A has spin as a good quantum number, and the long-wavelength spin edge excitations are gapped. In phase B, spin rotation symmetry is spontaneously broken at the mean-field level. Using symmetry arguments we find the effective theory near the interface of phase B. This effective theory is known to have gapless long-wavelength spin excitations. In the second project, we study the ground state of a tunnel-decoupled double-layer graphene system when both layers are undoped. We find a simple Hamiltonian in the continuum limit from symmetries of the system. Using the Hartree-Fock approximation we find a state with inter-layer coherence with broken layer U(1) symmetry. This phase becomes magnetized in presence of a non-zero Zeeman field. A first-order phase transition can be driven from the ferromagnetic phase to the magnetized inter-layer coherent phase by increasing the Zeeman field. We predict the number of gapless modes in the bulk

w1+∞w_{1+\infty} and Carrollian Holography

In a $1+2$D Carrollian conformal field theory, the Ward identities of the two local fields $S^+_0$ and $S^+_1$, entirely built out of the Carrollian conformal stress-tensor, contain respectively up to the leading and the subleading positive helicity soft graviton theorems in the $1+3$D asymptotically flat space-time. This work investigates how the subsubleading soft graviton theorem can be encoded into the Ward identity of a Carrollian conformal field $S^+_2$. The operator product expansion (OPE) $S^+_2S^+_2$ is constructed using general Carrollian conformal symmetry principles and the OPE commutativity property, under the assumption that any time-independent, non-Identity field that is mutually local with $S^+_0,S^+_1,S^+_2$ has positive Carrollian scaling dimension. It is found that, for this OPE to be consistent, another local field $S^+_3$ must automatically exist in the theory. The presence of an infinite tower of local fields $S^+_{k\geq3}$ is then revealed iteratively as a consistency condition for the $S^+_2S^+_{k-1}$ OPE. The general $S^+_kS^+_l$ OPE is similarly obtained and the symmetry algebra manifest in this OPE is found to be the Kac-Moody algebra of the wedge sub-algebra of $w_{1+\infty}$. The Carrollian time-coordinate plays the central role in this purely holographic construction. The 2D Celestial conformally soft graviton primary $H^k(z,\bar{z})$ is realized to be contained in the Carrollian conformal primary $S_{1-k}^+(t,z,\bar{z})$. Finally, the existence of the infinite tower of fields $S^+_{k}$ is shown to be directly related to an infinity of positive helicity soft graviton theorems.Comment: The correct justification for the anti-holomorphic truncation of the Carrollian field $S^+_2$ is added after eqn. (3.6). Reference adde

The Rise of SUV Market in India and the role of Advertisements in its Promotion: A Case study of Mahindra and Mahindra

India is the third largest car markets in the world, recording a sales figure of 4.11-million-unit sales in the passenger vehicle segment in the FY 23. Since India is an emerging market the scope of growth becomes more important. There has been a sizeable shift in the car segment with SUVs accounting for 50% market share in FY24. The consumer behavior has evolved over the period. According to media reports based on surveys, brand conscious, image conscious young buyers in India find SUVs more appealing that other segment of cars. The purity of the category of SUV has changed too. With compact SUVs coming to play, people are more interested in getting an SUV for everyday commuting than off-roading occasionally. Maruti Suzuki Brezza, Hyundai Venue, XUV 400, XUV 300, Bolero Neo are great examples of that. Mahindra has excelled at SUVs and the company’s focus has been mostly on SUVs only. The cars have been marketed well to the Indian consumers using television and digital media advertisements to reach a wider variety of audience. This research paper studies the journey of Mahindra SUVs through a case study. It analyses different aspects of the growth of SUVs in India. The audio-visual advertisements shown in TV and later in digital has been analyzed by accessing them on social media platforms like YouTube. The findings of such a study of advertisements through the period of last 15 years showcases minute details of the company’s communication and messages to the audience

Understanding the Scope and Problems of Artificial Intelligence and Assisted Learning in Higher Education

Learning is a dynamic experience. We need to create learning experiences that assist all kinds of learners. Human beings have different patterns of learning. Assisted learning helps in decentralizing the learning experience in a more individualistic approach. Artificial Intelligence has helped in automating many tasks of administrative nature, evaluation and has even helped personalize learning, countering the problems of teacher exhaustion. Not just efficient grading use of AI through educational chatbots and applications can help in helping students get a 24/7 mentoring option which in a real-world scenario might be difficult for human teachers to cater to. With technology has come ease of global accessibility and insights that are backed by data. But it also brings along with it an enhanced scenario of digital divide, technological hurdle and inequality. The paper through case studies tries to analyze the scopes and problems of using Artificial Intelligence in Assisted Learning in Higher Education

Transport signatures of Bogoliubov Fermi surfaces in normal metal/time-reversal symmetry broken dd-wave superconductor junctions

In recent times, Bogoliubov Fermi surfaces (BFSs) in superconductors (SCs) have drawn significant attention due to a substantial population of Bogoliubov quasiparticles (BQPs) together with Cooper pairs (CPs) in them. The BQPs as zero energy excitations give rise to captivating and intricate charge dynamics within the BFSs. In this theoretical study, we propose to reveal the unique signatures of the topologically protected BFSs in a normal metal/time-reversal symmetry (TRS) broken $d$-wave SC, in terms of the differential conductance and Fano factor (FF). For an isotropic $d$-wave SC, an enhancement in zero-bias conductance (ZBC) can be identified as a key signature of BFSs. However, for the anisotropic SC, this feature does not replicate due to the presence of the localized Andreev bound state (ABS) at the interface. The interplay of ABS and BFSs gives rise to an anomalous behavior in ZBC. We explain this anomalous behavior by analyzing the effective charge of the carriers in terms of the FF. The simplicity of our setup based on $d$-wave SC makes our proposal persuasive.Comment: 6+6 pages, 4+4 figures, comments welcom

Multiple Topological Phase Transitions Unveiling Gapless Topological Superconductivity in Magnet/Unconventional Superconductor Hybrid Platform

We propose a theoretical framework for generating gapless topological superconductivity (GTSC) hosting Majorana flat edge modes (MFEMs) in the presence of a two-dimensional (2D) array of magnetic adatoms with noncollinear spin texture deposited on top of a unconventional superconductor. Our observations reveal two distinct topological phase transitions within the emergent Shiba band depending on the exchange coupling strength ($J$) between magnetic adatom spins and superconducting electrons: the first one designates transition from gapless non-topological to gapless topological phase at lower $J$, while the second one denotes transition from gapless topological to a trivial gapped superconducting phase at higher $J$. The gapless topological superconducting phase survives at intermediate values of $J$, hosting MFEMs. Further, we investigate the nature of the bulk effective pairings which indicate that GTSC appears due to the interplay between pseudo "$s$-wave" and pseudo "$p_{x}+p_y$" types of pairing. Consequently, our study opens a promising avenue for the experimental realization of GTSC in 2D Shiba lattice based on $d$-wave superconductors as a high-temperature platform.Comment: Invited article for APL Special Collection: Topological and Chiral Matter - Physics and Applications. This is the Published Versio

Emergence of spin-active channels at a quantum Hall interface

We study the ground state of a system with an interface between $\nu=4$ and $\nu=3$ in the quantum Hall regime. Far from the interface, for a range of interaction strengths, the $\nu=3$ region is fully polarized but $\nu=4$ region is locally a singlet. Upon varying the strength of the interactions and the width of the interface, the system chooses one of two distinct edge/interface phases. In phase A, stabilized for wide interfaces, spin is a good quantum number, and there are no gapless long-wavelength spin fluctuations. In phase B, stabilized for narrow interfaces, spin symmetry is spontaneously broken at the Hartree-Fock level. Going beyond Hartree-Fock, we argue that phase B is distinguished by the emergence of gapless long-wavelength spin excitations bound to the interface, which can, in principle, be detected by a measurement of the relaxation time $T_2$ in nuclear magnetic resonance.Comment: 9 pages 10 figures including supplemental materia

Changing forest water yields in response to climate warming: results from long-term experimental watershed sites across North America

Climate warming is projected to affect forest water yields but the effects are expected to vary. We investigated how forest type and age affect water yield resilience to climate warming. To answer this question, we examined the variability in historical water yields at long-term experimental catchments across Canada and the United States over 5-year cool and warm periods. Using the theoretical framework of the Budyko curve, we calculated the effects of climate warming on the annual partitioning of precipitation (P) into evapotranspiration (ET) and water yield. Deviation (d) was defined as a catchment’s change in actual ET divided by P [AET/P; evaporative index (EI)] coincident with a shift from a cool to a warm period – a positive d indicates an upward shift in EI and smaller than expected water yields, and a negative d indicates a downward shift in EI and larger than expected water yields. Elasticity was defined as the ratio of inter annual variation in potential ET divided by P (PET/P; dryness index) to inter annual variation in the EI – high elasticity indicates low d despite large range in drying index (i.e., resilient water yields), low elasticity indicates high d despite small range in drying index (i.e., non-resilient water yields). Although the data needed to fully evaluate ecosystems based on these metrics are limited, we were able to identify some characteristics of response among forest types. Alpine sites showed the greatest sensitivity to climate warming with any warming leading to increased water yields. Conifer forests included catchments with lowest elasticity and stable to larger water yields. Deciduous forests included catchments with intermediate elasticity and stable to smaller water yields. Mixed coniferous/deciduous forests included catchments with highest elasticity and stable water yields. Forest type appeared to influence the resilience of catchment water yields to climate warming, with conifer and deciduous catchments more susceptible to climate warming than the more diverse mixed forest catchments