arXiv subjects

Deepanshu Aggarwal

Publications and source records attributed to Deepanshu Aggarwal.

5 recordsLinked to original sources

arXiv2025

Emergent fractals in hBN-encapsulated graphene based supermoir\'e structures and their experimental signatures

Supermoir\'e structures (SMS), formed by overlapping moir\'e-patterns in van der Waals heterostructures, display complex behaviour that lacks a comprehensive low-energy theoretical description. We demonstrate that these structures can form emergent fractals under specific conditions and identify the parameter space where this occurs in hexagonal trilateral SMS. This fractality enables a reliable calculation of low-energy band counts, which are crucial for understanding both single-particle and correlation effects. Using an effective Hamiltonian that includes in- and out-of-plane lattice relaxation, we analyze SMS in hBN-encapsulated single and bilayer graphene. We prescribe methods to experimentally verify these fractals and extract their fractal dimension through angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM).

cond-mat.mes-hall↗

arXiv2023

Photon absorption in twisted bilayer graphene

We investigate one- and two-photon absorption in twisted bilayer graphene (TBLG) by examining the effects of tuning the twist angle $ \theta $ and the excitation energy $ E_l $ on its absorption coefficients $ \alpha_{i=1,2}$. We find that $ \alpha_1 $ as a function of $ E_l $ for TBLG exhibits distinct peaks corresponding to its van Hove singularities (vHs). For small twist angles, such as $\theta \sim 1.8^{\circ}$, the magnitude of the resonant peak for $\alpha_1$ is roughly twice that of bilayer graphene (BLG). This enhanced response, compared to BLG, can be attributed to the increased density of states (DOS) in the twisted structure. However, as the twist angle increases the magnitude of the resonant peak approaches that of two decoupled single-layer graphene (SLG) sheets. On the other hand, the two-photon absorption coefficient $ \alpha_2 $ for TBLG at low twist angles displays an enhancement of about one order of magnitude compared to SLG at the energies corresponding to the resonant peak, as well as a small but notable increase relative to BLG. As the twist angle decreases from $ 8^{\circ} $ to $ 2.5^{\circ} $, the resonant peak intensifies by three orders of magnitude. Interestingly, as $\theta$ increases the resonant features exhibited by $\alpha_{i=1,2}$ \textit{vs.} $ E_l $ shift progressively from the infrared to the visible. On doping TBLG, both $\alpha_1 $ and $ \alpha_2 $ \textit{vs.} $ E_l $ remain essentially unchanged but with a slight red-shift in their resonant peaks. Additionally, we explore various polarization configurations for two-photon absorption and determine the conditions under which $\alpha_2$ becomes extremal.

cond-mat.mes-hall↗

arXiv2023

Moir\'e fractals in twisted graphene layers

Twisted bilayer graphene (TBLG) subject to a sequence of commensurate external periodic potentials reveals the formation of moir\'{e} fractals (MF) that share striking similarities with the central place theory (CPT) of economic geography, thus uncovering a remarkable connection between twistronics and the geometry of economic zones. MFs arise from the self-similarity of the emergent hierarchy of Brillouin zones (BZ), forming a nested subband structure within the bandwidth of the original moir\'{e} bands. We derive the fractal generators (FG) for TBLG under these external potentials and explore their impact on the hierarchy of the BZ edges and the wavefunctions at the Dirac point. By examining realistic super-moir\'{e} structures (SMS) and demonstrating their equivalence to MFs with periodic perturbations under specific conditions, we establish MFs as a general description for such systems. Furthermore, we uncover parallels between the modification of the BZ hierarchy and magnetic BZ formation in Hofstadter's butterfly (HB), allowing us to construct an incommensurability measure for MFs \textit{vs.} twist angle. The resulting bandstructure hierarchy bolsters correlation effects, pushing more bands within the same energy window for both commensurate and incommensurate TBLG.

cond-mat.mes-hall↗

arXiv2022

Interference effects in polarization controlled Rayleigh scattering in twisted bilayer graphene

We calculate the \tco{polarization}-controlled Rayleigh scattering response of twisted bilayer graphene (tBLG) based on the continuum electronic band model developed by Bistritzer and MacDonald while considering its refinements which address the effects of structural corrugation, doping-dependent Hartree interactions and particle-hole asymmetry. The dominant wave vectors for the Rayleigh scattering process emanate from various regions of the Moir\'e Brillouin zone (MBZ) in contrast to single-layer graphene (SLG) and AB-stacked bilayer graphene (AB-BLG), where the dominant contributions always stem from the vicinity of the $\bm{K}$ point for optical laser energies and below. Compared to SLG, the integrated Rayleigh intensity is strongly enhanced for small twist angles (\emph{e.g.}, at a twist angle $ \theta = 1.2^{\circ} $, the integrated Rayleigh intensity at laser energy $ E_l=2~\si{\electronvolt} $ enhances by a factor of $\sim $ 100 for the case of parallel \tco{polarization}). While for the case of cross-\tco{polarization}, it exhibits a markedly complex \tco{behavior} suggestive of strong interference effects mediated by the optical matrix elements. We find that at small twist angles, \emph{e.g.}, $ \theta = 1.05^{\circ} $, the corrugation effects strongly enhances the ratio $ \bm{R}_A = \frac{ \text{integrated Rayleigh intensity for parallel \tco{polarization}}}{\text{integrated Rayleigh intensity for cross-\tco{polarization}}} $ by $ \sim $ $ 1300 $ times \emph{viz a viz} SLG or AB-BLG.

cond-mat.mes-hall↗

arXiv2022

A primer on twistronics: A massless Dirac fermion's journey to moir\'{e} patterns and flat bands in twisted bilayer graphene

The recent discovery of superconductivity in magic-angle twisted bilayer graphene has sparked a renewed interest in the strongly-correlated physics of $sp^2$ carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moir\'{e} pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and twisted bilayer graphene. Subsequently, we illuminate the origin of flat bands in twisted bilayer graphene at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of twisted bilayer graphene not covered by this review but may readily be approached with the help of this primer.

cond-mat.mes-hall↗