Geometric approach to nonequilibrium hasty shortcuts

Thermodynamic systems can exhibit monotonic or non-monotonic responses to external control. The latter can result in counter-intuitive effects such as the Mpemba effect -- hot water freezes faster than cold water. The existence of non-monotonic responses opens the possibility of designing non-equilibrium shortcuts to drive a system from an initial steady state to a desired final steady state. We explore the existence of hasty shortcuts in general thermodynamic systems that can be described by master equations parameterized by an externally controlled parameter. Here ``hasty shortcuts'' refer to time protocols of external control that steer a system from its initial state to a desired state, involving only fast dynamics without requiring any slow relaxations. By time-scale separation and eigenmode decomposition of the dynamics's generator, we provide a geometric representation of such shortcuts in the space of probability distributions (probability simplex). Using the geometric approach, we identify the necessary and sufficient condition for the existence of non-equilibrium hasty shortcuts. Further, we propose that the eigenvalue crossing of the generator could constitute the necessary geometric properties that allow for hasty shortcuts in plain systems with relatively simple responses to external stimuli. Finally, we validate our theory by applying it to the self-assembly of an octahedral model inspired by viral capsid assembly processes

Orbital Hall Conductivity in Bilayer Graphene

We investigate the orbital Hall conductivity in bilayer graphene (G/G), by modifying one of the layer as Haldane type with the next nearest neighbour (NNN) hopping strength and flux. The Haldane flux in one of the layer breaks the time reversal symmetry in both the layers and induces the gap opening at the Dirac points $K$ and $K'$ points. It is observed that the low energy isolated bands show large orbital magnetization and induce the Hall potential for opposite magnetic polarization under the external fields, thereby contribute to the orbital Hall conductivity (OHC). The self-rotation of the isolated electrons in their respective orbits leads to strong orbital angular momentum, which is more fundamental in non-magnetic materials. The observed OHC is similar to the anomalous Hall conductivity (AHC). Moreover, the orbital magnetization with opposite sign among the occupied states adds up to the higher OHC in the gap, whereas the AHC get vanishes. We further show the results of bilayer graphene with both the layers as Haldane type ($\rm \tilde G/ \tilde G$), and found that the OHC behaves similar to AHC which indicate that, the OHC is strongly depends on the band dispersion. Similarly, we show that in the heterobilayers with one of the layer is Haldane type generates the orbital magnetization and induces the OHC. It is concluded that, the isolated bands in Graphene bilayers with external stimuli are of orbital nature and show orbital ferromagnetism in the valleys in BZ

METHOD AND SYSTEM FOR DETERMINING SUSTAINABILITY INFORMATION IN AUTHORISATION MESSAGE

The present disclosure relates to method and system for calculating sustainability information in authorisation message based on transaction data. The present invention uses payment rails, sourcing for delivering sustainability information. The method also comprises sourcing and providing payment network entities and consumers the information on carbon intensity of a purchase. The present disclosure provides a solution for calculating the sustainability score of the registered Permanent Account Number (PAN) using transaction history, where transaction history is used to establish direct connectivity between merchants and issuers for the purpose of processing card transactions

Topological properties of nearly flat bands in bilayer α−T3\alpha-\mathcal{T}3 lattice

We study the effect of Haldane flux in the bilayer $\alpha$-$\mathcal{T}_3$ lattice system, considering possible non-equivalent, commensurate stacking configurations with a tight-binding formalism. The bilayer $\alpha$-$\mathcal{T}_3$ lattice comprises six sublattices in a unit cell, and its spectrum consists of six bands. In the absence of Haldane flux, threefold band crossings occur at the two Dirac points for both valence and conduction bands. The introduction of Haldane flux in a cyclically stacked bilayer $\alpha$-$\mathcal{T}_3$ lattice system separates all six bands, including two low-energy, corrugated nearly flat bands, and assigns non-zero Chern numbers to each band, rendering the system topological. We demonstrate that the topological evolution can be induced by modifying the hopping strength between sublattices with the scaling parameter $\alpha$ in each layer. In the dice lattice limit ($\alpha = 1$) of the Chern-insulating phase, the Chern numbers of the three pairs of bands, from low energy to higher energies, are $\pm 2$, $\pm 3$, and $\pm 1$. Interestingly, a continuous change in the parameter $\alpha$ triggers a topological phase transition through band crossings between the two lower energy bands. These crossings occur at different values for the conduction and valence bands and depend further on the next nearest neighbor (NNN) hopping strength. At the transition point, the Chern numbers of the two lower conduction and valence bands change discontinuously from $\pm 2$ to $\pm 5$ and $\pm 3$ to $0$, respectively, while leaving the Chern number of the third band intact

Topological flat bands in rhombohedral tetralayer and multilayer graphene on hexagonal boron nitride moire superlattices

We show that rhombohedral four-layer graphene (4LG) nearly aligned with a hexagonal boron nitride (hBN) substrate often develops nearly flat isolated low energy bands with non-zero valley Chern numbers. The bandwidths of the isolated flatbands are controllable through an electric field and twist angle, becoming as narrow as $\sim10~$meV for interlayer potential differences between top and bottom layers of $|\Delta|\approx 10\sim15~$meV and $\theta \sim 0.5^{\circ}$ at the graphene and boron nitride interface. The local density of states (LDOS) analysis shows that the nearly flat band states are associated to the non-dimer low energy sublattice sites at the top or bottom graphene layers and their degree of localization in the moire superlattice is strongly gate tunable, exhibiting at times large delocalization despite of the narrow bandwidth. We verified that the first valence bands' valley Chern numbers are $C^{\nu=\pm1}_{V1} = \pm n$, proportional to layer number for $n$LG/BN systems up to $n = 8$ rhombohedral multilayers