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In recent years, there has been a surge of interest in exploring higher-order topology and their semi-metallic counterparts, particularly in the context of Dirac and Weyl semimetals, termed as higher-order Dirac semimetal (HODSM) and higher-order Weyl semimetal (HOWSM). The HODSM phase exhibits hinge Fermi arcs (FAs) with a quantized higher-order topological invariant. Conversely, the HOWSM phase is a hybrid-order topological phase manifesting both surface and hinge FAs as a signature of first- and second-order topology and also possesses both first- and second-order topological invariants. In this work, we investigate a tight binding model for multi-HODSM (mHODSM) hosting multiple hinge FAs having a quantized quadrupolar winding number (QWN) greater than one. Furthermore, we obtain a multi-HOWSM (mHOWSM) phase from the mHODSM by applying an external magnetic field. The mHOWSM phase possesses both the Chern number and the QWN, featuring both surface and multiple hinge FAs. We study the spectral properties of the mHODSM and mHOWSM in different geometries. We also investigate the hinge FA-mediated transport in mHOWSM employing a two-terminal setup., Comment: 10 pages, 7 figures; comments are welcome

Periodically driven systems offer a perfect breeding ground for out-of-equilibrium engineering of topological boundary states at zero energy ($0$-mode), as well as finite energy ($\pi$-mode), with the latter having no static analog. The Floquet operator and the effective Floquet Hamiltonian, which encapsulate the stroboscopic features of the driven system, capture both spectral and localization properties of the $0$- and $\pi$-modes but sometimes fail to provide complete topological characterization, especially when $0$- and $\pi$-modes coexist. In this work, we utilize the spectral localizer, a powerful local probe that can provide numerically efficient, spatially local, and energy-resolved topological characterization. In particular, we apply the spectral localizer to the effective Floquet Hamiltonian for driven one- and two-dimensional topological systems with no or limited symmetries and are able to assign topological invariants, or local markers, that characterize the $0$- and the $\pi$-boundary modes individually and unambiguously. Due to the spatial resolution, we also demonstrate that the extracted topological invariants are suitable for studying driven disordered systems and can even capture disorder-induced phase transitions., Comment: 11 pages, 6 figures; Comments are welcome

In the ever-evolving landscape of Deep Neural Networks (DNN) hardware acceleration, unlocking the true potential of systolic array accelerators has long been hindered by the daunting challenges of expertise and time investment. Large Language Models (LLMs) offer a promising solution for automating code generation which is key to unlocking unprecedented efficiency and performance in various domains, including hardware descriptive code. The generative power of LLMs can enable the effective utilization of preexisting designs and dedicated hardware generators. However, the successful application of LLMs to hardware accelerator design is contingent upon the availability of specialized datasets tailored for this purpose. To bridge this gap, we introduce the Systolic Array-based Accelerator Data Set (SA-DS). SA-DS comprises a diverse collection of spatial array designs following the standardized Berkeley's Gemmini accelerator generator template, enabling design reuse, adaptation, and customization. SA-DS is intended to spark LLM-centered research on DNN hardware accelerator architecture. We envision that SA-DS provides a framework that will shape the course of DNN hardware acceleration research for generations to come. SA-DS is open-sourced under the permissive MIT license at https://github.com/ACADLab/SA-DS.git}{https://github.com/ACADLab/SA-DS., Comment: 4 pages, 5 Figures

We consider a non-Hermitian (NH) analog of a second-order topological insulator, protected by chiral symmetry, in the presence of next-nearest neighbor hopping elements to theoretically investigate the interplay beyond the first nearest neighbor hopping amplitudes and topological order away from Hermiticity. In addition to the four zero-energy corner modes present in the first nearest neighbor hopping model, we uncover that the second nearest neighbor hopping introduces another topological phase with sixteen zero-energy corner modes. Importantly, the NH effects are manifested in altering the Hermitian phase boundaries for both the models. While comparing the complex energy spectrum under open boundary conditions, and bi-orthogonalized quadrupolar winding number in real space, we resolve the apparent anomaly in the bulk boundary correspondence of the NH system as compared to the Hermitian counterpart by incorporating the effect of non-Bloch form of momentum into the mass term. The above invariant is also capable of capturing the phase boundaries between the two different topological phases where the degeneracy of the corner modes is evident, as exclusively observed for the second nearest neighbor model., Comment: This is the published version

Condensed matter systems are continuously subjected to dissipation, which often has adverse effects on quantum phenomena. We focus on the impact of dissipation on a superconducting Rashba nanowire. We reveal that the system can still host Majorana zero-modes (MZMs) with a finite lifetime in the presence of dissipation. Most interestingly, dissipation can also generate two kinds of dissipative boundary states: four robust zero-modes (RZMs) and two MZMs, in the regime where the non-dissipative system is topologically trivial. The MZMs appear via bulk gap closing and are topologically characterized by a winding number. The RZMs are not associated with any bulk states and possess no winding number, but their emergence is instead tied to exceptional points. Further, we confirm the stability of the dissipation-induced RZMs and MZMs in the presence of random disorder. Our study paves the way for both realizing and stabilizing MZMs in an experimental setup, driven by dissipation.