arXiv subjects

Dipendu Halder

Publications and source records attributed to Dipendu Halder.

7 recordsLinked to original sources

arXiv2026

Second-order Skin Effect in a Brick-Wall Lattice

Non-Hermitian skin effect, which is a unique feature of non-Hermitian systems, exhibits the formation of an extensive number of boundary modes under open boundary conditions. However, its manifestation in higher dimensions remains elusive. In our work, we demonstrate a hybrid skin-topological effect arising from the interplay between first-order band topology and non-reciprocal hopping in an engineered two-dimensional brick-wall geometry. The non-Hermitian brick-wall lattice under open boundary conditions in both directions exhibits several unconventional spectral features. Notably, the eigenvalues associated with the corner skin modes do not exhibit non-trivial windings in the complex energy plane; instead, they exhibit dynamically stable exceptional point-like features that do not originate from eigenvector coalescence. In contrast, the remaining modes accumulate at the opposite pair. Of all the corner skin modes, only the two that originate from the topological corner states of the Hermitian brick-wall lattice remain localized at individual corners, while the rest accumulate at the pair of opposite corners. This spatial distribution contrasts sharply with the second-order skin effect, where corner skin modes are more uniformly distributed. Finally, for the non-Hermitian Brick-wall lattice, we design and implement the corresponding topolectrical circuit (circuit for a square lattice is included for comparison) to directly visualize the hybrid skin-topological modes.

cond-mat.mes-hall↗

arXiv2025

Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits

Periodically driven systems intertwined with non-Hermiticity opens a rich arena for topological phases that transcend conventional Hermitian limits. The physical significance of these phases hinges on obtaining the topological invariants that restore the bulk-boundary correspondence, a task well explored for static non-Hermitian (NH) systems, while it remains elusive for the driven scenario. Here, we address this problem by constructing a generalized Floquet non-Bloch framework that analytically captures the spectral and topological properties of time-periodic NH systems. Employing a high-frequency Magnus expansion, we analytically derive an effective Floquet Hamiltonian and formulate the generalized Brillouin zone for a periodically driven quasi-one-dimensional system, namely, the Creutz ladder with a staggered complex potential. Our study demonstrates that the skin effect remains robust (despite the absence of non-reciprocal hopping) across a broad range of driving parameters, and is notably amplified in the low-frequency regime due to emergent longer-range couplings. We further employ a symmetric time frame approach that generates chiral-partner Hamiltonians, whose invariants, when appropriately combined, account for the full edge-state structure. To substantiate the theoretical framework, we propose a topolectrical circuit (TEC) that serves as a viable experimental setting. Apart from capturing the skin modes, the proposed TEC design faithfully reproduces the presence of distinct Floquet edge states, as revealed through the voltage and impedance profiles, respectively. Thus, our work not only offers a theoretical framework for exploring NH-driven systems, but also provides an experimentally feasible TEC architecture for realizing these phenomena stated above in a laboratory.

cond-mat.mes-hall↗

arXiv2025

Controlled probing of localization effects in the non-Hermitian Aubry-Andr\'e model via topolectrical circuits

Anderson localization and the non-Hermitian skin effect are two distinct confinement phenomena of the eigenfunctions that are driven, respectively, by disorder and nonreciprocity. Understanding their interplay within a unified framework offers valuable insights into the localization properties of low-dimensional systems. To this end, we investigate a non-Hermitian version of the celebrated Aubry-Andr\'e model, which serves as an ideal platform due to its unique self-dual properties and ability to demonstrate a delocalization-localization transition in one dimension. Interestingly, in our setting, the competition between Anderson localization and the skin effect can be precisely controlled via the complex phase of the quasiperiodic disorder. Additionally, by analyzing the time evolution, we demonstrate that quantum jumps between the skin states and the Anderson-localized states occur in the theoretical model. Further, to gain support for our theoretical predictions in an experimental platform, we propose a topolectrical circuit featuring an interface that separates two distinct electrical circuit networks. The voltage profile of the circuit exhibits confinement at the interface, analogous to the skin effect, while the phenomenon of Anderson localization in the circuit can be perceived via a predicted localization behavior near the excitation node, rather than exhibiting sudden non-Hermitian jumps, as observed in the tight-binding framework. This interplay leads to a spatially tunable localization of the output voltage of the circuit. Our findings provide deeper insights into the controlled confinement of the eigenstates of the non-Hermitian Aubry-Andr\'e model by designing analogous features in topolectrical circuits, opening avenues in the fabrication of advanced electronic systems such as highly sensitive sensors and efficient devices for information transfer and communication.

cond-mat.dis-nn↗

arXiv2024

Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model

The Bernevig-Hughes-Zhang (BHZ) model, which serves as a cornerstone in the study of the quantum spin Hall insulators, showcases robust spin-filtered helical edge states in a nanoribbon geometry. In the presence of an in-plane magnetic field, these (first-order) helical states gap out to be replaced by second-order corner states under suitable open-boundary conditions. Here, we show that the inclusion of a spin-dependent non-Hermitian balanced gain/loss potential induces a competition between these first and second-order topological phases. Surprisingly, the previously dormant first-order helical edge states in the nanoribbon resurface as the non-Hermitian effect intensifies, effectively neutralizing the role played by the magnetic field. By employing the projected spin spectra and the spin Chern number, we conclusively explain the resurgence of the first-order topological properties in the time-reversal symmetry-broken BHZ model in presence of non-Hermiticity. Finally, the biorthogonal spin-resolved Berry phase, exhibiting a non-trivial winding, definitively establishes the topological nature of these revived edge states, emphasizing the dominance of non-Hermiticity over the magnetic field.

cond-mat.mes-hall↗

arXiv2023

Circuit realisation of a two-orbital non-Hermitian tight-binding chain

We examine a non-Hermitian (NH) tight-binding system comprising of two orbitals per unit cell and their electrical circuit analogues. We distinguish the PT-symmetric and non-PT symmetric cases characterised by non-reciprocal nearest neighbour couplings and onsite gain/loss terms, respectively. The localisation of the edge modes or the emergence of the topological properties are determined via the maximum inverse participation ratio, which has distinct dependencies on the parameters that define the Hamiltonian. None of the above scenarios exhibits the non-Hermitian skin effect. We investigate the boundary modes corresponding to the topological phases in a suitably designed electrical circuit by analyzing the two-port impedance and retrieve the admittance band structure of the circuit via imposing periodic boundary conditions. The obtained results are benchmarked against the Hermitian version of the two-orbital model to compare and discriminate against those obtained for the NH variants.

cond-mat.mes-hall↗

arXiv2023

Parsing skin effect in a non-Hermitian spinless BHZ-like model

This work comprehensively investigates the non-Hermitian skin effect (NHSE) in a spinless Bernevig- Hughes-Zhang (BHZ)-like model in one dimension. It is generally believed that a system with non-reciprocal hopping amplitudes demonstrates NHSE. However, we show that there are exceptions, and more in-depth analyses are required to decode the presence of NHSE or its variants in a system. The fascinating aspects of our findings, depending on the inclusion of non-reciprocity in the inter-orbital hopping terms, concede the existence of conventional NHSE or NHSE at both edges and even a surprising absence of NHSE. The topological properties and the (bi-orthogonal) bulk-boundary correspondence, enumerated via computation of the (complex) Berry phase and spatial localization of the edge modes, highlight the topological phase transitions occurring therein. Further, to facilitate a structured discussion of the non-Hermitian model, we split the results into PT symmetric and non-PT symmetric cases with a view to comparing the two.

cond-mat.mes-hall↗

arXiv2022

Properties of the non-Hermitian SSH model: role of PT-symmetry

The present work addresses the distinction between the topological properties of PT symmetric and non-PT symmetric scenarios for the non-Hermitian Su-Schrieffer-Heeger (SSH) model. The non-PT symmetric case is represented by non-reciprocity in both the inter- and the intra-cell hopping amplitudes, while the one with PT symmetry is modeled by a complex on-site staggered potential. In particular, we study the loci of the exceptional points, the winding numbers, band structures, and explore the breakdown of bulk-boundary correspondence (BBC). We further study the interplay of the dimerization strengths on the observables for these cases. The non-PT symmetric case denotes a more familiar situation, where the winding number abruptly changes by a half-integer through tuning of the non-reciprocity parameters, and demonstrates a complete breakdown of BBC, thereby showing the non-Hermitian skin effect. The topological nature of the PT symmetric case appears to follow closely to its Hermitian analogue, except that it shows unbroken (broken) regions with complex (purely real) energy spectra, while another variant of the winding number exhibits a continuous behavior as a function of the strength of the potential, while the conventional BBC is preserved.

quant-ph↗