Non-Hermitian semi-Dirac semi-metals

Banerjee, Ayan; Narayan, Awadhesh

doi:10.1088/1361-648x/abe796

Cited by 11 publications

(10 citation statements)

References 97 publications

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“…Unusual properties, such as complex band spectra and non-orthogonal eigenstates, are the outcomes of such non-Hermitian Hamiltonians [41]. In particular, non-Hermitian systems can show a distinct class of spectral degeneracies known as exceptional points (EPs) [42][43][44][45][46][47][48][49][50][51][52][53], as well as exceptional contours [54,55]. At an EP the eigenvalues and the eigenvectors simultaneously coalesce making the Hamiltonian defective, i.e., nondiagonalizable.…”

Section: Introductionmentioning

confidence: 99%

Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

2023

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The interplay of topology and non-Hermiticity has led to diverse, exciting manifestations in a plethora of systems. In this work, we systematically investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice. Due to the presence of a nondispersive flat band, the dice-Haldane model hosts a topologically rich phase diagram with the nontrivial phases accommodating Chern numbers ±2. We introduce non-Hermiticity into this model in two ways-through balanced non-Hermitian gain and loss, and by nonreciprocal hopping in one direction. Both these types of non-Hermiticity induce higher-order exceptional points of order three. Remarkably, the exceptional points at high-symmetry points occur at odd integer values of the non-Hermiticity strength in the case of balanced gain and loss, and at odd integer multiples of 1/ √ 2 for nonreciprocal hopping. We substantiate the presence and the order of these higher-order exceptional points using the phase rigidity and its scaling. Furthermore, we construct a phase diagram to identify and locate the occurrence of these exceptional points in the parameter space. Non-Hermiticity has yet more interesting consequences on a finite-sized lattice. Unlike for balanced gain and loss, in the case of nonreciprocal hopping, the nearest-neighbor lattice system under periodic boundary conditions accommodates a finite, nonzero spectral area in the complex plane. This manifests as the non-Hermitian skin effect when open boundary conditions are invoked. In the more general case of the dice-Haldane lattice model, the non-Hermitian skin effect can be caused by both gain and loss or nonreciprocity. Fascinatingly, the direction of localization of the eigenstates depends on the nature and strength of the non-Hermiticity. We establish the occurrence of the skin effect using the local density of states, inverse participation ratio, and the edge probability and demonstrate its robustness to disorder. Our results place the dice-Haldane model as an exciting platform to explore non-Hermitian physics.

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Section: Introductionmentioning

confidence: 99%

Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

2023

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“…Topological phases, localization and novel phase transitions in non-Hermitian systems with periodic or aperiodic order have recently sparked a great interest in a wide variety of physical systems, ranging from condensed matter physics to cold atoms and classical systems (see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13] and references therein). Non-interacting particles in crystalline systems described by an effective non-Hermitian Hamiltonian display a variety of exotic physical effects, such as a non-trivial point-gap topology, the non-Hermitian skin effect, the breakdown of the bulkboundary correspondence based on Bloch band topological invariants, and a variety of dynamical and transport signatures .…”

Section: Introductionmentioning

confidence: 99%

Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal

Longhi

2023

Phys. Rev. B

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Non-interacting particles in non-Hermitian quasi crystals display localization-delocalization and spectral phase transitions in complex energy plane, that can be characterized by point-gap topology. Here we investigate the spectral and dynamical features of two interacting particles in a non-Hermitian quasi crystal, described by an effective Hubbard model in an incommensurate sinusoidal potential with a complex phase, and unravel some intriguing effects without any Hermitian counterpart. Owing to the effective decrease of correlated hopping introduced by particle interaction, doublon states, i.e. bound particle states, display a much lower threshold for spectral and localization-delocalization transitions than single-particle states, leading to the emergence of mobility edges. Remarkably, since doublons display longer lifetimes, two particles initially placed in distant sites tend to bunch and stick together, forming a doublon state in the long time limit of evolution, a phenomenon that can be dubbed non-Hermitian particle bunching.

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“…The NH effects on the topological aspects of the WSMs is a recent topic of interest [14][15][16][17][18][19][20]. Numerous theoretical and experimental efforts [21][22][23][24][25][26][27][28][29] have enhanced the understanding of different aspects of such systems in the presence of NH perturbations. What makes the NH systems special is the existence of unique degenerate exceptional points (EPs), which are formed when both the eigenvalues as well as the eigenvectors coalesce [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Exceptional hexagonal warping effect in multi-Weyl semimetals

2022

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Hexagonal warping (HW) in three-dimensional topological insulators is, by now, well known. We show that non-Hermitian (NH) loss/gain can generate an exceptional HW effect in double Weyl semimetals (DWSMs). This unique feature of DWSMs has distinctive effects on Fermi surface topology. Importantly, in the presence of such a k 3 spin orbit coupling mimicking term, the symmetry associated with the DWSMs is changed, leading to four exceptional points, among which two are degenerate. Introducing a driving field removes this degeneracy. The combined action of the NH warping and driving parameters leads to notable effects, including merging and tuning of exceptional points. We analyze the topological nature of the generated exceptional contours by evaluating several topological invariants, such as winding number, vorticity, and NH Berry curvature. We hope that our theoretical results will initiate possible experiments exploring NH HW effects.

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Non-Hermitian semi-Dirac semi-metals

Cited by 11 publications

References 97 publications

Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

Non-Hermiticity induced exceptional points and skin effect in the Haldane model on a dice lattice

Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal

Exceptional hexagonal warping effect in multi-Weyl semimetals

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