General bounded corner states in the two-dimensional Su-Schrieffer-Heeger model with intracellular next-nearest-neighbor hopping

Xu, Xun-Wei; Yu-zeng, LI; Liu, Zhengfang; Chen, Ai-Xi

doi:10.1103/physreva.101.063839

Cited by 32 publications

(13 citation statements)

References 72 publications

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“…[2], we consider a Benalcazar-Bernevig-Hughes (BBH) model of Majorana fermions and will show that it is a suitable model to realize an HOTSC with robust corner Majorana zero modes. It has been demonstrated that the original fermionic 2D SSH model cannot support topological corner states [10,11] unless one considers a negative coupling per plaquette, as theoretically proposed [2] and experimentally demonstrated in [12][13][14]. On the other hand, in our model, the mapping of Majorana fermions onto complex fermion operators gives rise to a model of Kitaev chains coupled by a staggered pairing coupling, showing a higher order topological phase.…”

Section: Introductionmentioning

confidence: 53%

Topological Edge States of a Majorana BBH Model

Maiellaro

Citro

2021

Condensed Matter

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We investigate a Majorana Benalcazar–Bernevig–Hughes (BBH) model showing the emergence of topological corner states. The model, consisting of a two-dimensional Su–Schrieffer–Heeger (SSH) system of Majorana fermions with π flux, exhibits a non-trivial topological phase in the absence of Berry curvature, while the Berry connection leads to a non-trivial topology. Indeed, the system belongs to the class of second-order topological superconductors (HOTSC2), exhibiting corner Majorana states protected by C4 symmetry and reflection symmetries. By calculating the 2D Zak phase, we derive the topological phase diagram of the system and demonstrate the bulk-edge correspondence. Finally, we analyze the finite size scaling behavior of the topological properties. Our results can serve to design new 2D materials with non-zero Zak phase and robust edge states.

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Section: Introductionmentioning

confidence: 53%

Topological Edge States of a Majorana BBH Model

Maiellaro

Citro

2021

Condensed Matter

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“…Various such generalizations of the 1D Kitaev model have been introduced [46-49, 92, 93], but the simplest instance can be realized by coupling multiple Kitaev chains with transverse hopping and pairing terms to form nlegs Kitaev ladders [50,94]. The two-leg Kitaev ladder is the simplest model which takes into account multimode topological phases, which usually arise in models of significant complexity, often involving two-dimensional platforms [95][96][97].…”

Section: Systems With Multiple Edge Modes: Tse Of the Kitaev Laddermentioning

confidence: 99%

Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors

Maiellaro,

Marino,

Illuminati

2022

Preprint

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Identifying entanglement-based order parameters characterizing topological systems has remained a major challenge for the physics of quantum matter in the last two decades. Here we show that squashed entanglement between the system edges, defined in terms of the edge-edge quantum conditional mutual information, is the natural order parameter for topological superconductors and for systems with edge modes. In the topological phase, the long-distance edge-edge squashed entanglement is quantized to log(2)/2, half the maximal Bell-state entanglement, and vanishes in the trivial phase. Such topological squashed entanglement exhibits the correct scaling at the quantum phase transition, discriminates between topological order and ordered phases associated to broken symmetries, counts the number of Majorana excitations for systems of increasing geometrical complexity, and is robust against the effects of disorder and local perturbations. In fact, it turns out to be a valid signature of topological order even for systems with weakened bulk-edge correspondence. Squashed entanglement is defined for all quantum states, reducing to the von Neumann entanglement entropy on pure states. As such, it provides a unified framework for the characterization of topological order in any dimension and, moreover, can be generalized to any setting, including finite temperature, multipartite correlations, and nonequilibrium. Squashed entanglement and quantum conditional mutual information are defined in terms of linear combinations of reduced entropies and can thus be probed using currently available experimental setups and techniques.

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“…The SSH model [88] is one of the simplest examples hosting one-dimensional topological phases. This model and its various extensions have been widely used to study different physical phenomena [103][104][105][106][107][108][109][110]. In the standard SSH model, each unit cell has two sublattices.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary entangled state transfer via a topological qubit chain

Wang¹,

Li²,

Gong³

et al. 2021

Preprint

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Quantum state transfer is one of the basic tasks in quantum information processing. We here propose a theoretical approach to realize arbitrary entangled state transfer through a qubit chain, which is a class of extended Su-Schrieffer-Heeger models and accommodates multiple topological edge states separated from the bulk states. We show that an arbitrary entangled state, from 2-qubit to N -qubit, can be encoded in the corresponding edge states, and then adiabatically transferred from one end to the other of the chain. The dynamical phase differences resulting from the time evolutions of different edge states can be eliminated by properly choosing evolution time. Our approach is robust against both the qubit-qubit coupling disorder and the evolution time disorder. For the concreteness of discussions, we assume that such a chain is constructed by an experimentally feasible superconducting qubit system, meanwhile, our proposal can also be applied to other systems.

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General bounded corner states in the two-dimensional Su-Schrieffer-Heeger model with intracellular next-nearest-neighbor hopping

Cited by 32 publications

References 72 publications

Topological Edge States of a Majorana BBH Model

Topological Edge States of a Majorana BBH Model

Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors

Arbitrary entangled state transfer via a topological qubit chain

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