Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes

Tan, Yi; Huang, Zhihao; Liu, Xiong-Jun

doi:10.1103/physrevb.105.l041105

Cited by 23 publications

(5 citation statements)

References 59 publications

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“…Since edge states only exist along one direction, topologically protected corner states emerge at the intersection of two boundaries. To enhance clarity, we analyze our model using the edge theory [32,[91][92][93][94], which is analogous to the Jackiw-Rebbi solitons [95], to provide a more intuitive understanding .…”

Section: B Edge Theory and Corner Modesmentioning

confidence: 99%

Economic Radiating Effects of the Guangdong–Hong Kong–Macao Greater Bay Area in China Effects of the Guangdong–Hong Kong–Macao Greater Bay Area

2021

Guangdong-Hong Kong-Macao Greater Bay Area

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In a dual weighted residual based adaptive finite element method for solving partial differential equations, a new finite element space needs to be built for solving the dual problem, due to the Galerkin orthogonality. Two popular approaches in the literature are h-refinement and p-refinement for the purpose, respectively, which would cause nonignorable requirement on computational resources. In this paper, a novel approach is proposed for implementing the dual weighted residual method through a multiple precision technique, i.e., the primal and dual problems are solved in two finite element spaces, respectively, built with the same mesh, degrees of freedom, and basis functions, yet different precisions. The feasibility of such an approach is discussed in detail. Besides effectively avoiding the issue introduced by the Galerkin orthogonality, remarkable benefits can also be expected for the efficiency from this new approach, since i). operations on reorganizing mesh grids and/or degrees of freedom in building a finite element space in hand p-refinement methods can be avoided, and ii). both CPU time and storage needed for solving the derived system of linear equations can be significantly reduced compared with hand p-refinement methods. In coding the algorithm with a library AFEPack, no extra module is needed compared with the program for solving the primal problem with the employment of a C++

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Section: B Edge Theory and Corner Modesmentioning

confidence: 99%

Economic Radiating Effects of the Guangdong–Hong Kong–Macao Greater Bay Area in China Effects of the Guangdong–Hong Kong–Macao Greater Bay Area

2021

Guangdong-Hong Kong-Macao Greater Bay Area

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“…Besides, a topological superconducting system with controllable number and position of MZMs is a prerequisite for implementing topological qubits. Higher-order topological superconductors [17][18][19][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] have shown their potential in fulfilling this condition [18,[46][47][48][49][50][51][52][53].…”

mentioning

confidence: 99%

Meissner effect induced Majorana zero modes at small magnetic field

Pan¹,

Chen²,

Liu³

et al. 2023

Preprint

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One fundamental difficulty in realizing Majorana zero modes (MZMs) is the required high magnetic field, which causes serious issues, e.g., shrinks the superconducting gap, reduces topological region, and weakens their robustness against disorder. In this work, we propose that the Meissner effect can bring the topological superconducting phase to a superconductor/topologicalinsulator/superconductor (SC/TI/SC) hybrid system. Remarkably, the required magnetic field strength (<10 mT) to support MZMs has been reduced by several orders of magnitude compared to that (>0.5 T) in the previous schemes. Tuning the phase difference between the top and bottom superconductors can control the number and position of the MZMs. In addition, we account for the electrostatic potential in the superconductor/topological-insulator (SC/TI) interface through the self-consistent Schrödinger-Poisson calculation, which shows the experimental accessibility of our proposal. Our proposal only needs a small magnetic eld of less than 10 mT and is robust against the chemical potential fluctuation, which makes SC/TI/SC hybrid an ideal Majorana platform.

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“…Zhao et al compared the geometric phase acquired for a two-level atom with different motions in Minkowski spacetime [23]. Besides, geometric phase also has important applications in other fields, such as wormhole quantum mechanics [24], nonlinear optical regime [25], condensed matter system [26]. Because of the accumulative nature of the geometric phase [1,16], it is sensitive to detect weak effects, such as the noninertial modifications to the field correlators [27].…”

mentioning

confidence: 99%

Geometric phase acquired by the two-level atom with different trajectories in cosmic string scalar field

Yang

Zhang²,

Xiangyun³

et al. 2023

EPL

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We consider the geometric phase induced by the two-level atom with inertial and uniformly accelerated motion, which is coupled to massless scalar field in cosmic string spacetime. Our result shows that when the atom is very close to the string, the geometric phase of cosmic string spacetime is $\nu$ times that of Minkowski spacetime. By comparing phase difference induced by the inertial and accelerated motion, we find the sensitive dependence of the phase difference on deficit angle parameter, transition frequencies of the atom, atomic acceleration and the initial state parameter. We also obtain phase difference increases with deficit angle parameter and the atomic acceleration. Although reaching the measurable magnitude of geometric phase requires extremely high acceleration, the detection experiment may be implemented in the future. Our work may suggest a possible way to detect cosmic string scalar field by using geometric phase.

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Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes

Cited by 23 publications

References 59 publications

Economic Radiating Effects of the Guangdong–Hong Kong–Macao Greater Bay Area in China Effects of the Guangdong–Hong Kong–Macao Greater Bay Area

Economic Radiating Effects of the Guangdong–Hong Kong–Macao Greater Bay Area in China Effects of the Guangdong–Hong Kong–Macao Greater Bay Area

Meissner effect induced Majorana zero modes at small magnetic field

Geometric phase acquired by the two-level atom with different trajectories in cosmic string scalar field

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