Geometrical effect on the non-Abelian spin-orbital gauge field of a curved surface

Cheng, Tai-Chung; Chen, Jiann‐Yeu; Chang, Ching‐Ray

doi:10.1103/physrevb.84.214423

Cited by 14 publications

(6 citation statements)

References 38 publications

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“…This kind of curvature induced geometric potential can possibly induce local anisotropy or local effective magnetic field on curved surfaces. [ 5 ] Magnetism in curved geometries has been rather intensively discussed recently [ 70 ] and curvature induced local anisotropy and effective magnetic field can then counterbalance fluctuations and sustain spontaneous magnetization. Therefore magnetism in 2D curved system can also arise from the curvature induced anisotropy.…”

Section: Low Dimensional Theory For Magnetizationmentioning

confidence: 99%

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Prospects and Opportunities of 2D van der Waals Magnetic Systems

et al. 2020

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The existence of spontaneous magnetization in low dimensional magnetic systems has attracted intensive studies since the early 60s and research remains very active even now. Only recently, magnetic van der Waals (vdW) systems down to a few layers have been broadly discussed for their magnetic order ground states at finite temperature. The naturally inherited layered structure of the vdW magnetic systems possessing onsite magnetic anisotropy from band electrons can suppress the long-range fluctuations. This provides an excellent vehicle to study the transition of magnetism to 2D limits both theoretically and experimentally. Here the current status of 2D vdW magnetic system and its potential applications are briefly summarized and discussed.

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Section: Low Dimensional Theory For Magnetizationmentioning

confidence: 99%

“…Recently, intensive studies suggested that a curved 2D system introduces effective magnetic field, which can possibly counterbalance fluctuations. [ 5 ] Last, current results of magnetic space group and ab initio calculations of 2D vdW magnetic system are summarized in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Prospects and Opportunities of 2D van der Waals Magnetic Systems

et al. 2020

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“…The dependence of the spin-orbit interactions (SOI) on the momentum of the charge carriers suggests that the SOI can be manipulated by introducing (real-space) geometrical curvature into the (constrained) motion of charge carriers so that the direction and magnitude of their momentum vary with their positions [1]. The modification of the effective SOI and appearance of curvature-induced terms [2,3] due to the curved motion has led to various interesting phenomena, such the modification to the spin texture [4,5], spin precession [6,7], and charge density [8], suggesting potential applications for the generation of spin-polarized currents [9,10]. Recently, the independent geometrical control of the spin and charge resistances in a curved nanosystem has been demonstrated experimentally [11].…”

Section: Introductionmentioning

confidence: 99%

“…The first term on the right of the equal sign comprises the kinetic energy, the second term the SOI, and the third term the potential energy terms due to the applied potential, da Costa potential, and applied magnetization coupling. We obtain the eigenstates and eigenvectors of the Hamiltonian through direct numerical diagonalization of the real-space finite-difference approximation of the Hamiltonian equation (7), which would be described in detail in the following sub-sections.…”

mentioning

confidence: 99%

Higher Chern number states in curved periodic nanowires

Siu¹,

Tan²,

Jalil³

2022

Nanotechnology

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The coupling between the spin and momentum degrees of freedom due to spin-orbit interactions (SOI) suggests that the strength of the latter can be modified by controlling the motion of the charge carriers. In this paper, we investigate how the effective SOI can be modulated by constraining the motion of charge carriers to curved waveguides thereby introducing real-space geometric curvature in their motion. The change in the SOI can in turn induce topological phase transitions in the system. Specifically, we study how the introduction of periodic sinusoidal curvature in nanowires with intrinsic SOC can induce the onset of mid-gap topologically protected edge states, which can be characterized by a topological invariant or Chern number. The Chern number corresponds to the number of discrete charges that would be pumped across the length of the nanowire when the phase of a sliding gate potential relative to that of the sinusoidal curvature is varied adiabatically over a complete period. In addition, coupling to an external magnetization can be utilized as an experimental knob to modify the Chern number by displacing the energies of the curvature-induced bands relative to one another. The magnetization can be tuned to achieve large discrete jumps in the number of pump charges per phase period.

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Section: Introductionmentioning

confidence: 99%

Higher Chern Number States in Curved Periodic Nanowires

Siu,

Tan,

Jalil

2021

Preprint

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The coupling between the spin and momentum degrees of freedom due to spin-orbit interactions (SOI) suggests that the strength of the latter can be modified by controlling the motion of the charge carriers. In this paper, we investigate how the effective SOI can be modulated by constraining the motion of charge carriers to curved waveguides thereby introducing real-space geometric curvature in their motion. The change in the SOI can in turn induce topological phase transitions in the system. Specifically, we study how the introduction of periodic sinusoidal curvature in nanowires with intrinsic SOC can induce the onset of mid-gap topologically protected edge states, which can be characterized by a topological invariant or Chern number. The Chern number corresponds to the number of discrete charges that would be pumped across the length of the nanowire when the phase of a sliding gate potential relative to that of the sinusoidal curvature is varied adiabatically over a complete period. In addition, coupling to an external magnetization can be utilized as an experimental knob to modify the Chern number by changing the ordering of the nanowire energy bands. The magnetization can be tuned to achieve large discrete jumps in the number of pump charges per phase period.

show abstract

Geometrical effect on the non-Abelian spin-orbital gauge field of a curved surface

Cited by 14 publications

References 38 publications

Prospects and Opportunities of 2D van der Waals Magnetic Systems

Prospects and Opportunities of 2D van der Waals Magnetic Systems

Higher Chern number states in curved periodic nanowires

Higher Chern Number States in Curved Periodic Nanowires

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