Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond

Cohen, Eliahu; Larocque, Hugo; Bouchard, Frédéric; Nejadsattari, Farshad; Gefen, Yuval; Karimi, Ebrahim

doi:10.1038/s42254-019-0071-1

Cited by 220 publications

(179 citation statements)

References 201 publications

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“…Clearly, N D and N C have the same parity, so that Figure 4 shows examples of spatial contours enclosing zero, one, or two C-points with different topological numbers (N D , N C ) and the corresponding quantized phases Φ D and Φ C , Eqs. (8) and (13).…”

Section: B Paraxial 2d Fields: the Pancharatnam-berry Phase And C-pomentioning

confidence: 99%

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Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

2019

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Geometric phases are a universal concept that underpins numerous phenomena involving multicomponent wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem.Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincaré sphere and the Majoranasphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization Möbius strips.

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Section: B Paraxial 2d Fields: the Pancharatnam-berry Phase And C-pomentioning

confidence: 99%

“…Calculating the total, dynamical, geometric, and Cpoint phases (6), (8), (12), and (13) along the circular contour {r = const, ϕ ∈ (0, 2π)} for the fields (41), we obtain:…”

Section: Other Propertiesmentioning

confidence: 99%

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

2019

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“…Interestingly, in this case, even if the temperature is zero, the initial correlations change the decay rate of the offdiagonal elements since Γ (1) corr (t) = 0 at zero temperature while Γ (2) corr (t) = 0. On the other hand, at zero temperature, χ(t) is once again equal to Φ(t).…”

Section: A System State Preparation By Projective Measurementmentioning

confidence: 98%

“…where Γ(t) = Γ uc (t) + Γ (1) corr (t) + Γ (2) corr (t) with Γ (1) corr (t) the same as before [see Eq. (25)], while Γ (2) corr (t) is given by Γ (2) corr (t) = − ln abs…”

Section: B System State Preparation By Unitary Operationmentioning

confidence: 99%

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Geometric phase corrected by initial system-environment correlations

2020

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We find the geometric phase of a two-level system undergoing pure dephasing via interaction with an arbitrary environment, taking into account the effect of the initial system-environment correlations. We use our formalism to calculate the geometric phase for the two-level system in the presence of both harmonic oscillator and spin environments, and we consider the initial state of the two-level system to be prepared by a projective measurement or a unitary operation. The geometric phase is evaluated for a variety of parameters such as the system-environment coupling strength to show that the initial correlations can affect the geometric phase very significantly even for weak and moderate system-environment coupling strengths. Moreover, the correction to the geometric phase due to the system-environment coupling generally becomes smaller (and can even be zero) if initial system-environment correlations are taken into account, thus implying that the system-environment correlations can increase the robustness of the geometric phase.

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Widely Tunable Berry Curvature in the Magnetic Semimetal Cr₁₊_δTe₂

et al. 2023

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Magnetic semimetals have increasingly emerged as lucrative platforms hosting spin‐based topological phenomena in real and momentum spaces. Cr1+δTe2 is a self‐intercalated magnetic transition metal dichalcogenide (TMD), which exhibits topological magnetism and tunable electron filling. While recent studies have explored real‐space Berry curvature effects, similar considerations of momentum‐space Berry curvature are lacking. Here, the electronic structure and transport properties of epitaxial Cr1+δTe2 thin films are systematically investigated over a range of doping, δ (0.33 – 0.71). Spectroscopic experiments reveal the presence of a characteristic semi‐metallic band region, which shows a rigid like energy shift with δ. Transport experiments show that the intrinsic component of the anomalous Hall effect (AHE) is sizable and undergoes a sign flip across δ. Finally, density functional theory calculations establish a link between the doping evolution of the band structure and AHE: the AHE sign flip is shown to emerge from the sign change of the Berry curvature, as the semi‐metallic band region crosses the Fermi energy. These findings underscore the increasing relevance of momentum‐space Berry curvature in magnetic TMDs and provide a unique platform for intertwining topological physics in real and momentum spaces.

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Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond

Cited by 220 publications

References 201 publications

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phase corrected by initial system-environment correlations

Widely Tunable Berry Curvature in the Magnetic Semimetal Cr₁₊_δTe₂

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Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond

Cited by 220 publications

References 201 publications

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phase corrected by initial system-environment correlations

Widely Tunable Berry Curvature in the Magnetic Semimetal Cr1+δTe2

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Product

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Widely Tunable Berry Curvature in the Magnetic Semimetal Cr₁₊_δTe₂