Visualizing Electronic Chirality and Berry Phases in Graphene Systems Using Photoemission with Circularly Polarized Light

Liu, Yang; Bian, Guang; Miller, T.; Chiang, T.‐C.

doi:10.1103/physrevlett.107.166803

Cited by 200 publications

(185 citation statements)

References 30 publications

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“…Especially for graphene, chirality describes the connection of the direction along which an electron propagates in this 2D system and the amplitude of its wave function. This has been demonstrated, e.g., by the intensity dependence of angular-resolved photoelectron spectra on the usage left or right circularly polarized light [264]. Chiral effects in electron scattering by molecules, e.g., scattering of spin polarized electrons in chiral media is another fascinating topic in physics and will be such soon in materials science [265,266].…”

Section: Diastereomers and Diastereomeric Recognitionmentioning

confidence: 99%

Molecular chirality at surfaces

Ernst

2012

Physica Status Solidi (b)

223

264

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With the adsorption of larger molecules being increasingly tackled by surface scientists, the aspect of chirality often plays a role. This paper gives a topical review of molecular chirality at surfaces and gives a phenomenological overview of different aspects of adsorption and self‐assembly of chiral and prochiral molecules and the principles of mirror‐symmetry breaking at a surface. After a brief introduction into the history of molecular chirality and the important role it played for understanding the spatial structure of molecules, definitions of chirality are presented. Topics treated here are principle ways to create single chiral adsorbates, chiral ensembles, and monolayers by achiral molecules, adsorption of intrinsically chiral molecules at achiral and chiral surfaces, long‐range symmetry breaking in two‐dimensional (2D) crystals due to additional chiral bias, chiral restructuring of solid surfaces under the influence of chiral molecules, switching the handedness of adsorbates, and chirality at the liquid/air interface. An outlook onto further potential research directions and recommendations for further reading, including nonsurface‐related sources of chiral topics completes this paper.

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Section: Diastereomers and Diastereomeric Recognitionmentioning

confidence: 99%

Molecular chirality at surfaces

Ernst

2012

Physica Status Solidi (b)

223

264

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“…Concentrated at the Dirac point is a π Berry flux, which is analogous to a magnetic flux generated by an infinitely narrow solenoid [12]. This localized flux gives rise to several striking properties of graphene, including the half-integer shift in the positions of quantum Hall plateaus [13,14], the phase of Shubnikov-de Haas oscillations [13,14], and the polarization dependence in photoemission spectra [15,16]. A similar π flux also plays a crucial role in the nuclear dynamics of molecules featuring conical intersections of energy surfaces [2].…”

mentioning

confidence: 99%

An Aharonov-Bohm interferometer for determining Bloch band topology

Duca

Reitter

et al. 2015

Science

274

281

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The geometric structure of an energy band in a solid is fundamental for a wide range of many-body phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an Aharonov-Bohm interferometer that measures the magnetic flux penetrating a given area in real space, we realize an atomic interferometer to measure Berry flux in momentum space. We demonstrate the interferometer for a graphene-type hexagonal lattice, where it has allowed us to directly detect the singular π Berry flux localized at each Dirac point. We show that the interferometer enables one to determine the distribution of Berry curvature with high momentum resolution. Our work forms the basis for a general framework to fully characterize topological band structures and can also facilitate holonomic quantum computing through controlled exploitation of the geometry of Hilbert space.More than thirty years ago, Berry [1] delineated the effects of the geometric structure of Hilbert space on the adiabatic evolution of quantum mechanical systems. These ideas have found widespread applications in science [2] and are routinely used to calculate the geometric phase shift acquired by a particle moving along a closed path-a phase shift that is determined only by the geometry of the path and is independent of the time spent en route. Geometric phases provide an elegant description of the celebrated Aharonov-Bohm effect [3], where a magnetic flux in a confined region of space influences the eigenstates everywhere via the magnetic vector potential. In condensed-matter physics, an analogous Berry flux in momentum space is responsible for various anomalous velocities and Hall responses [4] and lies at the heart of many-body phenomena ranging from quantum Hall physics [5] to topological insulators [6]. The Berry flux density (Berry curvature) is indeed essential to the characterization of an energy band and determines its topological invariants. However, mapping out the geometric structure of an energy band [7][8][9] has remained a major unresolved challenge for experiments.Here, we demonstrate a versatile technique for measuring geometric phases in reciprocal space using spin-echo interferometry with ultracold atoms [9, 10]. In contrast to typical solid state experiments, where all geometric effects are averaged over the Fermi sea, the use of a Bose-Einstein condensate (BEC) enables measurements with high momentum resolution. We exploit this resolution to directly detect the singular topological properties of an individual Dirac cone [11] in a graphene-type hexagonal optical lattice (see Fig. 1). Concentrated at the Dirac point is a π Berry flux, which is analogous to a magnetic flux generated by an infinitely narrow solenoid [12]. This localized flux gives rise to several striking properties of graphene, including the half-integer shift in the positions of quantum Hall plateaus [13,14], the phase of Shubnikov-de Haas oscillations [13,14], and the polarization dependence in photoemission spec...

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“…27 . However, in the general case, the evaluation of the δ−phase still attracts a widespread interest [54][55][56][57][58][59] . In the simplest case of bilayer graphene without trigonal warping, we find the Berry phase…”

Section: Graphene In Magnetic Fieldsmentioning

confidence: 99%

Magneto-optics of monolayer and bilayer graphene

Falkovsky

2013

Jetp Lett.

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The optical conductivity of graphene and bilayer graphene in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall's, are analytically evaluated. The conductivity peaks are explained in terms of electron transitions. Correspondences between the transition frequencies and the magneto-optical features are established using the theoretical results. The main optical transitions obey the selection rule with ∆n = 1 for the Landau number n. The Faraday rotation and light transmission in the quantizing magnetic fields are calculated. The effects of temperatures and magnetic fields on the chemical potential are considered.

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Visualizing Electronic Chirality and Berry Phases in Graphene Systems Using Photoemission with Circularly Polarized Light

Cited by 200 publications

References 30 publications

Molecular chirality at surfaces

Molecular chirality at surfaces

An Aharonov-Bohm interferometer for determining Bloch band topology

Magneto-optics of monolayer and bilayer graphene

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