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Cheng Peng Chang - One of the best experts on this subject based on the ideXlab platform.
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evolution and dimensional crossover from the bulk subbands in abc stacked graphene to a three dimensional dirac cone structure in Rhombohedral Graphite
Physical Review B, 2016Co-Authors: Ching Hong Ho, Cheng Peng ChangAbstract:The band structure of ABC-stacked N-layer graphene comprises topologically corresponding flat surface and gapped bulk subbands, as a consequence of the unique stacking configuration. In this paper, the bulk subbands are for the first times ever obtained for arbitrary N. A non-perturbative effective Hamiltonian closed in the bulk subspace is derived and used. The gapped bulk subbands are shown to evolve towards the zero energy with increasing N and in the infinite limit, they touch linearly along a circle. This outcome is a manifestation of the dimensional crossover to a three-dimensional Dirac cone structure known to exist in the bulk of Rhombohedral Graphite. The Dirac points, forming continuous nodal lines in a spiraling fashion, are projected onto the circle, within which the surface subbands are confined and flatten.
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evolution and dimensional crossover from the bulk subbands in abc stacked graphene to a three dimensional dirac cone structure in Rhombohedral Graphite
Physical Review B, 2016Co-Authors: Cheng Peng Chang, Mingfa LinAbstract:Rhombohedral Graphite behaves like a topological semimetal, possessing flat surface subbands while being semimetallic in the bulk. The bulk-surface correspondence arises from the ABC-stacking configuration of graphene layers. The bulk subbands in Rhombohedral Graphite can be interpreted as a three-dimensional Dirac cone structure, whose Dirac points form continuous lines spiraling in momentum space. In this paper, we study the evolution of gapped bulk subbands in ABC-stacked $N$-layer graphene with an increase of $N$, and their dimensional crossover to the three-dimensional Dirac cone structure in the bulk limit, where the bulk gap closes up at the Dirac-point spirals. To clarify the effect of coupling to the surface subbands, we use a nonperturbative effective Hamiltonian closed in the bulk subspace. As a consequence, the wavelength of the standing-wave function across the stack of layers depends on the in-plane Bloch momentum. In the bulk limit, the coupling vanishes and hence the wavelength is irrelevant to the surface.
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Evolution and crossover from bulk subbands in ABC-stacked graphene to a three-dimensional Dirac cone structure in Rhombohedral Graphite
arXiv: Mesoscale and Nanoscale Physics, 2015Co-Authors: Ching Hong Ho, Cheng Peng ChangAbstract:The band structure of ABC-stacked $N$-layer graphene comprises topologically corresponding flat surface and gapped bulk subbands, as a result of the unique stacking configuration. In this paper, the bulk subbands are for the first times ever obtained for arbitrary $N$. A non-perturbative effective Hamiltonian closed in the bulk subspace is derived and used. The gapped bulk subbands are shown to evolve toward the zero energy with increasing $N$ and in the infinite limit, they touch linearly along a circle. This outcome is a manifestation of the dimensional crossover to a three-dimensional Dirac cone structure known to exist in the bulk of Rhombohedral Graphite. The Dirac points, forming continuous nodal lines in a spiraling fashion, are projected onto the circle, within which the flat surface subbands are confined.
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Optical magnetoplasmons in Rhombohedral Graphite with a three-dimensional Dirac cone structure
Journal of Physics: Condensed Matter, 2015Co-Authors: Ching Hong Ho, Cheng Peng ChangAbstract:Rhombohedral Graphite has a three-dimensional Dirac cone structure, differing only perturbatively from the bulk stack of independent graphene layers, so that the three-dimensional integer quantum Hall effect can be well exhibited in this system. In this paper, optical magnetoplasmons are obtained by using the random phase approximation. Such collective excitations do not exist in monolayer graphene but are shown to originate from Landau level mixing due to interlayer Coulomb interaction in the quantum Hall effect regime. The three-dimensional character of Rhombohedral Graphite is thus demonstrated. The results should be realized in response to a longitudinal external electric field or an incident infrared electromagnetic wave.
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landau subband wave functions and chirality manifestation in Rhombohedral Graphite
Solid State Communications, 2014Co-Authors: Cheng Peng Chang, Min-fa LinAbstract:Abstract Recently, Rhombohedral Graphite has been known to have a three-dimensional Dirac cone structure composed of tilted anisotropic Dirac cones, as a result of the perturbative interlayer electron hoppings. The corresponding Landau subbands have weak energy dispersions, a characteristic indicating the possible occurrence of a three-dimensional quantum Hall effect in weak magnetic fields. Since the robust zero-mode Landau subband should be topologically protected by the chirality of the Dirac fermions, here we investigate the chirality for Rhombohedral Graphite with regard to the Dirac cone tilt and anisotropy, for which there could exist phases mixing in the Landau subband wave functions. Both a perturbation analysis and an exact diagonalization are performed for showing the effects of the interlayer hoppings on the phases mixing. In the results the perturbations due to the interlayer hoppings are not resolvable. Rhombohedral Graphite turns out to have the same chiral nature as monolayer graphene. The realizability of the three-dimensional quantum Hall effect in Rhombohedral Graphite is thus further supported by the manifestation of chiralities.
Vladimir I Falko - One of the best experts on this subject based on the ideXlab platform.
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engineering of the topological magnetic moment of electrons in bilayer graphene using strain and electrical bias
Physical Review B, 2020Co-Authors: Christian Moulsdale, Angelika Knothe, Vladimir I FalkoAbstract:The topological properties of electronic states in multivalley two-dimensional materials, such as mono- and bilayer graphene, or thin films of Rhombohedral Graphite give rise to various unusual magnetotransport regimes. Here, we investigate the tunability of the topological magnetic moment (related to the Berry curvature) of electronic states in bilayer graphene using strain and vertical bias. We show how one can controllably vary the valley $g$ factor of the band-edge electrons ${g}_{v}^{*}$ across the range $10l|{g}_{v}^{*}|l200$, and we discuss the manifestations of the topological magnetic moment in the anomalous contribution towards the Hall conductivity and in the Landau level spectrum.
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engineering of the topological magnetic moment of electrons in bilayer graphene using strain and electrical bias
arXiv: Mesoscale and Nanoscale Physics, 2019Co-Authors: Christian Moulsdale, Angelika Knothe, Vladimir I FalkoAbstract:Topological properties of electronic states in multivalley two-dimensional materials, such as mono- and bilayer graphene, or thin films of Rhombohedral Graphite, give rise to various unusual magneto-transport regimes. Here, we investigate the tunability of the topological magnetic moment (related to the Berry curvature) of electronic states in bilayer graphene using strain and vertical bias. We show how one can controllably vary the valley $g$-factor of the band-edge electrons, $g_v^*$, across the range $10 < |g_v^*| < 200$, and we discuss the manifestations of the topological magnetic moment in the anomalous contribution towards the Hall conductivity and in the Landau level spectrum.
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spectroscopic signatures of electronic excitations in raman scattering in thin films of Rhombohedral Graphite
Nano Letters, 2019Co-Authors: Aitor Garciaruiz, Sergey Slizovskiy, Marcin Muchakruczynski, Vladimir I FalkoAbstract:Rhombohedral Graphite features peculiar electronic properties, including persistence of low-energy surface bands of a topological nature. Here, we study the contribution of electron-hole excitations toward inelastic light scattering in thin films of Rhombohedral Graphite. We show that, in contrast to the featureless electron-hole contribution toward Raman spectrum of graphitic films with Bernal stacking, the inelastic light scattering accompanied by electron-hole excitations in crystals with Rhombohedral stacking produces distinct features in the Raman signal which can be used both to identify the stacking and to determine the number of layers in the film.
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films of Rhombohedral Graphite as two dimensional topological semimetals
arXiv: Mesoscale and Nanoscale Physics, 2019Co-Authors: Sergey Slizovskiy, Edward Mccann, Mikito Koshino, Vladimir I FalkoAbstract:Topologically non-trivial states characterized by Berry curvature appear in a number of materials ranging from spin-orbit-coupling driven topological insulators to graphene. In multivalley conductors, such as mono- and bilayer graphene, despite a zero total Chern number for the entire Brillouin zone, Berry curvature with different signs concentrated in different valleys can affect the observable material's transport characteristics. Here we consider thin films of Rhombohedral Graphite, which appear to retain truly two-dimensional properties up to tens of layers of thickness and host two-dimensional electron states with a large Berry curvature, accompanied by a giant intrinsic magnetic moment carried by electrons. The size of Berry curvature and magnetization in the vicinity of each valley can be controlled by electrostatic gating leading to a tuneable anomalous Hall effect and a peculiar structure of the two-dimensional Landau level spectrum.
Mingfa Lin - One of the best experts on this subject based on the ideXlab platform.
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evolution and dimensional crossover from the bulk subbands in abc stacked graphene to a three dimensional dirac cone structure in Rhombohedral Graphite
Physical Review B, 2016Co-Authors: Cheng Peng Chang, Mingfa LinAbstract:Rhombohedral Graphite behaves like a topological semimetal, possessing flat surface subbands while being semimetallic in the bulk. The bulk-surface correspondence arises from the ABC-stacking configuration of graphene layers. The bulk subbands in Rhombohedral Graphite can be interpreted as a three-dimensional Dirac cone structure, whose Dirac points form continuous lines spiraling in momentum space. In this paper, we study the evolution of gapped bulk subbands in ABC-stacked $N$-layer graphene with an increase of $N$, and their dimensional crossover to the three-dimensional Dirac cone structure in the bulk limit, where the bulk gap closes up at the Dirac-point spirals. To clarify the effect of coupling to the surface subbands, we use a nonperturbative effective Hamiltonian closed in the bulk subspace. As a consequence, the wavelength of the standing-wave function across the stack of layers depends on the in-plane Bloch momentum. In the bulk limit, the coupling vanishes and hence the wavelength is irrelevant to the surface.
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diagonalization of landau level spectra in Rhombohedral Graphite
Journal of the Physical Society of Japan, 2012Co-Authors: Yingyen Liao, Yuhuang Chiu, C P Chang, Mingfa LinAbstract:The Landau level (LL) spectra in Rhombohedral Graphite are calculated within the tight-binding model without any perturbation expansion. All significant interlayer atomic interactions are included, up to next-nearest-neighbor graphene layers. The magnetic Hamiltonian matrix is derived and manipulated in a band-like form for numerical efficiency. The results of this diagonalization scheme manifest the effects of lattice symmetry and interlayer interaction in the specific stacking configuration. Three-dimensional character associated with the mirror symmetry of the ABC-stacking configuration is exhibited in the LL spectra.
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low frequency electronic and optical properties of Rhombohedral Graphite
Physical Chemistry Chemical Physics, 2011Co-Authors: Chihwei Chiu, Mingfa Lin, Yuancheng Huang, Szu Chao Chen, Fenglin ShyuAbstract:Low-energy electronic and optical properties of ABC-stacked Graphite are respectively studied by the tight-binding model and gradient approximation. The band structures include linear and parabolic bands with and without degeneracy. They show strongly anisotropic dispersions. ABC-stacked Graphite is a semimetal due to the slight overlap near the Fermi level between the conduction and valence bands. The interlayer interactions change the energy dispersion, state degeneracy, and the positions of band-crossings and band-edge states. When the state energy is higher than the degenerate energy of the conduction band (E(2d)(c)) or lower than that of the valence bands (E(2d)(v)), a greater number of states might exist. The special band structures would be reflected in the density of states (DOS), the joint density of states (JDOS), and the absorption spectra (A(ω)). For example, the DOS exhibits a cave-like structure at ω = E(2d)(c) and E(2d)(v). Both a special jump in the JDOS and a turning point in the A(ω) occur at ω = E(2d)(c) - E(2d)(v). The DOS and A(ω) could be respectively verified by scanning tunneling spectroscopy and optical absorption spectroscopy.
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electronic properties of Rhombohedral Graphite
Computer Physics Communications, 2011Co-Authors: Jenhsien Wong, Mingfa LinAbstract:Abstract Electronic properties of ABC-stacked Graphite are studied by the first-principles method. There are linear and parabolic bands with strong anisotropic dispersions; both non-degenerate and degenerate bands are observed. The bandwidths of occupied π and σ bands are 8.41 eV and 16.65 eV, respectively. The low valence and conduction bands only have slight overlapping near the Fermi level, mainly owing to the interlayer atomic interactions. State degeneracy and energy dispersions are strongly affected by such interactions. The band-edge states, with the high density of states, are located near or at the high symmetry points. Some significant differences exist among ABC-, AB-, and AA-stacked Graphites in electronic properties.
Ching Hong Ho - One of the best experts on this subject based on the ideXlab platform.
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evolution and dimensional crossover from the bulk subbands in abc stacked graphene to a three dimensional dirac cone structure in Rhombohedral Graphite
Physical Review B, 2016Co-Authors: Ching Hong Ho, Cheng Peng ChangAbstract:The band structure of ABC-stacked N-layer graphene comprises topologically corresponding flat surface and gapped bulk subbands, as a consequence of the unique stacking configuration. In this paper, the bulk subbands are for the first times ever obtained for arbitrary N. A non-perturbative effective Hamiltonian closed in the bulk subspace is derived and used. The gapped bulk subbands are shown to evolve towards the zero energy with increasing N and in the infinite limit, they touch linearly along a circle. This outcome is a manifestation of the dimensional crossover to a three-dimensional Dirac cone structure known to exist in the bulk of Rhombohedral Graphite. The Dirac points, forming continuous nodal lines in a spiraling fashion, are projected onto the circle, within which the surface subbands are confined and flatten.
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Evolution and crossover from bulk subbands in ABC-stacked graphene to a three-dimensional Dirac cone structure in Rhombohedral Graphite
arXiv: Mesoscale and Nanoscale Physics, 2015Co-Authors: Ching Hong Ho, Cheng Peng ChangAbstract:The band structure of ABC-stacked $N$-layer graphene comprises topologically corresponding flat surface and gapped bulk subbands, as a result of the unique stacking configuration. In this paper, the bulk subbands are for the first times ever obtained for arbitrary $N$. A non-perturbative effective Hamiltonian closed in the bulk subspace is derived and used. The gapped bulk subbands are shown to evolve toward the zero energy with increasing $N$ and in the infinite limit, they touch linearly along a circle. This outcome is a manifestation of the dimensional crossover to a three-dimensional Dirac cone structure known to exist in the bulk of Rhombohedral Graphite. The Dirac points, forming continuous nodal lines in a spiraling fashion, are projected onto the circle, within which the flat surface subbands are confined.
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Optical magnetoplasmons in Rhombohedral Graphite with a three-dimensional Dirac cone structure
Journal of Physics: Condensed Matter, 2015Co-Authors: Ching Hong Ho, Cheng Peng ChangAbstract:Rhombohedral Graphite has a three-dimensional Dirac cone structure, differing only perturbatively from the bulk stack of independent graphene layers, so that the three-dimensional integer quantum Hall effect can be well exhibited in this system. In this paper, optical magnetoplasmons are obtained by using the random phase approximation. Such collective excitations do not exist in monolayer graphene but are shown to originate from Landau level mixing due to interlayer Coulomb interaction in the quantum Hall effect regime. The three-dimensional character of Rhombohedral Graphite is thus demonstrated. The results should be realized in response to a longitudinal external electric field or an incident infrared electromagnetic wave.
Sergey Slizovskiy - One of the best experts on this subject based on the ideXlab platform.
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electronic phase separation in multilayer Rhombohedral Graphite
Nature, 2020Co-Authors: Yanmeng Shi, Yaping Yang, Sergey Slizovskiy, S V Morozov, Seokkyun Son, Servet Ozdemir, Ciaran Mullan, Julien Barrier, Jun YinAbstract:Of the two stable forms of Graphite, hexagonal and Rhombohedral, the former is more common and has been studied extensively. The latter is less stable, which has so far precluded its detailed investigation, despite many theoretical predictions about the abundance of exotic interaction-induced physics1–6. Advances in van der Waals heterostructure technology7 have now allowed us to make high-quality Rhombohedral Graphite films up to 50 graphene layers thick and study their transport properties. Here we show that the bulk electronic states in such Rhombohedral Graphite are gapped8 and, at low temperatures, electron transport is dominated by surface states. Because of their proposed topological nature, the surface states are of sufficiently high quality to observe the quantum Hall effect, whereby Rhombohedral Graphite exhibits phase transitions between a gapless semimetallic phase and a gapped quantum spin Hall phase with giant Berry curvature. We find that an energy gap can also be opened in the surface states by breaking their inversion symmetry by applying a perpendicular electric field. Moreover, in Rhombohedral Graphite thinner than four nanometres, a gap is present even without an external electric field. This spontaneous gap opening shows pronounced hysteresis and other signatures characteristic of electronic phase separation, which we attribute to emergence of strongly correlated electronic surface states. High-quality Rhombohedral Graphite films are found to offer an alternative to twisted bilayer graphene as a platform for studying correlated physics in carbon materials.
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Films of Rhombohedral Graphite as two-dimensional topological semimetals
Communications Physics, 2019Co-Authors: Sergey Slizovskiy, Edward Mccann, Mikito Koshino, Vladimir I. Fal’koAbstract:Topologically non-trivial states appear in a number of materials ranging from spin-orbit-coupling driven topological insulators to graphene. In multivalley conductors, such as mono- and bilayer graphene, despite a zero total Chern number for the entire Brillouin zone, Berry curvature with different signs concentrated in different valleys can affect the material’s transport characteristics. Here we consider thin films of Rhombohedral Graphite, which appear to retain truly two-dimensional properties up to tens of layers of thickness and host two-dimensional electron states with a large Berry curvature, accompanied by a giant intrinsic magnetic moment carried by electrons. The size of Berry curvature and magnetization in the vicinity of each valley can be controlled by electrostatic gating leading to a tuneable anomalous Hall effect and a peculiar structure of the two-dimensional Landau level spectrum. The crystal symmetry of a material impacts on its electronic structure and can lead to a range of interesting non-trivial topological phases and properties. Here, the authors theoretically study thin films of Rhombohedral Graphite and investigate the Berry curvature induced anomalous transport properties.
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electronic phase separation in topological surface states of Rhombohedral Graphite
arXiv: Mesoscale and Nanoscale Physics, 2019Co-Authors: Yanmeng Shi, Yaping Yang, Sergey Slizovskiy, S V Morozov, Seokkyun Son, Servet Ozdemir, Ciaran Mullan, Julien Barrier, Jun Yin, Alexei I BerdyuginAbstract:Of the two stable forms of Graphite, hexagonal (HG) and Rhombohedral (RG), the former is more common and has been studied extensively. RG is less stable, which so far precluded its detailed investigation, despite many theoretical predictions about the abundance of exotic interaction-induced physics. Advances in van der Waals heterostructure technology have now allowed us to make high-quality RG films up to 50 graphene layers thick and study their transport properties. We find that the bulk electronic states in such RG are gapped and, at low temperatures, electron transport is dominated by surface states. Because of topological protection, the surface states are robust and of high quality, allowing the observation of the quantum Hall effect, where RG exhibits phase transitions between gapless semimetallic phase and gapped quantum spin Hall phase with giant Berry curvature. An energy gap can also be opened in the surface states by breaking their inversion symmetry via applying a perpendicular electric field. Moreover, in RG films thinner than 4 nm, a gap is present even without an external electric field. This spontaneous gap opening shows pronounced hysteresis and other signatures characteristic of electronic phase separation, which we attribute to emergence of strongly-correlated electronic surface states.
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spectroscopic signatures of electronic excitations in raman scattering in thin films of Rhombohedral Graphite
Nano Letters, 2019Co-Authors: Aitor Garciaruiz, Sergey Slizovskiy, Marcin Muchakruczynski, Vladimir I FalkoAbstract:Rhombohedral Graphite features peculiar electronic properties, including persistence of low-energy surface bands of a topological nature. Here, we study the contribution of electron-hole excitations toward inelastic light scattering in thin films of Rhombohedral Graphite. We show that, in contrast to the featureless electron-hole contribution toward Raman spectrum of graphitic films with Bernal stacking, the inelastic light scattering accompanied by electron-hole excitations in crystals with Rhombohedral stacking produces distinct features in the Raman signal which can be used both to identify the stacking and to determine the number of layers in the film.
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films of Rhombohedral Graphite as two dimensional topological semimetals
arXiv: Mesoscale and Nanoscale Physics, 2019Co-Authors: Sergey Slizovskiy, Edward Mccann, Mikito Koshino, Vladimir I FalkoAbstract:Topologically non-trivial states characterized by Berry curvature appear in a number of materials ranging from spin-orbit-coupling driven topological insulators to graphene. In multivalley conductors, such as mono- and bilayer graphene, despite a zero total Chern number for the entire Brillouin zone, Berry curvature with different signs concentrated in different valleys can affect the observable material's transport characteristics. Here we consider thin films of Rhombohedral Graphite, which appear to retain truly two-dimensional properties up to tens of layers of thickness and host two-dimensional electron states with a large Berry curvature, accompanied by a giant intrinsic magnetic moment carried by electrons. The size of Berry curvature and magnetization in the vicinity of each valley can be controlled by electrostatic gating leading to a tuneable anomalous Hall effect and a peculiar structure of the two-dimensional Landau level spectrum.