The effect of spin-orbit interaction on optical conductivity in graphene.
TL;DR: Key findings are: level splitting at various crystal symmetry points caused by true spin as well as pseudospin of the electrons gives rise to a resonant current response, and under heavy doping, the spin-orbit interaction leads to a re-entrance of finite conductivity at very low frequency.
Abstract: We present a systematic investigation of the effect of spin-orbit interaction on optical conductivity in monolayer graphene. Our key findings are: (i) level splitting at various crystal symmetry points caused by true spin as well as pseudospin of the electrons gives rise to a resonant current response; (ii) under heavy doping, the spin-orbit interaction leads to a re-entrance of finite conductivity at very low frequency which was strictly forbidden in the absence of spin-orbit coupling; (iii) deformation of band structure and the topological properties of trigonal warping are analytically identified in a low-energy conical-like approximation.
Citations
More filters
TL;DR: In this paper, the ultrafast relaxation and recombination dynamics of photogenerated electrons and holes in epitaxial graphene were studied using optical-pump Terahertz-probe spectroscopy.
Abstract: The ultrafast relaxation and recombination dynamics of photogenerated electrons and holes in epitaxial graphene are studied using optical-pump Terahertz-probe spectroscopy. The conductivity in graphene at Terahertz frequencies depends on the carrier concentration as well as the carrier distribution in energy. Time-resolved studies of the conductivity can therefore be used to probe the dynamics associated with carrier intraband relaxation and interband recombination. We report the electron-hole recombination times in epitaxial graphene for the first time. Our results show that carrier cooling occurs on sub-picosecond time scales and that interband recombination times are carrier density dependent.
508 citations
Journal Article•
TL;DR: The strong and layer-dependent optical transitions of graphene and the tunability by simple electrical gating hold promise for new applications in infrared optics and optoelectronics.
Abstract: Two-dimensional graphene monolayers and bilayers exhibit fascinating electrical transport behaviors. Using infrared spectroscopy, we find that they also have strong interband transitions and that their optical transitions can be substantially modified through electrical gating, much like electrical transport in field-effect transistors. This gate dependence of interband transitions adds a valuable dimension for optically probing graphene band structure. For a graphene monolayer, it yields directly the linear band dispersion of Dirac fermions, whereas in a bilayer, it reveals a dominating van Hove singularity arising from interlayer coupling. The strong and layer-dependent optical transitions of graphene and the tunability by simple electrical gating hold promise for new applications in infrared optics and optoelectronics.
146 citations
Journal Article•
Abstract: Even though graphene is a low-energy system consisting of a two-dimensional honeycomb lattice of carbon atoms, its quasiparticle excitations are fully described by the (2+1)-dimensional relativistic Dirac equation. In this paper we show that, while the spin-orbit interaction in graphene is of the order of 4 meV, it opens up a gap of the order of 10(-3) meV at the Dirac points. We present a first-principles calculation of the spin-orbit gap, and explain the behavior in terms of a simple tight-binding model. Our result also shows that the recently predicted quantum spin Hall effect in graphene can occur only at unrealistically low temperature.
41 citations
TL;DR: In this paper, the electronic contribution to the nonlinear optical response of the $\ensuremath{\alpha}text{-}}{T}_{3}$ model is studied.
Abstract: We study the electronic contribution to the nonlinear optical response of the $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ model. This model is an interpolation between a graphene $(\ensuremath{\alpha}=0)$ and dice $(\ensuremath{\alpha}=1)$ lattice. Using a second-quantized formalism, we calculate the first- and third-order responses for a range of $\ensuremath{\alpha}$ and chemical potential values as well as considering a band gap in the first-order case. Conductivity quantization is observed for the first-order, while higher-order harmonic generation is observed in the third-order response with the chemical potential determining which applied field frequencies both quantization and harmonic generation occur at. We observe a range of experimentally accessible critical fields between ${10}^{2}--{10}^{6}$ V/m with dynamics depending on $\ensuremath{\alpha},\ensuremath{\mu}$, and the applied field frequency. Our results suggest an $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$-like lattice could be an ideal candidate for use in terahertz devices.
23 citations
TL;DR: In this article, the linear and nonlinear optical response can be applied to probe the underlying symmetry of gapped and proximitized graphene, and the spin-orbit sublattice symmetry is clearly revealed by the optical spectra.
Abstract: The properties of graphene can be significantly modified by interaction with a commensurate substrate. Via proximity effects, both band gaps and substantial spin-orbit coupling can be induced, opening a route to novel applications. In this work, we ask whether the linear and nonlinear optical response can be applied to probe the underlying symmetry of gapped and proximitized graphene. Answering in the affirmative, we show that, in particular, optical second-harmonic generation is a highly sensitive tool for characterization. Importantly, the spin-orbit sublattice symmetry is clearly revealed by the optical spectra. In addition, the topological phase of the materials is revealed via linear and nonlinear spin-optical effects.
7 citations
References
More filters
TL;DR: This study reports an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.
Abstract: Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.
18,958 citations
TL;DR: In this paper, an experimental investigation of magneto-transport in a high-mobility single layer of Graphene is presented, where an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene is observed.
Abstract: When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality1,2. Indeed, a distinctive half-integer quantum Hall effect has been predicted3,4,5 theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure6,7. Recent advances in micromechanical extraction and fabrication techniques for graphite structures8,9,10,11,12 now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
11,122 citations
Journal Article•
TL;DR: An experimental investigation of magneto-transport in a high-mobility single layer of graphene observes an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene.
Abstract: When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect has been predicted theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure. Recent advances in micromechanical extraction and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
10,112 citations
TL;DR: It is shown that the opacity of suspended graphene is defined solely by the fine structure constant, a = e2/hc � 1/137 (where c is the speed of light), the parameter that describes coupling between light and relativistic electrons and that is traditionally associated with quantum electrodynamics rather than materials science.
Abstract: There are few phenomena in condensed matter physics that are defined only by the fundamental constants and do not depend on material parameters. Examples are the resistivity quantum, h/e2 (h is Planck's constant and e the electron charge), that appears in a variety of transport experiments and the magnetic flux quantum, h/e, playing an important role in the physics of superconductivity. By and large, sophisticated facilities and special measurement conditions are required to observe any of these phenomena. We show that the opacity of suspended graphene is defined solely by the fine structure constant, a = e2/hc feminine 1/137 (where c is the speed of light), the parameter that describes coupling between light and relativistic electrons and that is traditionally associated with quantum electrodynamics rather than materials science. Despite being only one atom thick, graphene is found to absorb a significant (pa = 2.3%) fraction of incident white light, a consequence of graphene's unique electronic structure.
7,952 citations
TL;DR: In this article, it was shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor and a general formula for γ(C) was derived in terms of the spectrum and eigen states of the Hamiltonian over a surface spanning C.
Abstract: A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.
7,425 citations