arXiv subjects

T. Stauber

Publications and source records attributed to T. Stauber.

At least 37 records · Page 2Linked to original sources

arXiv2018

Linear response of twisted bilayer graphene: continuum vs. tight-binding models

We present a linear response calculation for twisted bilayer graphene. The calculation is performed for both the continuum and tight-binding models, with the aim of assessing the validity of the former. All qualitatively important features previously reported by us [T. Stauber et al. Phys. Rev. Lett. 120, 046801 (2018)] for the Drude matrix in the continuum model are also present in the tight-binding calculation, with increasing quantitative agreement for decreasing twist angle. These features include the chiral longitudinal magnetic moment associated with plasmonic modes, and the anomalous counterflow around the neutrality point, better interpreted as a paramagnetic response. We have addressed the differences between Drude and equilibrium response, and shown that orbital paramagnetism is the equilibrium response to a parallel magnetic field over a substantial doping region around the neutrality point. Chirality also makes the equilibrium response to exhibit a non trivial current structure associated with the non-vertical character of interlayer bonds in the tight-binding calculation.

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arXiv2018

Plasmonics in topological insulators: Spin-charge separation, the influence of the inversion layer, and phonon-plasmon coupling

We demonstrate via three examples that topological insulators (TI) offer a new platform for plasmonics. First, we show that the collective excitations of a thin slab of a TI display spin-charge separation. This gives rise to purely charge-like optical and purely spin-like acoustic plasmons, respectively. Second, we argue that the depletion layer mixes Dirac and Schrödinger electrons which can lead to novel features such as high modulation depths and interband plasmons. The analysis is based on an extension of the usual formula for optical plasmons that depends on the slab width and on the dielectric constant of the TI. Third, we discuss the coupling of the TI surface phonons to the plasmons and find strong hybridisation especially for samples with large slab widths.

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arXiv2018

Chiral response of twisted bilayer graphene

We present an effective (minimal) theory for chiral two-dimensional materials. These materials possess an electro-magnetic coupling without exhibiting a topological gap. As an example, we study the response of doped twisted bilayers, unveiling unusual phenomena in the zero frequency limit. An in-plane magnetic field induces a huge paramagnetic response at the neutrality point and, upon doping, also gives rise to a substantial longitudinal Hall response. The system also accommodates nontrivial longitudinal plasmonic modes which are associated with a longitudinal magnetic moment, thus endowing them with a chiral character. Finally, we note that the optical activity can be considerably enhanced upon doping.

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arXiv2017

Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response

We have developed a Hartree-Fock theory for electrons on a honeycomb lattice aiming to solve a long-standing problem of the Fermi velocity renormalization in graphene. Our model employs no fitting parameters (like an unknown band cutoff) but relies on a topological invariant (crystal structure function) that makes the Hartree-Fock sublattice spinor independent of the electron-electron interaction. Agreement with the experimental data is obtained assuming static self-screening including local field effects. As an application of the model, we derive an explicit expression for the optical conductivity and discuss the renormalization of the Drude weight. The optical conductivity is also obtained via precise quantum Monte Carlo calculations which compares well to our mean-field approach.

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arXiv2016

Quasi-flat plasmonic bands in twisted bilayer graphene

The charge susceptibility of twisted bilayer graphene is investigated in the Dirac cone, respectively random-phase approximation. For small enough twist angles $θ\lesssim 2^\circ$ we find weakly Landau damped interband plasmons, i.~e., collective excitonic modes which exist in the undoped material, with an almost constant energy dispersion. In this regime, the loss function can be described as a Fano resonance and we argue that these excitations arise from the interaction of quasi-localised states with the incident light field. These predictions can be tested by nano-infrared imaging and possible applications include a "perfect" lens without the need of left-handed materials.

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arXiv2015

Tight-binding approach to penta-graphene

We introduce an effective tight-binding model to discuss penta-graphene and present an analytical solution. This model only involves the $π$-orbitals of the sp$^2$-hybridized carbon atoms and reproduces the two highest valence bands. By introducing energy-dependent hopping elements, originating from the elimination of the sp$^3$-hybridized carbon atoms, also the two lowest conduction bands can be well approximated - but only after the inclusion of a Hubbard onsite interaction as well as of assisted hopping terms. The eigenfunctions can be approximated analytically for the effective model without energy-dependent hopping elements and the optical absorption is discussed. We find large isotropic absorption of up to 24\% for transitions at the $Γ$-point, but the general absorption will show a strongly anisotropic behaviour depending on the linear polarization of the incident light.

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arXiv2015

Mass-profile quantum dots in graphene

We analyze the bound-state spectra of mass-profile quantum dots in graphene, a system at current experimental reach. Homogeneous perpendicular magnetic fields are also considered which result in breaking the valley degeneracy. The spectra show rich features, arising from the chiral band structure of graphene and its Landau levels and we identify three different regimes depending on the ratio between the radius of the dot and the magnetic length. We further carry out a comparison with potential-well quantum dots discussed in [Recher et al, Phys. Rev. B 79, 085407 (2009)] and conclude that mass confinement may offer significant advantages for optical applications in the THz and infrared regime. Also due to experimental advances, we additionally analyze the band structure of a linear chain of mass-profile quantum dots, where overlap-assisted hopping processes play a main role for closely packed arrays. Here, the inclusion of Coulomb interactions shows that Frenkel excitons can be hosted by the system for certain values of the lattice constant. A Bose-Hubbard model can be mimicked under such a choice of the distance between the dots.

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arXiv2015

Universal absorption of two-dimensional systems

We discuss the optical conductivity of several non-interacting two-dimensional (2D) semiconducting systems focusing on gapped Dirac and Schrödinger fermions as well as on a system mixing these two types. Close to the band-gap, we can define a universal optical conductivity quantum of $σ_0=\frac{1}{16}\frac{e^2}{\hbar}$ for the pure systems. The effective optical conductivity then depends on the degeneracy factors $g_s$ (spin) and $g_v$ (valley) and on the curvature around the band-gap $ν$, i.e., it generally reads $σ=g_sg_vνσ_0$. For a system composed of both types of carriers, the optical conductivity becomes non-universal.

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arXiv2014

Towards scalable nano-engineering of graphene

By merging bottom-up and top-down strategies we tailor graphene's electronic properties within nanometer accuracy, which opens up the possibility to design optical and plasmonic circuitries at will. In a first step, graphene electronic properties are macroscopically modified exploiting the periodic potential generated by the self assembly of metal cluster superlattices on a graphene/Ir(111) surface. We then demonstrate that individual metal clusters can be selectively removed by a STM tip with perfect reproducibility and that the structures so created are stable even at room temperature. This enables one to nanopattern circuits down to the 2.5 nm only limited by the periodicity of the Moiré-pattern, i.e., by the distance between neighbouring clusters, and different electronic and optical properties should prevail in the covered and uncovered regions. The method can be carried out on micro-meter-sized regions with clusters of different materials permitting to tune the strength of the periodic potential.

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arXiv2014

Plasmonics in Dirac systems: from graphene to topological insulators

The recent developments in the emerging field of plasmonics in graphene and other Dirac systems are reviewed and a comprehensive introduction to the standard models and techniques is given. In particular, we discuss intrinsic plasmon excitations of single and bilayer graphene via hydrodynamic equations and the random phase approximation, but also comment on double and multilayer structures. Additionally, we address Dirac systems in the retardation limit and also with large spin-orbit coupling including topological insulators. Finally, we summarize basic properties of the charge, current and photon linear response functions in an appendix.

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arXiv2014

Extraordinary absorption of decorated undoped graphene

We theoretically study absorption by an undoped graphene layer decorated with arrays of small particles. We discuss periodic and random arrays within a common formalism, which predicts a maximum absorption of $50\%$ for suspended graphene in both cases. The limits of weak and strong scatterers are investigated and an unusual dependence on particle-graphene separation is found and explained in terms of the effective number of contributing evanescent diffraction orders of the array. Our results can be important to boost absorption by single layer graphene due to its simple setup with potential applications to light harvesting and photodetection based on energy (Förster) rather than charge transfer.

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arXiv2013

Spin-charge separation of plasmonic excitations in thin topological insulators

We discuss plasmonic excitations in a thin slab of a topological insulators. In the limit of no hybridization of the surface states and same electronic density of the two layers, the electrostatic coupling between the top and bottom layers leads to optical and acoustic plasmons which are purely charge and spin collective oscillations. We then argue that a recent experiment on the plasmonic excitations of Bi2Se3 [Di Pietro et al, Nat. Nanotechnol. 8, 556 (2013)] must be explained by including the charge response of the two-dimensional electron gas of the depletion layer underneath the two surfaces. We also present an analytic formula to fit their data.

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arXiv2013

Transverse current current response of graphene at finite temperature, plasmons and absorption

We calculate the linear transverse current current response function for graphene at finite temperature and chemical potential. Within the Random Phase Approximation, we then discuss general aspects of transverse plasmons beyond the local response such as their dependence on temperature and on the surrounding dielectric media. We find, e.g., maximal confinement of this mode for a homogeneous dielectric media with refractive index $n\simeq 40$. Confinement can further be enhanced by placing the graphene sheet inside an optical cavity, but there exists a critical width below which no transverse mode can be sustained. For zero doping and finite temperature, there are no well-defined transverse plasmonic excitations in contrast to the longitudinal channel. We also discuss the absorption of electromagnetic radiation in single and double-layer systems for $s$ and $p$ polarizations and point out that the theoretical limit of 50% is reached for $s$-polarized light with incident angle of $θ\approx89^o$.

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arXiv2013

Enhancement of graphene visibility on transparent substrates by refractive index optimization

Optical reflection microscopy is one of the main imaging tools to visualize graphene microstructures. Here is reported a novel method that employs refractive index optimization in an optical reflection microscope, which greatly improves the visibility of graphene flakes. To this end, an immersion liquid with a refractive index that is close to that of the glass support is used in-between the microscope lens and the support improving the contrast and resolution of the sample image. Results show that the contrast of single and few layer graphene crystals and structures can be enhanced by a factor of 4 compared to values commonly achieved with transparent substrates using optical reflection microscopy lacking refractive index optimization.

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arXiv2012

Plasmons in layered structures including graphene

We investigate the optical properties of layered structures with graphene at the interface for arbitrary linear polarization at finite temperature including full retardation by working in the Weyl gauge. As a special case, we obtain the full response and the related dielectric function of a layered structure with two interfaces. We apply our results to discuss the longitudinal plasmon spectrum of several single and double layer devices such as systems with finite and zero electronic densities. We further show that a nonhomogeneous dielectric background can shift the relative weight of the in-phase and out-of-phase mode and discuss how the plasmonic mode of the upper layer can be tuned into an acoustic mode with specific sound velocity.

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arXiv2012

Graphene plasmons and retardation: strong light-matter coupling

We study the retardation regime of doped graphene plasmons, given by the nominal crossing of the unretarded plasmon and light-cone. In addition to modifications in the plasmon dispersion relation, retardation implies strong coupling between propagating light and matter, even for homogeneous graphene, which opens up the possibility of efficient plasmonics in simple graphene devices. We exemplify this enhancement in a double-layer configuration that exhibits {\em perfect} (if lossless) light transmissions across a classically forbidden region, providing a simpler analog of the corresponding phenomenon in perforated metal sheets. We also show that (broad) Fabry-Pérot resonances present without graphene turn into sharply peaked, quasi-discrete modes in the presence of graphene where graphene's response function is given by the typical Fano lineshape.

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arXiv2012

Efficient graphene-based photodetector with two cavities

We present an efficient graphene-based photodetector with two Fabri-Pérot cavities. It is shown that the absorption can reach almost 100% around a given frequency, which is determined by the two-cavity lengths. It is also shown that hysteresis in the absorbance is possible, with the transmittance amplitude of the mirrors working as an external driving field. The role of non-linear contributions to the optical susceptibility of graphene is discussed.

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arXiv2012

Plasmons and near-field amplification in double-layer graphene

We study the optical properties of double-layer graphene for linearly polarized evanescent modes and discuss the in-phase and out-of-phase plasmon modes for both, longitudinal and transverse polarization. We find a energy for which reflection is zero, leading to exponentially amplified transmitted modes similar to what happens in left-handed materials. For layers with equal densities $n=10^{12}$cm$^{-2}$, we find a typical layer separation of $d\approx500μ$m to detect this amplification for transverse polarization which may serve as an indirect observation of transverse plasmons. When the two graphene layers lie on different chemical potentials, the exponential amplification either follows the in-phase or out-of-phase plasmon mode depending on the order of the low- and high-density layer. This opens up the possibility of a tunable near-field amplifier or switch.

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