Hydrodynamics and plasmonics in two-dimensional materials

This Thesis is devoted to the study of two different aspects of electron behavior in two-dimensional materials, namely hydrodynamic electron transport and plasmon propagation. The Thesis is structured as follows. In Chapter 1 the main experimental facts that motivated our work on electron hydrodynamics and plasmonics are presented and critically discussed. Chapter 2 contains our main results on hydrodynamic electron transport. After deriving the basic equations of the electron hydrodynamics and discussing their limit of applicability, we use them to quantify the impact of two different transport coffcients, the shear and Hall viscosities of the electron liquid, on steady-state transport. Our results are used to propose experimental protocols that allow an experimental determination of these transport coeffcients. Chapter 3 deals with plasmon propagation through inhomogeneous media. We consider three dfferent geometries: an interface between two dfferent materials, a one dimensional perturbation, and a zero dimensional perturbation in an otherwise uniform electron system. We calculate scattering observables for plasmons in these geometries. For the interface geometry we also investigated the presence of plasmonic bound states localized near the interface, while for the second and third geometries we quantify the impact of non-local fects. Chapter 4 presents a theory of chiral plasmons in materials with a non-trivial Berry curvature in the electronic band structure. We firstly employ the results of Chapter 3 to obtain a semi-classical theory of Chiral Berry Plasmons (CBPs) at a generic interface between two materials having different Berry uxes across the Fermi surface. We then test the impact of different types of screened electron-electron interaction, and of a finite damping rate on the dispersion and lifetime of CBPs

Edge modes and Fabry-Perot Plasmonic Resonances in anomalous-Hall Thin Films

We study plasmon propagation on a metallic two-dimensional surface partially coated with a thin film of anomalous-Hall material. The resulting three regions, separated by two sharp interfaces, are characterised by different Hall conductivities but identical normal conductivities. A single bound mode is found, which can localise to either interface and has an asymmetric potential profile across the region. For propagating modes, we calculate the reflection and transmission coefficients through the magnetic region. We find Airy transmission patterns with sharp maxima and minima as a function of the plasmon incidence angle. The system therefore behaves as a high-quality filter.Comment: 11 pages, 7 figures. Upon revision, the basic content and analysis of the paper is unchanged but the emphasis on topological insulators has been removed. The title and abstract has been changed to reflect this. Damping of the bound mode has been include

Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids

In a fluid subject to a magnetic field the viscous stress tensor has a dissipationless antisymmetric component controlled by the so-called Hall viscosity. We here propose an all-electrical scheme that allows a determination of the Hall viscosity of a two-dimensional electron liquid in a solid-state device.Comment: 12 pages, 4 figure

Non-local transport and the hydrodynamic shear viscosity in graphene

Motivated by recent experimental progress in preparing encapsulated graphene sheets with ultra-high mobilities up to room temperature, we present a theoretical study of dc transport in doped graphene in the hydrodynamic regime. By using the continuity and Navier-Stokes equations, we demonstrate analytically that measurements of non-local resistances in multi-terminal Hall bar devices can be used to extract the hydrodynamic shear viscosity of the two-dimensional (2D) electron liquid in graphene. We also discuss how to probe the viscosity-dominated hydrodynamic transport regime by scanning probe potentiometry and magnetometry. Our approach enables measurements of the viscosity of any 2D electron liquid in the hydrodynamic transport regime.Comment: 12 pages, 4 multi-panel figure

Electron hydrodynamics dilemma: whirlpools or no whirlpools

In highly viscous electron systems such as, for example, high quality graphene above liquid nitrogen temperature, a linear response to applied electric current becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena including negative nonlocal resistance and current whirlpools. It has also been shown that, although both effects originate from high electron viscosity, a negative voltage drop does not principally require current backflow. In this work, we study the role of geometry on viscous flow and show that confinement effects and relative positions of injector and collector contacts play a pivotal role in the occurrence of whirlpools. Certain geometries may exhibit backflow at arbitrarily small values of the electron viscosity, whereas others require a specific threshold value for whirlpools to emerge

Optical and plasmonic properties of twisted bilayer graphene: Impact of interlayer tunneling asymmetry and ground-state charge inhomogeneity

We present a theoretical study of the local optical conductivity, plasmon spectra, and thermoelectric properties of twisted bilayer graphene (TBG) at different filling factors and twist angles $\theta$. Our calculations are based on the electronic band structures obtained from a continuum model that has two tunable parameters, $u_0$ and $u_1$, which parametrize the intra-sublattice inter-layer and inter-sublattice inter-layer tunneling rate, respectively. In this Article we focus on two key aspects: i) we study the dependence of our results on the value of $u_0$, exploring the whole range $0\leq u_0\leq u_1$; ii) we take into account effects arising from the intrinsic charge density inhomogeneity present in TBG, by calculating the band structures within the self-consistent Hartree approximation. At zero filling factor, i.e. at the charge neutrality point, the optical conductivity is quite sensitive to the value of $u_0$ and twist angle, whereas the charge inhomogeneity brings about only modest corrections. On the other hand, away from zero filling, static screening dominates and the optical conductivity is appreciably affected by the charge inhomogeneity, the largest effects being seen on the intra-band contribution to it. These findings are also reflected by the plasmonic spectra. We compare our results with existing ones in the literature, where effects i) and ii) above have not been studied systematically. As natural byproducts of our calculations, we obtain the Drude weight and Seebeck coefficient. The former displays an enhanced particle-hole asymmetry stemming from the inhomogeneous ground-state charge distribution. The latter is shown to display a broad sign-changing feature even at low temperatures ($\approx 5~{\rm K}$) due to the reduced slope of the bands, as compared to those of single-layer graphene.Comment: 28 pages, 16 figures, 6 appendice

GW Theory of Magic-Angle Twisted Bilayer Graphene

Strong correlations occur in magic-angle twisted bilayer graphene (MATBG) when the octet of flat moir\'e minibands centered on charge neutrality (CN) is partially occupied. The octet consists of a single valence band and a single conduction band for each of four degenerate spin-valley flavors. Motivated by the importance of Hartree electrostatic interactions in determining the filling-factor dependent band structure, we use a time-dependent Hartree (GW) approximation to gain insight into electronic correlations. We find that the electronic compressibility is dominated by Hartree interactions, that paramagnetic states are stable over a range of density near CN, and that the dependence of energy on flavor polarization is strongly overestimated by mean-field theory

Quantitative scattering theory of near-field response for 1D polaritonic structures

Scattering-type scanning near-field optical microscopy is a powerful imaging technique for studying materials beyond the diffraction limit. However, interpreting near-field measurements poses challenges in mapping the response of polaritonic structures to meaningful physical properties. To address this, we propose a theory based on the transfer matrix method to simulate the near-field response of 1D polaritonic structures. Our approach provides a computationally efficient and accurate analytical theory, relating the near-field response to well-defined physical properties. This work enhances the understanding of near-field images and complex polaritonic phenomena. Finally, this scattering theory can extend to other systems like atoms or nanoparticles near a waveguide

Electrical plasmon detection in graphene waveguides

We present a simple device architecture that allows all-electrical detection of plasmons in a graphene waveguide. The key principle of our electrical plasmon detection scheme is the non-linear nature of the hydrodynamic equations of motion that describe transport in graphene at room temperature and in a wide range of carrier densities. These non-linearities yield a dc voltage in response to the oscillating field of a propagating plasmon. For illustrative purposes, we calculate the dc voltage arising from the propagation of the lowest-energy modes in a fully analytical fashion. Our device architecture for all-electrical plasmon detection paves the way for the integration of graphene plasmonic waveguides in electronic circuits.Comment: 9 pages, 3 figure