Graphene hosts a unique electron system in which electron-phonon scattering is extremely weak but electron-electron collisions are sufficiently frequent to provide local equilibrium above liquid nitrogen temperature. Under these conditions, electrons can behave as a viscous liquid and exhibit hydrodynamic phenomena similar to classical liquids. Here we report strong evidence for this long-sought transport regime. In particular, doped graphene exhibits an anomalous (negative) voltage drop near current injection contacts, which is attributed to the formation of submicrometer-size whirlpools in the electron flow. The viscosity of graphene's electron liquid is found to be ≈0.1 m 2 s -1, an order of magnitude larger than that of honey, in agreement with many-body theory. Our work shows a possibility to study electron hydrodynamics using high quality graphene.Collective behavior of many-particle systems that undergo frequent inter-particle collisions has been studied for more than two centuries and is routinely described by the theory of hydrodynamics (1,2). The theory relies only on the conservation of mass, momentum and energy and is highly successful in explaining the response of classical gases and liquids to external perturbations varying slowly in space and time. More recently, it has been shown that hydrodynamics can also be applied to strongly interacting quantum systems including ultra-hot nuclear matter and ultra-cold atomic Fermi gases in the unitarity limit (3-6). In principle, the hydrodynamic approach can also be employed to describe many-electron phenomena in condensed matter physics (7-13). The theory becomes applicable if electron-electron scattering provides the shortest spatial scale in the problem such that ℓ ee ≪ , ℓ where ℓ ee is the electron-electron scattering length, the characteristic sample size, ℓ ≡ F the mean free path, F the Fermi velocity, and the mean free time with respect to momentum-non-conserving collisions such as those involving impurities, phonons, etc. The above 2 inequalities are difficult to meet experimentally. Indeed, at low temperatures ( ) ℓ ee varies approximately as ∝ −2 reaching a micrometer scale at liquid-helium (14), which necessitates the use of ultra-clean systems to satisfy ℓ ee ≪ ℓ. At higher , electron-phonon scattering rapidly reduces ℓ. However, for two-dimensional (2D) systems with dominating acoustic phonon scattering, ℓ decays only as ∝ −1 , slower than ℓ ee , which should in principle allow the hydrodynamic description over a certain temperature range, until other phonon-mediated processes become important. So far, there has been little evidence for hydrodynamic electron transport. An exception is an early work on 2D electron gases in ballistic devices (ℓ ~ ) made from GaAlAs heterostructures (15). They exhibited nonmonotonic changes in differential resistance as a function of a large applied current that was used to increase the electron temperature (making ℓ ee short) while the lattice temperature remained low (allowing long ℓ).The nonmonotonic behavior ...

Motivated by recent experimental progress in preparing encapsulated graphene sheets with ultrahigh 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.

Materials subjected to a magnetic field exhibit the Hall effect, a phenomenon studied and understood in fine detail. Here we report a qualitative breach of this classical behavior in electron systems with high viscosity. The viscous fluid in graphene is found to respond to non-quantizing magnetic fields by producing an electric field opposite to that generated by the classical Hall effect. The viscous contribution is large and identified by studying local voltages that arise in the vicinity of current-injecting contacts. We analyze the anomaly over a wide range of temperatures and carrier densities and extract the Hall viscosity, a dissipationless transport coefficient that was long identified theoretically but remained elusive in experiment. Good agreement with theory suggests further opportunities for studying electron magnetohydrodynamics.

In highly viscous electron systems such as 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.

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.arXiv:1706.08363v2 [cond-mat.mes-hall]

The field of 2D materials-based nanophotonics has been growing at a rapid pace, triggered by the ability to design nanophotonic systems with in-situ control 1 , unprecedented degrees of freedom, and to build material heterostructures from bottom up with atomic precision 2 . A wide palette of polaritonic classes [3][4][5][6] have been identified, comprising ultra-confined optical fields, even approaching characteristic length-scales of a single atom 7 . These advances have been a real boost for the emerging field of quantum nanophotonics, where the quantum mechanical nature of the electrons and/or polaritons and their interactions become relevant. Examples include, quantum nonlocal effects [8][9][10][11] , ultrastrong light-matter interactions [11][12][13][14][15][16] , Cherenkov radiation 13,17,18 , access to forbidden transitions 11 , hydrodynamic effects [19][20][21] , single-plasmon nonlinearities 22,23 , polaritonic quantization 24 , topological effects etc. 3,4 . In addition to these intrinsic quantum nanophotonic phenomena, the 2D material system can also be used as a sensitive probe for the quantum properties of the material that carries the nanophotonics modes, or quantum materials in its vicinity. Here, polaritons act as a probe for otherwise invisible excitations, e.g. in superconductors 25 , or as a new tool to monitor the existence of Berry curvature in topological materials and superlattice effects in twisted 2D materials.In this article, we present an overview of the emergent field of 2D-material quantum nanophotonics, and provide a future perspective on the prospects of both fundamental emergent phenomena and emergent quantum technologies, such as quantum sensing, single-photon sources and quantum emitters manipulation. We address four main implications (cf. Figure 1): i) quantum sensing, featuring polaritons to probe superconductivity and explore new electronic transport hydrodynamic behaviours, ii) quantum technologies harnessing single-photon generation, manipulation and detection using 2D materials, iii) polariton engineering with quantum materials enabled by twist angle and stacking order control in van der Waals heterostructures and iv) extreme light-matter interactions enabled by the strong confinement of light at atomic level by 2D materials, which provide new tools to manipulate light fields at the nano-scale (e.g., quantum chemistry 26 , nonlocal effects, high Purcell enhancement).

Modulating the amplitude and phase of light is at the heart of many applications such as wavefront shaping, 1 transformation optics, 2,3 phased arrays, 4 modulators 5 and sensors. 6 Performing this task with high efficiency and small footprint is a formidable challenge. 7,8 Metasurfaces 5,9 and plasmonics 10 are promising , but metals exhibit weak electro-optic effects. Two-dimensional materials, such as graphene, have shown great performance as modulators with small drive voltages. 11,12 Here we show a graphene plasmonic phase modulator which is capable of tuning the phase between 0 and 2π in situ. With a footprint of 350 nm it is more than 30 times smaller than the 10.6 µm free space wavelength. The modulation is achieved by spatially controlling the plasmon phase velocity in a device where the spatial carrier density profile is tunable. We provide a scattering theory for plasmons propagating through spatial density profiles. This work constitutes a first step towards twodimensional transformation optics 3 for ultra-compact modulators 7 and biosensing. 13 Graphene plasmons are a versatile tool for integrated photonics and nano-optoelectronics as they provide extreme sub-wavelength confinement of light 14-16 while still offering a long lifetime approaching 1 ps. 16 The graphene plasmon phase velocity (and thus wavelength) is in situ tunable, and can be varied spatially, making it a unique platform for for transformation optics in two dimensions. 3,17 The full spatial and dynamic control of the plasmon velocity profile makes completely new device concepts possible. This includes on-chip interferometers and tunable metamaterials such as phased arrays for a full dynamical beam manipulation. 4 This full control has thus far remained a great challenge and the plasmon propagation was mainly controlled by physical features in the graphene. [18][19][20] Here, we manipulate for the first time the spatial profile of the plasmon phase velocity actively employing local metal gates, achieving in situ control of the plasmon wavelength, as sketched in Fig. 1. A plasmon (launched by scattering light on a gold edge) that propagates trough the tunable spatial carrier density profile picks up a phase, that is transferred to the photon after scatter-10.6 μm Mirror B S λ 0 /2 λ pl /2 Launching contact 150 nm 100 nm 100 nm 27 nm 5 nm V PS h-BN V 0 = -10 V Figure 1 | Device sketch and measurement principle.The three local gates are used to independently tune the carrier concentration in the different graphene regions. The phase shifter voltage V PS is tuned and during all experiments V0 = −10 V is kept constant. The gate thickness is 15 nm. The plasmons propagate from the launching contact over the phase shifter region and are ultimately scattered into far-field light using a metallized AFM tip, and subsequently interfered with the incoming light.ing of a metallized atomic force microscopy probe tip. In this way, we are able to continuously tune the phase shift of the plasmon and the outcoming photons from 0 to 2π, and experimentally ...

Optical sensing in the mid- and long-wave infrared (MWIR, LWIR) is of paramount importance for a large spectrum of applications including environmental monitoring, gas sensing, hazard detection, food and product manufacturing inspection, and so forth. Yet, such applications to date are served by costly and complex epitaxially grown HgCdTe quantum-well and quantum-dot infrared photodetectors. The possibility of exploiting low-energy intraband transitions make colloidal quantum dots (CQD) an attractive low-cost alternative to expensive low bandgap materials for infrared applications. Unfortunately, fabrication of quantum dots exhibiting intraband absorption is technologically constrained by the requirement of controlled heavy doping, which has limited, so far, MWIR and LWIR CQD detectors to mercury-based materials. Here, we demonstrate intraband absorption and photodetection in heavily doped PbS colloidal quantum dots in the 5–9 μm range, beyond the PbS bulk band gap, with responsivities on the order of 10–4 A/W at 80 K. We have further developed a model based on quantum transport equations to understand the impact of electron population of the conduction band in the performance of intraband photodetectors and offer guidelines toward further performance improvement.