Accessing intrinsic properties of a graphene device can be hindered by the influence of contact electrodes. Here, we capacitively couple graphene devices to superconducting resonant circuits and observe clear changes in the resonance- frequency and -widths originating from the internal charge dynamics of graphene. This allows us to extract the density of states and charge relaxation resistance in graphene p-n junctions without the need of electrical contacts. The presented characterizations pave a fast, sensitive and non-invasive measurement of graphene nanocircuits.
We study fully hexagonal boron nitride (hBN)-encapsulated graphene spin valve devices at room temperature. The device consists of a graphene channel encapsulated between two crystalline hBN flakes; thick-hBN flake as a bottom gate dielectric substrate which masks the charge impurities from SiO2/Si substrate and single-layer thin-hBN flake as a tunnel barrier. Full encapsulation prevents the graphene from coming in contact with any polymer/chemical during the lithography and thus gives homogeneous charge and spin transport properties across different regions of the encapsulated graphene. Furthe…
Feedback-controlled electric breakdown of graphene in air or vacuum is a well-established way of fabricating tunnel junctions, nanogaps, and quantum dots. We show that the method is equally applicable to encapsulated graphene constrictions fabricated using hydrogen silsesquioxane. The silica-like layer left by hydrogen silsesquioxane resist after electron-beam exposure remains intact after electric breakdown of the graphene. We explore the conductance switching behavior that is common in graphene nanostructures fabricated via feedback-controlled breakdown, and show that it can be attributed to…
We have developed an analytical formulation to calculate the plasmon dispersion relation for a two-dimensional layer which is encapsulated within a narrow spatial gap between two bulk half-space plasmas. This is based on a solution of the inverse dielectric function integral equation within the random-phase approximation (RPA). We take into account the nonlocality of the plasmon dispersion relation for both gapped and gapless graphene as the sandwiched two-dimensional (2D) semiconductor plasma. The associated nonlocal graphene plasmon spectrum coupled to the "sandwich" system is exhibited in d…
We report a proof-of-concept study of extraordinary magnetoresistance (EMR) in devices of monolayer graphene encapsulated in hexagonal boron nitride, having metallic edge contacts and a central metal shunt. Extremely large EMR values, $MR=(R(B) - R_0) / R_0\sim 10^5$, are achieved in part because $R_0$ approaches or crosses zero as a function of the gate voltage, exceeding that achieved in high mobility bulk semiconductor devices. We highlight the sensitivity, $dR/dB$, which in two-terminal measurements is the highest yet reported for EMR devices, and in particular exceeds prior results in gra…
We have performed spin and charge transport measurements in dual gated high mobility bilayer graphene encapsulated in hexagonal boron nitride. Our results show spin relaxation lengths $λ_s$ up to 13~\textmu m at room temperature with relaxation times $τ_s$ of 2.5~ns. At 4~K, the diffusion coefficient rises up to 0.52~m$^2$/s, a value 5 times higher than the best achieved for graphene spin valves up to date. As a consequence, $λ_s$ rises up to 24~\textmu m with $τ_s$ as high as 2.9~ns. We characterized 3 different samples and observed that the spin relaxation times increase with the device leng…
We study the infrared cyclotron resonance of high mobility monolayer graphene encapsulated in hexagonal boron nitride, and simultaneously observe several narrow resonance lines due to interband Landau level transitions. By holding the magnetic field strength, $B$, constant while tuning the carrier density, $n$, we find the transition energies show a pronounced non-monotonic dependence on the Landau level filling factor, $ν\propto n/B$. This constitutes direct evidence that electron-electron interactions contribute to the Landau level transition energies in graphene, beyond the single-particle …
We present a novel method to establish inner point contacts on hexagonal boron nitride (hBN) encapsulated graphene heterostructures with dimensions as small as 100 nm by pre-patterning the top-hBN in a separate step prior to dry-stacking. 2 and 4-terminal field effect measurements between different lead combinations are in qualitative agreement with an electrostatic model assuming pointlike contacts. The measured contact resistances are 0.5-1.5 k$Ω$ per contact, which is quite low for such small contacts. By applying a perpendicular magnetic fields, an insulating behaviour in the quantum Hall …
We perform a comprehensive analysis of the spectrum of graphene plasmons which arise when a pair of sheets are confined between conducting materials. The associated enhanced local fields may be employed in the manipulation of light on the nanoscale by adjusting the separation between the graphene layers, the energy band gap as well as the concentration of charge carriers in the conducting media surrounding the two-dimensional (2D) layers. We present a theoretical formalism, based on the calculation of the surface response function, for determining the plasmon spectrum of an encapsulated pair o…
We present a thermal annealing study on single-layer and bilayer (BLG) graphene encapsulated in hexagonal boron nitride. The samples are characterized by electron transport and Raman spectroscopy measurements before and after each annealing step. While extracted material properties such as charge carrier mobility, overall doping, and strain are not influenced by the annealing, an initial annealing step lowers doping and strain variations and thus results in a more homogeneous sample. Additionally, the narrow 2D-sub-peak widths of the Raman spectrum of BLG, allow us to extract information about…
The encapsulation of graphene in hexagonal boron nitride provides graphene on substrate with excellent material quality. Here, we present the fabrication and characterization of Hall sensor elements based on graphene boron nitride heterostructures, where we gain from high mobility and low charge charier density at room temperature. We show a detailed device characterization including Hall effect measurements under vacuum and ambient conditions. We achieve a current- and voltage-related sensitivity of up to 5700 V/AT and 3 V/VT, respectively, outpacing state-of- the-art silicon and III/V Hall s…
Graphene/carbon-nanotube (CNT) hybrid material can be useful in energy storage and nanoelectronic technologies. Here we address the CNT-oscillator encapsulated in a graphene-nanoribbon (GNR) trench as a novel design, and investigate its properties via classical molecular dynamics simulations. Since the energy barrier was very low while the CNT was encapsulated in the GNR trench, the CNT absorbed on the GNR surface could easily be encapsulated in the GNR trench. MD simulations showed that the CNT oscillator encapsulated in a GNR trench is compatible with simple CNT oscillators, so we anticipate…
We experimentally study the electronic spin transport in hBN encapsulated single layer graphene nonlocal spin valves. The use of top and bottom gates allows us to control the carrier density and the electric field independently. The spin relaxation times in our devices range up to 2 ns with spin relaxation lengths exceeding 12 $μ$m even at room temperature. We obtain that the ratio of the spin relaxation time for spins pointing out-of-plane to spins in-plane is $τ_{\bot} / τ_{||} \approx$ 0.75 for zero applied perpendicular electric field. By tuning the electric field this anisotropy changes t…
The presence of finite bandgap and high mobility in semiconductor few-layer black phosphorus offers an attractive prospect for using this material in future two-dimensional electronic devices. Here we demonstrate for the first time fully encapsulated ultrathin (down to bilayer) black phosphorus field effect transistors in Van der Waals heterostructures to preclude their stability and degradation problems which have limited their potential for applications. Introducing monolayer graphene in our device architecture for one-atom-thick conformal source-drain electrodes enables a chemically inert b…
The excellent electronic and mechanical properties of graphene allow it to sustain very large currents, enabling its incandescence through Joule heating in suspended devices. Although interesting scientifically and promising technologically, this process is unattainable in ambient environment, because graphene quickly oxidises at high temperatures. Here, we take the performance of graphene-based incandescent devices to the next level by encapsulating graphene with hexagonal boron nitride (hBN). Remarkably, we found that the hBN encapsulation provides an excellent protection for hot graphene fi…
A periodic spatial modulation, as created by a moiré pattern, has been extensively studied with the view to engineer and tune the properties of graphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightly misaligned with the top and bottom hBN layers experiences two interfering moiré patterns, resulting in a so-called super-moiré (SM). This leads to a lattice and electronic spectrum reconstruction. A geometrical construction of the non-relaxed SM patterns allows us to indicate qualitatively the induced changes in the electronic properties and to locate the SM features in the …
Devices made from two dimensional materials such as graphene and transition metal dichalcogenides exhibit remarkable electronic properties of interest to many subdisciplines of nanoscience. Owing to their 2D nature, their quality is highly susceptible to contamination and degradation when exposed to the ambient environment. Protecting the 2D layers by encapsulation between hexagonal boron nitride layers significantly improves their quality. Locating these samples within the encapsulant and assessing their integrity prior to further processing then becomes challenging. Here we show that conduct…
Devices made from two-dimensional (2D) materials such as graphene or transition metal dichalcogenides possess interesting electronic properties that can become accessible to experimental probes when the samples are protected from deleterious environmental effects by encapsulating them between hexagonal boron nitride (hBN) layers. While the encapsulated flakes can be detected through post-processing of optical images or confocal Raman mapping, these techniques lack the sub-micrometer scale resolution to identify tears, structural defects or impurities, which is crucial for the fabrication of hi…
More than a decade after the discovery of graphene, ballistic transport in nanostructures based on this intriguing material still represents a challenging field of research in two-dimensional electronics. The presence of rough edges in nanostructures based on this material prevents the appearance of truly ballistic electron transport as theo\-re\-tically predicted and, therefore, not well-developed plateaus of conductance have been revealed to date. In this work we report on a novel implementation of the cryo-etching method, which enabled us to fabricate graphene nanoconstrictions encapsulated…
We investigate the zero-bias behavior of Josephson junctions made of encapsulated graphene boron nitride heterostructures in the long ballistic junction regime. For temperatures down to 2.7K, the junctions appear non-hysteretic with respect to the switching and retrapping currents $I_C$ and $I_R$. A small non-zero resistance is observed even around zero bias current, and scales with temperature as dictated by the phase diffusion mechanism. By varying the graphene carrier concentration we are able to confirm that the observed phase diffusion mechanism follows the trend for an overdamped Josephs…
Van der Waals heterostructures provide a rich platform for emergent physics due to their tunable hybridization of electronic orbital- and spin-degrees of freedom. Here, we show that a heterostructure formed by twisted bilayer graphene sandwiched between ferromagnetic insulators develops flat bands stemming from the interplay between twist, exchange proximity and spin-orbit coupling. We demonstrate that in this flat-band regime, the spin degree of freedom is hybridized, giving rise to an effective triangular superlattice with valley as a degenerate pseudospin degree of freedom. Incorporating el…
Using a simple setup to bend a flexible substrate, we demonstrate deterministic and reproducible in-situ strain tuning of graphene electronic devices. Central to this method is the full hBN encapsulation of graphene, which preserves the exceptional quality of pristine graphene for transport experiments. In addition, the on-substrate approach allows one to exploit strain effects in the full range of possible sample geometries and at the same time guarantees that changes in the gate capacitance remain negligible during the deformation process. We use Raman spectroscopy to spatially map the strai…
Interference of double moire patterns of graphene (G) encapsulated by hexagonal boron nitride (BN) can alter the electronic structure features near the primary/secondary Dirac points and the electron-hole symmetry introduced by a single G/BN moire pattern depending on the relative stacking arrangements of the top/bottom BN layers. We show that strong interference effects are found in nearly aligned BN/G/BN and BN/G/NB and obtain the evolution of the associated density of states as a function of moire superlattice twist angles. For equal moire periods and commensurate patterns with $Δϕ= 0^{\cir…
Devices made from graphene encapsulated in hexagonal boron-nitride exhibit pronounced negative bend resistance and an anomalous Hall effect, which are a direct consequence of room-temperature ballistic transport on a micrometer scale for a wide range of carrier concentrations. The encapsulation makes graphene practically insusceptible to the ambient atmosphere and, simultaneously, allows the use of boron nitride as an ultrathin top gate dielectric.
We report the batch fabrication of graphene field-effect-transistors (GFETs) with nanoperforated graphene as channel. The transistors were cut and encapsulated. The encapsulated GFETs display saturation regions that can be tuned by modifying the top gate voltage, and have on/off ratios of up to 10^8 at room temperature. In addition, the nanoperforated GFETs display orders of magnitude higher photoresponses than any room-temperature graphene detector configurations that do not involve heterostructures with bandgap materials.
The encapsulation of graphene based Hall sensors on foil is shown to be an effective method for improving the performance in terms of higher sensitivity for magnetic field detection. Two types of encapsulation were investigated: a simple encapsulation of graphene with polymethyl methacrylate (PMMA) as a proof of concept and an encapsulation with mechanically exfoliated hexagonal boron nitride (hBN). The Hall sensor with PMMA encapsulation already shows higher sensitivity compared to the one without encapsulation. However, the Hall sensor with graphene encapsulated between two stacks of hBN sho…
Low frequency 1/f noise is investigated in graphene, encapsulated between hexagonal boron nitride (hBN) substrate in dual gated geometry. The overall noise magnitude is smaller as compared to graphene on Si/SiO2 substrate. The noise amplitude in the hole doped region is independent of carrier density while in the electron doped region, a pronounced peak is observed, at Fermi energy, EF ~ 90 meV. The physical mechanism of the anomalous noise peak in the electron doped region is attributed to the impurity states originating from the Carbon atom replacing the Nitrogen site in hBN crystal. Further…
We investigate the electronic properties of ballistic planar Josephson junctions with multiple superconducting terminals. Our devices consist of monolayer graphene encapsulated in boron nitride with molybdenum-rhenium contacts. Resistance measurements yield multiple resonant features, which are attributed to supercurrent flow among adjacent and non-adjacent Josephson junctions. In particular, we find that superconducting and dissipative currents coexist within the same region of graphene. We show that the presence of dissipative currents primarily results in electron heating and estimate the a…
Stacking switching between correlation-protected radial Rashba field and persistent spin textures in graphene encapsulated by 1T-TaS$_2$ monolayers
Institute of Physics, Pavol Jozef Šafárik University in Košice（帕沃尔·约瑟夫·沙法里克大学科希策物理研究所）；Institute of Informatics, Slovak Academy of Sciences（斯洛伐克科学院信息学研究所）；Faculty of Physics, University of Belgrade（贝尔格莱德大学物理学院）；Institute of Experimental Physics, Slovak Academy of Sciences（斯洛伐克科学院实验物理研究所）；New Technologies Research Centre, University of West Bohemia（西波希米亚大学新技术研究中心）
Graphene sheets encapsulated between hexagonal Boron Nitride (hBN) slabs display superb electronic properties due to very limited scattering from extrinsic disorder sources such as Coulomb impurities and corrugations. Such samples are therefore expected to be ideal platforms for highly-tunable low-loss plasmonics in a wide spectral range. In this Article we present a theory of collective electron density oscillations in a graphene sheet encapsulated between two hBN semi-infinite slabs (hBN/G/hBN). Graphene plasmons hybridize with hBN optical phonons forming hybrid plasmon-phonon (HPP) modes. W…
Hysteresis-Free High Mobility Graphene Encapsulated in Tungsten Disulfide
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科学技术研究院）；Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice（威尼斯大学分子科学与纳米系统系）；School for Engineering of Matter, Transport and Energy, Arizona State University（亚利桑那州立大学物质、交通与能源工程学院）
Deep-UV bleaching of charge disorder in encapsulated graphene
University of Manchester（曼彻斯特大学）；National Graphene Institute, University of Manchester（国家石墨烯研究所，曼彻斯特大学）；National Institute for Materials Science（国立材料科学研究所）；University of Lancaster（兰卡斯特大学）
Hexagonal boron nitride (h-BN) encapsulation significantly improves carrier transport in graphene. This work investigates the benefit of implementing the encapsulation technique in graphene field-effect transistors (GFET) in terms of their radio frequency (RF) performance. For such a purpose, a drift-diffusion self-consistent simulator is prepared to get the GFET electrical characteristics. Both the mobility and saturation velocity information are obtained by means of an ensemble Monte Carlo simulator upon considering the relevant scattering mechanisms that affect carrier transport. RF figures…
We develop the device model for the proposed injection (electrically) driven thermal light emitters (IDLEs) based on the vertical Hexagonal Boron Nitride Layer/Graphene Layer/ Hexagonal Boron Nitride Layer (hBNL/GL/hBNL) heterostructures and analyze their dynamic response. The operation of the IDLEs is associated with the light emission of the hot two-dimensional electron-hole plasma (2DEHP) generated in the GL by both the lateral injection from the side contacts and the vertical injection through the hBNL (combined injection) heating the 2DEHP. The temporal variation of the injection current …
Systems in which interparticle interactions prevail can be described by hydrodynamics. This regime is typically difficult to access in the solid state for electrons. However, the high purity of encapsulated graphene combined with its advantageous phonon properties make it possible, and hydrodynamic corrections to the conductivity of graphene have been observed. Examples include electron whirlpools, enhanced flow through constrictions as well as a Poiseuille flow profile. An electronic device relying specifically on viscous behaviour and acting as a viscometer has however been lacking. Here, we…
Electron-electron interactions in graphene are sufficiently strong to induce a correlated and momentum-conserving flow such that charge carriers behave similarly to the Hagen-Poiseuille flow of a classical fluid. In the current work, we investigate the electronic signatures of such a viscous charge flow in high-mobility graphene FETs. In two complementary measurement schemes, we monitor differential resistance of graphene for different channel widths and for different effective electron temperatures. By combining both approaches, the presence of viscous effects is verified in a temperature ran…
Opto-electronic devices utilizing graphene have already demonstrated unique capabilities, which are much more difficult to realize with conventional technologies. However, the requirements in terms of material quality and uniformity are very demanding. A major roadblock towards high-performance devices are the nanoscale variations of graphene properties, which strongly impact the macroscopic device behaviour. Here, we present and apply opto-electronic nanoscopy to measure locally both the optical and electronic properties of graphene devices. This is achieved by combining scanning near-field i…
Terahertz magneto-nanoscopy of encapsulated monolayer graphene
Ames National Laboratory, US Department of Energy（艾姆斯国家实验室）；Kangwon National University（江原国立大学）；Incheon National University（仁川国立大学）；Iowa State University（爱荷华州立大学）
Van der Waals (vdW) heterostructures consisting of bilayer graphene (BLG) encapsulated within monolayers of strong spin-orbit semiconductor WS$_2$ or ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$ (CGT), are investigated. By performing realistic first-principles calculations we capture the essential BLG band structure features, including layer- and sublattice-resolved proximity spin-orbit or exchange couplings. For different relative twist angles (0 or 60$^{\circ}$) of the WS$_2$ layers, and the magnetizations (parallel or antiparallel) of the CGT layers, with respect to BLG, the low energy ba…
Tailoring pure valley-Zeeman spin-orbit coupling in WSe$_2$-encapsulated monolayer graphene
National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室、先进微结构协同创新中心、物理学院）；Center for Quantum Matter, School of Physics, Zhejiang University（浙江大学量子物质科学研究中心、物理学院）
We observe a dc electric current in response to terahertz radiation in lateral inter-digitated double-comb graphene p-n junctions. The junctions were fabricated by selective ultraviolet irradiation inducing p-type doping in intrinsic n-type epitaxial monolayer graphene. The photocurrent exhibits a strong polarization dependence and is explained by electric rectification in p-n junctions.
We study spin transport in normal/ferromagnetic/normal graphene junctions where a gate electrode is attached to the ferromagnetic graphene. We find that due to the exchange field of the ferromagnetic graphene, spin current through the junctions has an oscillatory behavior with respect to the chemical potential in the ferromagnetic graphene, which can be tuned by the gate voltage. Especially, we obtain a controllable spin current reversal by the gate voltage. Our prediction of high controllability of spin transport in ferromagnetic graphene junction may contribute to the development of the spin…
Using ab-initio methods we investigate the possibility of three-terminal graphene "T-junction" devices and show that these all-graphene edge contacts are energetically feasible when the 1D interface itself is free from foreign atoms. We examine the energetics of various junction structures as a function of the atomic scale geometry. Three-terminal equilibrium Green's functions are used to determine the transmission spectrum and contact resistance of the system. We find that the most symmetric structures have a significant binding energy, and we determine the contact resistances in the junction…
Hexagonal boron nitride is the only substrate that has so far allowed graphene devices exhibiting micron-scale ballistic transport. Can other atomically flat crystals be used as substrates for making quality graphene heterostructures? Here we report on our search for alternative substrates. The devices fabricated by encapsulating graphene with molybdenum or tungsten disulphides and hBN are found to exhibit consistently high carrier mobilities of about 60,000 cm$^{2}$V$^{-1}$s$^{-1}$. In contrast, encapsulation with atomically flat layered oxides such as mica, bismuth strontium calcium copper o…
Thermopower of graphene-superconductor (GS) junction is analyzed within the extended Blonder- Tinkham-Klapwijk formalism. Within this approach we have also calculated the temperature de- pendence of the zero-bias conductance for GS junction. Both quantities reflect quasi-relativistic nature of massless Dirac fermions in graphene. Both, the linear and the non-linear regimes are considered.
We show that the wavefunctions form caustics in circular graphene p-n junctions which in the framework of geometrical optics can be interpreted with negative refractive index.
In this work, we investigate thermoelectric properties of junctions consisting of two partially overlapped graphene sheets coupled to each other in the cross-plane direction. It is shown that because of the weak van-der Waals interactions between graphene layers, the phonon conductance in these junctions is strongly reduced, compared to that of single graphene layer structures, while their electrical performance is weakly affected. By exploiting this effect, we demonstrate that the thermoelectric figure of merit can reach values higher than 1 at room temperature in junctions made of gapped gra…
We present low-temperature Raman measurements on gate tunable graphene encapsulated in hexagonal boron nitride, which allows to study in detail the Raman G and 2D mode frequencies and line widths as function of the charge carrier density. We observe a clear softening of the Raman G mode (of up to 2.5 cm$^{-1}$) at low carrier density due to the phonon anomaly and a residual G~mode line width of $\approx$ 3.5 cm$^{-1}$ at high doping. From analyzing the G mode dependence on doping and laser power we extract an electron-phonon-coupling constant of $\approx$ 4.4 $\times$ 10$^{-3}$ (for the G mode…
Imperfections change essentially the electronic transport properties of graphene. Motivated by a recent experiment reporting on the possible application of graphene as junctions, we study transport properties in graphene-based junctions with single localized defect. We solve the Dirac-Bogoliubov-de-Gennes equation with a single localized defect superconductor-normal(graphene)-superconductor (SNS) junction. We consider the properties of tunneling conductance and Josephson current through an undoped strip of graphene with heavily doped s-wave superconducting electrodes in the dirty limit. We fin…
Uncooled Terahertz (THz) photodetectors (PDs) showing fast (ps) response and high sensitivity (noise equivalent power (NEP) < $nWHz^{-1/2}$) over a broad (0.5THz-10THz) frequency range are needed for applications in high-resolution spectroscopy (relative accuracy ~ $10^{-11}$), metrology, quantum information, security, imaging, optical communications. However, present THz receivers cannot provide the required balance between sensitivity, speed, operation temperature and frequency range. Here, we demonstrate an uncooled THz PD combining the low (~2000 $k_{B}μm^{-2}$) electronic specific heat of…
Electronic transport in BN-encasulated graphene limited by remote phonon scattering
Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier（蒙彼利埃大学查尔斯·库隆实验室）；Aix Marseille Univ, CNRS, CINaM, AMUTech（艾克斯马赛大学）；University of Modena and Reggio Emilia（摩德纳和雷焦艾米利亚大学）；Sapienza Università di Roma（罗马第一大学）
We show that an electrostatically created n-p junction separating the electron and hole gas regions in a graphene monolayer transmits only those quasiparticles that approach it almost perpendicularly to the n-p interface. Such a selective transmission of carriers by a single n-p junction would manifest itself in non-local magnetoresistance effect in arrays of such junctions and determines the unusual Fano factor in the current noise universal for the n-p junctions in graphene.
The proper understanding of semiconductor devices begins at the metal-semiconductor interface. The metal/semiconductor interface itself can also be an important device, as Schottky junctions often forms when the doping in the semiconductors is low. Here, we extend the analysis of metal-silicon Schottky junctions by using graphene, an atomically thin semimetal. We show that a fundamentally new transport model is needed to describe the graphene-silicon Schottky junction. While the current-voltage behavior follows the celebrated ideal diode behavior, the details of the diode characteristics is be…
We use the non-equilibrium Green function (NEGF) method in the ballistic limit to provide a quantitative description of the conductance of graphene pn junctions - an important building block for graphene electronics devices. In this paper, recent experiments on graphene junctions are explained by a ballistic transport model, but only if the finite junction transition width, Dw, is accounted for. In particular, the experimentally observed anamolous increase in the resistance asymmetry between nn and np junctions under low source/drain charge density conditions is also quantitatively captured by…
The focusing of electric current by a single \textit{p-n} junction in graphene is predicted. We show that precise focusing can be achieved by fine-tuning the densities of carriers on the n- and p-sides of the junction to equal values, whereas the current distribution in junctions with different densities resembles caustics in optics. This finding can be utilized in the engineering of electronic lenses and focused beam-splitters using gate-controlled \textit{n-p-n} junctions in graphene-based transistors.
