Session X30: Transport and Noise in 2D Materials

Johnson Noise Thermometry in Graphene under Magnetic Fields.

We measure Johnson noise in graphene under a magnetic field in response to Joule heating. The measurement was performed at high frequency utilizing a noise matching circuit with a large dynamic range of source impedance required for high magnetic field. The graphene channel is self heated via current induced joule heating. The temperature and bias voltage are kept low so that the heat carried by the phonon system is negligible and direct electronic cooling is measured. In the high magnetic field regime, we observed hot spot formation in the quantum edge states where most of the heat dissipation occurs. We will also discuss the measured thermal conductance in the low magnetic field regime in relation to magneto hydrodynamics.   

Shot and Johnson Noise Measurement in Graphene Using Wide-Bandwidth Measurement Technique

We measure shot and Johnson noise in single and bilayer graphene devices as a function of carrier density. For this measurement, we have developed a technique for measuring high-frequency wide-bandwidth noise. We use a low-noise RF amplifier, high-frequency digitizer, and digital signal processing to measure noise in the range of several hundred MHz of a device whose resistance can vary several orders of magnitude. We precisely characterize the resistance-dependent gain and noise temperature of the entire circuit using Johnson noise from the device itself, in a temperature range of 3-300K. This technique presents a very flexible measurement of noise from devices, allowing device resistance fluctuations of several orders of magnitude, extreme nonlinear resistance behavior, and highly non-equilibrium conditions.   

Johnson noise thermometry of optically excited hot electrons in hBN encapsulated graphene

Hot electrons in graphene have unique thermal properties. Owed to graphene's unique combination of an exceedingly low electronic heat capacity and a strongly suppressed electron-phonon thermal conductivity G$_{\mathrm{th}}$, the electronic and phononic temperatures can be highly decoupled. Through space and time resolved laser excitation and a Johnson noise read out we can directly measure the spatial and time dependence of G$_{\mathrm{th\thinspace }}$and estimate the electronic heat capacity of graphene C$_{\mathrm{e}}=\tau $G$_{\mathrm{th}}$. We use these insights to design a photonic crystal integrated graphene bolometer with a NEP \textasciitilde 1pW/Hz$^{\mathrm{1/2}}$, a response time of \textasciitilde 1ps and a high operation temperature of 20K.   

Multifractal conductance fluctuations in graphene

A multifractal (MF) system is characterized by scaling laws involving an infinite number of exponents. In condensed-matter systems, signatures of multifractality have typically been found in the structure of the critical wave functions at localization delocalization (LD) transitions. We report here the first experimental observation of MF statistics in the transport coefficients of a quantum-condensed matter system. We unearth this through a careful investigation of the magneto-conductance fluctuations in ultra-high mobility single layer graphene at ultra-low temperatures. We obtain the MF spectra over a wide range of temperature and doping levels and show that the multifractality decreases as the temperature increases or as the doping moves the system away from the Dirac point. We show that the fractal exponents are a universal function of the phase coherence length of the carriers. We propose that a probable origin of the MF magneto-conductance fluctuations observed by us is an incipient Anderson LD transition in graphene near the charge neutrality point - a phenomenon predicted but never observed in single layer graphene. We also explore alternate possibilities of the origin of the multifractality – namely relativistic quantum scars.   

Anomalous drag resistivity at charge neutrality in double-layer graphene

We study the Coulomb drag resistivity of Dirac carriers between two spatially-separated monolayer graphene sheets, focusing on the anomalous nonzero drag effect around dual charge neutrality that was observed in experiments in the strong interlayer interaction regime. By employing the Boltzmann equation we derive a hydrodynamic description of the electric and energy transport in double-layer graphene based on fast interlayer equilibration as well as the intralayer equilibration. Incorporating weak quenched disorder we find that the drag resistivity at dual neutrality is finite due to inelastic interlayer carrier collisions. We also discuss the magnetodrag in the hydrodynamic regime. We compute this ``minimal'' drag by an unbiased numerical solution to the Boltzmann equation implemented with the help orthogonal polynomials, a technique conceptually analogous to the Chapman-Enskog method introduced in the kinetic theory of gases. To simulate experiments we calculate the drag resistivity as a function of various tuning parameters such as charge densities, temperature, and interlayer distance, incorporating Coulomb impurities that is the dominant elastic scattering mechanism in graphene on h-BN substrates, and also extract analytical expressions in certain limiting cases.   

Unconventional transport in ultraclean graphene constriction devices

Under mesoscopic conditions, strong electron-electron interactions and weak electron-phonon coupling in graphene lead to hydrodynamic behavior of electrons, resulting in unusual and unexpected transport phenomena. Specifically, this hydrodynamical collective cooperation of electrons is predicted to enhance the flow of electrical current, leading to a striking higher-than-ballistic conductance through a narrow geometrical constriction. To access the hydrodynamic regime, we fabricated high-quality, low-disorder graphene nano-constriction devices encapsulated by hexagonal boron nitride, where electron-electron scattering dominates impurity scattering. We will report on our systematic four-probe conductance measurements on devices with different constriction widths as a function of number density and temperature. The observation of quantum transport phenomena that are inconsistent with the non-interacting ballistic free-fermion model would suggest a macroscopic transport signature of electron viscosity.   

Graphene Channel for Guiding Charge Carriers

The propagation of ballistic charge carriers in high quality graphene resembles that of photons. For Fermi wavelength much smaller than the scale of a device their motion mimics ray optics but with the refraction index replaced by the Fermi wavevector which proportional to the square root of the carrier density. Similar to ray optics, when the incoming ray is on the high index side of an interface between regions with different carrier densities, there is a critical angle above which total reflection occurs. As a result, a channel with high carrier density bounded by lower density regions produces electrical guiding similar to an optical wave guide. We studied the effect of total reflection on the guiding efficiency, which defines the increase of the current collected, in high quality hBN-encapsulated graphene devices with the guiding channel defined by a thin top gate. We find that the guiding efficiency is controlled by the ratio of the carrier densities inside and outside the channel. The highest efficiency about 4.5{\%} is observed for a channel with the largest attainable carrier ratio but with the same type of carrier inside and outside. The measurement is supported by the tight-binding simulation.   

Theoretical study of the criteria and consequences of hydrodynamic electron flow in graphene.

Experiments on graphene electrons have succeeded in entering the hydrodynamic regime, as demonstrated by successful observations of Wiedemann-Franz law violations [J. Crossno et al. \textit{Science }\textbf{351}, 1058 (2016)], and evidence for electron vortices [D. A. Badurin et al. \textit{Science }\textbf{351}, 1055 (2016)].~ The hydrodynamic regime is expected to occur when electron-electron interactions dominate over all other electron collision mechanisms.~ We calculate the electron-electron, electron-impurity and electron-phonon scattering rates as a function of temperature, charge doping and disorder (charge puddle) strength. ~We find that there exists a window in parameter space where electron-electron scattering dominates and hydrodynamic effects become observable. ~However, we also find that disorder induced carrier density inhomogeneity continues to play an important role in the vicinity of charge neutrality, even in the strongly interacting hydrodynamic regime.~ For example, although the ratio of thermal conductivity and electrical conductivity show a violation of the Wiedemann-Franz law in the aforementioned experiment, the electrical conductivity as a function of temperature still follows a disorder-driven universal scaling theory first predicted in Adam and Stiles, Phys. Rev. B 82, 075423 (2010).~ This work was supported by the National Research Foundation of Singapore (NRF-NRFF2012-01).   

Geometric interference observed in a high-mobility graphene ring

We observe a strong quantum interference pattern in low-temperature resistance measurements of a ring-shaped h-BN/graphene/h-BN~pn-junction device. The graphene has a mobility of 200,000 cm$^{\mathrm{2}}$/Vs at a concentration of 10$^{\mathrm{10}}$~cm$^{\mathrm{-2}}$. The ring is placed on top of a pair of buried gates that allow the left and right halves of the ring to be independently gated, forming gate-voltage quadrants for different carrier types across the ring. At low-temperatures, 400~mK~to 10 K, the measured resistance as a function of gate voltage exhibits a~strong interference pattern. The peaks and valleys are much larger in amplitude than the relatively weak~Aharonov-Bohm oscillations observed when the magnetic field is swept at fixed gate voltage. The interference is robust and remains in the presence of moderate magnetic fields (on the order of 0.1~T). Tight-binding quantum transport calculations of the device geometry show a similar interference pattern, and systematic modeling indicates that the interference pattern arises from spatial quantization in the device.~   

Geometric manipulation of transport in Graphene monolayer with antidots

We report magneto transport studies of CVD monolayer graphene on SiO$_{\mathrm{2}}$/Si substrate with hexagonal arrays of antidots, up to 32 Tesla with temperature from 200mK to 50K. Weak localization is observed below 0.5T. Above 10T, prominent Shubnikov-de Haas oscillations are noticed. In the intermediate magnetic fields, some commensurability peaks are also observed due to cyclotron motion of carriers. From the temperature dependent amplitude of SdH oscillation and Dingle plot, the effective mass of electron is estimated as 0.0786m$_{\mathrm{e}}$, and quantum scattering time 0.016ps. Effect of antidot geometry with different radii from 50nm to 200nm and with different shapes will be reported.   

Effects of commensurate phase with kekule symmetry on the conductance of suspended graphene

I will present measurements of the effects of the adsorption of monatomic and diatomic gases on the conductance of suspended graphene devices. The devices support adsorbed monolayers with two-dimensional phases like those known to form on bulk graphite, although the phase transitions occur at slightly higher pressures due to the reduced binding energy. We find that the formation of the $\surd 3 \times \surd 3$ commensurate solid phases in the adsorbed monolayers greatly modifies the conductance of graphene, reducing it by as much as a factor of two. This is in sharp contrast with the much smaller effects of other adsorbed two-dimensional phases which are not in registry with the graphene lattice (e.g. 2D fluid, incommensurate solid). Further, we observe hysteretic behavior near the phase transition between the incommensurate solid and the commensurate solid phase which is absent when adsorption is restricted to one side of the graphene sheet, as when the graphene is supported on hexagonal boron nitride. We infer that the hysteresis results from interactions between the adsorbed monolayers on either side of the graphene sheet.   

Electronic transport properties of epitaxial graphene buffer layer on Silicon Carbide

The confinement control sublimation is used to produce high quality epitaxial graphene on SiC for nanoelectronics. We report here on the experimental investigation of the first graphene layer grown on SiC(0001) (the buffer layer). The buffer layer is a semiconducting form of graphene, with a gap in the density of state previously probed by ARPES and STM measurements. We characterize our samples by Raman spectroscopy, photoemission spectroscopy, and atomic and lateral force microscopy to confirm their structural properties and produce electronic devices on single SiC terraces. The temperature and electric field dependence of the bulk conductivity of the buffer layer are investigated and the effects of contacts and gas adsorption are considered. The observed behavior seem to be related to the known structural periodicity of the buffer layer.   

The modulation of electron-electron interactions in graphene via temperature.

Near the charge neutral point, graphene exhibits interesting many-body interactions beyond what Fermi liquid theory can predict. We investigate such many-body effects in charge neutral graphene using angle-resolved photoemission spectroscopy. The electron band structure shows strong deviation from the characteristic linearity at low temperatures. Our findings suggest a possible realization of strong correlations between Dirac fermions in graphene via temperature.   

Strong Josephson Coupling in Planar Graphene Junctions

A recent breakthrough of processing graphene, employing encapsulation by hexagonal boron nitride layers (BGB structure), allows realizing the ballistic carrier transport in graphene. Thereafter, ballistic Josephson coupling has been studied by closely edge-contacted BGB structure with two superconducting electrodes. Here, we report on the strong Josephson coupling with planar graphene junction in truly short and ballistic regime. Our device showed high transmission probability and the junction critical current ($I_{C} )$ oscillating for sweeping the gate voltage along with the normal conductance oscillation (Fabry-Perot oscillations), providing a direct evidence for the ballistic nature of the junction pair current. We also observed the convex-upward shape of decreasing critical currents with increasing temperature, canonical properties of the short Josephson coupling. By fitting these curves into theoretical models, we demonstrate the strong Josephson coupling in our devices, which is also supported by the exceptionally large value of $I_{C} R_{N} (\sim 2\Delta /e$; $R_{N} $is the normal resistance).   

Realistic model for electron-electron interactions in graphene

We study the effects of realistic electronic interactions in undoped graphene. Using projective quantum Monte Carlo simulations of tight-binding electrons on a honeycomb lattice interacting through a realistic effective Coulomb potential, we compute the phase diagram and renormalized Fermi velocity as a function of the strength of the short- and long-range components of the Coulomb potential. The short-range part of the interaction drives the semi-metal to antiferromagnetic Mott insulator transition, which is consistent with the Gross-Neveu-Yukawa critical theory. Far from the critical point, the Fermi velocity renormalization is dominated by the long-range part of the interaction, agreeing with the predictions from perturbative theory. In contrast, close to the antiferromagnetic Mott insulator transition, the Fermi velocity renormalization is modified by a competition between spin density wave and charge density wave fluctuations. Real graphene samples are typically halfway between these two limits. Since finite system sizes restrict the QMC results to large momentum scales, we perform a phenomenological reconstruction of the renormalization group flow of the Fermi velocity to make predictions that can be tested against current experimental observations.