Anomalous Resistance Behavior in Bilayer Graphene

Anomalous Resistance demeanor in Bi spirit aim Graphene remark of Anomalous Resistance Behavior in Bi stratum Graphene Yanping Liu 1,2, pilar cyst Siang Lew 2,*and Zongwen Liu 3,*AbstractOur measurement results pass water shown that bilayer graphene exhibits an unexpected sharply transition of the metro value in the temperature region cc250K. We argue that this manner originates from the interlayer blither dispersion fix betwixt the natural elevation and bottom ripple graphene layer. The inter- dissemination fundament mimic the speed of light break up, but is strongly dependent on temperature. The discovered behavior is consistent with the theoretical prediction that charged impurities argon the paramount scatters in bilayer graphene. The oppositeness increase with increase upright magnetized theme strongly supports the postulate that charismatic guinea pig induces an excitonic curtain raising in bilayer graphene. Our results go against that the relative chang e of bulwark induced by magnetised surface area in the bilayer graphene shows an anomalous caloricly touch off position.______________________________________IntroductionThe negatronic properties of monolayer graphene have been extensively studied receivable to its intriguing ability tidy sum social system with linear dispersion around the Dirac point and chirality exhibiting Berry phase of 1. at that place is a zero-energy Landau take (LL) with quad-fold degeneracy ascribable to interactions between electron spins and valleys in the magnetized domain of a die 2-4. belatedly, bilayer graphene became a subject of desirous research due to the low gear energy Hamiltonian of chiral quasiparticles and a Berry phase of 5-8. It has a double-degeneracy zero-energy Landau level that incorporates two diametric orbital states with the same energy under an outside magnetised theater of operations. The bilayer graphene with a Bernal (A-B) configuration loses some featu res of monolayer graphene and has a unique mountain expression where the conduction and valence ties are in contact with a nearly quadratic dispersion 5. In bilayer graphene, a parabolical quite a little expression ( ) with an transactionive aggregative m*=0.037, has been calculated by apply the interlayer coupling exemplification 9-14. What makes bilayer graphene an interesting material for lease is that the interlayer potential difference asymmetry drive out be controlled by an voltaic field, thus well-defineding an energy opening between the conduction and valence bands 16-18. Various applications for bilayer graphene are achievable due to the fact that its band gap can be spiel by exploitation an external out-of-plane electric field and chemical doping. thither is intensive research on bilayer graphene under the application of a perpendicular electric field, however, placardal reports on magnetic merchant vessels properties of bilayer graphene are not as well-studied. Recent theoretical work reports on excitonic condensation and quantum residence ferromagnetism in bilayer graphene 22. There are interesting features in bilayer graphene due to its unnecessary twofold orbital degeneracy in the LL spectrum, which results in an eightfold -degenerate LL at zero energy. The sprinkling mechanism of graphene is currently a subject of lifelike research and debate. The problem of magneto- enjoy properties in the mien of coke impurities is quiesce an open research problem. Our understanding of the nature of the disorder and how the mesoscopic ripple resolution affects the transport properties still need improvement hence, a better understanding on the general electric and magnetic transport properties of bilayer graphene is necessary.In this paper, we have systematically investigated the charge transport properties in bilayer graphene as a obligation of temperature, magnetic field, and electric field. Our measurement results have show n that bilayer graphene exhibits a semi-metallic R-T property and an unexpected sharp transition of the safeguard value in the temperature region 200250K. The longitudinal bulwark descends with increasing temperature and electric field, a behavior that is markedly different from the experimental reports of monolayer graphene. Our results reveal that the energy gap in the bilayer graphene shows an anomalous thermally activated property and increases with. We have shown that this phenomenon originates from a tuneable band structure behavior that can be controlled by a magnetic field, a property that had never previously been discover in bilayer graphene.It has been shown that Raman spectroscopy is a reliable, non-destructive turncock for identifying the second of graphene layers and it can be done through the 2D-band deconvolution procedure 23-25. The Raman spectra of our graphene structure were measured at room temperature using a WITEC CRM200 instrument at 532 nm excitation w avelength in the back sprinkle configuration 26-28. Fig.1a shows the characteristic Raman spectrum with a distinctly distinguishable G cap and 2D band. The two most intense features are the G peak and the 2D band which is sensitive to the number of layers of graphene. The position of the G peak and the shape of the 2D band brook the number of layers of graphene. Additionally, the number of layers of graphene can be easily distinguished from the beneficial width half maximum of the 2D band, as its mode changes from a narrow and radially symmetrical feature for monolayer graphene to an asymmetric distribution on the high-powered side for bilayer graphene 27. The 2D band inset in Fig.1a shows that the Raman spectrum of bilayer graphene is red-shifted and broadened with respect to that of the monolayer graphene. Fig. 1b shows the four terminal resistance as a function of letter carrier-density n, and the sample shows a pronounced peak at density . Note that the sharp peak in resi stance at low n is enhanced by the opening of the small energy gap owing to disorder-induced differences in carrier density between the top and the bottom layers of the flake.We have characterized the current (I)- electromotive force (V) characteristics of the bilayer graphene via four-terminal measurement, at different temperatures and magnetic fields. Shown in Fig. 2a are the I-V curl ups for bilayer graphene under the application of various magnetic fields at three different temperatures 2 K, 200 K and 340 K. The magnetic field is applied in the perpendicular fashion to the plane of the graphene. For all the temperatures and magnetic field strengths, the bilayer graphene exhibits a linear I-V curl up. This implies that the graphene layer is ohmic in nature. We observed that for a fit(p) magnetic field, the I-V wrestle displays a larger gradient at higher temperature than at take down temperature. Interestingly, the gradient of the I-V curve decreases with increasing magnet ic field. In our structure, the gradient of the curve corresponds to the conduction of the graphene layer. Such temperature and magnetic field dependent behaviour of conductivity is characteristic of an intrinsic semiconductor. The decrease in the conductivity of the bilayer graphene with increasing magnetic field is attributed to the excitonic energy gap induced by the magnetic field. This conductivity habituation on the magnetic field suggests that the resistance () of graphene is a qualitative fingerprint of its band gap.In the absence of a magnetic field, the band structure of the bilayer graphene at the Dirac valley has a parabolic dispersion relation. When a magnetic field is present, the band structure is changed to a split Landau level structure 19-21. Fig. 2(b) is an illustration of the bilayer bandgap and Landau level splitting under the influence of a magnetic field. Inset shows an optical image of the bilayer graphene with the metal contact electrodes. In Fig.2(c) we p lot the resistance of the bilayer graphene, as extracted from the I-V curve, as a function of magnetic field for three different temperatures. As the magnetic field was increase in a flavor of 4T, the resistance increase for each step was different, resulting in a non-linear relationship between the resistance and magnetic field. Interestingly, the observed non-line relationship is markedly different from Zeeman spin-splitting theoretical model with the line relationship, where gap with a free-electron g-factor g=2, where is the Bohr magneton. This potentially indicates sublattice symmetry breaking and gap geological validation due to many-body correction in this LL 32-34. This is further confirmation that magnetic field opens an excitonic gap in the bilayer graphene.The temperature dependency of monolayer graphene resistance is mainly attributed to the different dispersal mechanisms nose candy scattering 35-36, short set about scattering 37, and phonon scattering 38-39. How ever, the temperature addiction of bilayer graphene resistance has not been established yet. Shown in Fig.3a are the temperature dependance of the resistance of the bilayer graphene under the application of a magnetic field 0T and 12T, respectively. The results show that the resistance of the bilayer graphene drops following non-metallic behaviour as temperature increases from 2K to 340 K. This implies that the bilayer graphene resistors have intrinsic semiconductor properties as mentioned earlier. This can be explained by the decrease in Coulomb scattering with temperature for bilayer graphene due to its parabolic band structure. For B=12T, a kindred trend as B=0T is persisted in Fig 3a, where the resistance decreases with increasing temperature. However, the resistance for the entire temperature range is much larger than for B=0T. This indicates that the magnetic field opens an excitonic gap in the bilayer graphene that is thermally activated due to the Coulomb interaction ion -driven electronic instabilities 20, 31.Ripples are a common feature of cleaved graphene because it is never atomically flat, as it is placed on a substratum such as SiO2 in the term of nanometre-scale aberrations or ripples 40-42. Despite the magnitude of the ripples being quite small, it is still believed to be responsible for the unusual transport behaviour of graphene, also unvaccinated to adsorbed impurities, defects and the roughness of the underlying substrate 40-43. On the separate hand, it has been shown that suspended graphene films are corrugated on a mesoscopic scale, with out-of-plane deformations up to 1 nm 44-45. The deformation is a typically smaller than the Fermi wavelengthand these ripples induce predominant allelely short scattering. The observed height variation shows that the surface roughness beyond the atomic-level is per se present in bilayer graphene. Hence, one of the interesting features of corrugation of graphene is that it offers a new experimenta l opportunity to study how the corrugation-induced scattering impacts the transport properties of graphene. It is important to mention that at that place is a contrary sharp threshold like decrease in resistance observed above 200K. The strong temperature dependency is inconsistent with scattering by acoustic phonons. cardinal possible explanation is that the flexural phonons confined within ripples between the top and bottom layer causes the scattering. The presence of the ripple effect exhibits local out-of-plane ripples 44. Theoretical calculations41,46 show that the scattering rates for interripple flexural phonons with respect to two-phonon scattering process as, where is the flexural-phonon frequency, the derivative of the nearest-neighbour hopping integral with respect to deformation, a the lattice constant, , and the mass of carbon atom 46. For low temperatures T () , few flexural modes can be stirred inside ripples (). The conductivity of the surface roughness model at the limit at low temperature is45-46. As the temperature increases and typical wavelengths become shorter, short scattering excites the flexural phonons. For the high temperature limit, based on the above expression, we can bringing close together that , which yields 100 to 1000 at T=300K. The model of quenched-ripple disorder 46 suggested that the electron scattering of the static ripples quenched from the flexural phonon disorder can mimic Coulomb scattering when at room temperature. One should also note that the model predicts stronger temperature dependence (above a certain quenching temperature of about 100K) which is close to our experimental result at about 200K. However, the ripple effect normally leads to a rapid increase in the R-T curve rather than the sudden decrease in R-T as observed for our bilayer graphene. In the absence of a system to explain the stronger temperature dependence behaviour, we propose that the behaviour is consistent with the ripple effect i nterlayer scattering instead of interlayer scattering. Fig. 3b shows the schematically illustration of scattering mechanisms in bilayer graphene. For a bilayer graphene, the interlayer scattering between the top and bottom ripple graphene layer is similar to coulomb scattering with stronger dependence on temperature. The rapid decrease in R-T above 200K can be attributed to the transition between the low- and high-T limits in the interlayer ripple effect scattering.On the other hand, it was suggested that the observed strong T dependence could be explained by thermally excited surface polar phonons of the SiO2 substrate 35-38. The SiO2 optical phonons at the substrate-graphene interface induce an electric field which couples to the carriers in graphene due to it modulating the polarizability 38-39. However, Coulomb scattering is dominant for bilayer graphene and the substrate surface polar phonon induced field is to some extent screened by the additional graphene layers 39. Recentl y it has been shown that the substrate dielectric constant plays an important role in scattering in graphene. Theoretical predictions show that for dielectric constant , Coulomb scattering dominates, while for dielectric constant , short scattering dominates, as Coulomb scattering is more strongly screened for materials with a larger dielectric constant. In fact, our observed behaviour is consistent with the theory suggesting that scattering from charged impurities is dominant in graphene.We introduce a relaxation-time approximation and treat the unscreened Coulomb potential as 1,5 where Q is the charge of impurities. Based on the Boltzmann transport theory, we can obtain the bilayer graphene underground with massless Dirac-fermions (MDF) at low energies as. For high temperature , , we can obtain the bilayer graphene resistivity as47, where is the density of impurities per unit volume, is the permittivity of the semiconductor, and is the charge state of the impurity. This sho ws that the resistance of bilayer graphene limited by Coulomb scattering increases as increases and decreases with increasing temperature. Considering the above analysis, we deduce that the temperature dependence of resistance in bilayer graphene is mainly determined by Coulomb scattering. The short-range scattering is independent of temperature for bilayer graphene, as the density-of-states, the matrix element and the screening function are all energy independent. As a result of the parabolic band structure of bilayer graphene, the energy averaging of the Coulomb scattering time can give procession to the resistivity decreasing proportionality to temperature .Based on the above discussion, we give out the measured resistance in Fig.3a by using the following model for bilayer graphene, where and are the resistance due to the Coulomb and short-range scatterings, respectively. Fig.3b shows the relative resistance change under the biased and unbiased magnetic field as a function of temperature, and the clusterted line is the fit following the equation , where is the energy gap. The opening of the energy gap due to a potential difference between the two layers and Coulomb interactions could be a cause for this. These considerations explain qualitatively why the resistance of bilayer graphene decreases with increasing temperature. Note that the relative resistance change is a strong function of temperature. At temperatures of 2K180K and 220K250K, the relative resistance strongly increases as temperature increases, indicating that an energy gap forms due to many-body correction in Landau Level. When the temperature increases to T 250K, the relative resistance is just about independent of the increasing temperature this indicates that the energy gap is mostly stable at high temperatures. On the other hand, with the temperature increase from 180K to 220K, the relative resistance dependence of temperature shows a sharp decrease, which indicates that the ener gy gap shows an anomalous thermally activated behaviour as a function of temperature.For zero gate voltage (i.e., neutrality point), we measured changes in longitudinal resistance as a function of applied perpendicular field B. Fig. 4a shows the four-terminal longitudinal resistance of bilayer graphene as a function of magnetic field at T= 2K at the charge-neutrality point. We have plotted the resistance per square, because it is independent of a size effect of the sample. As seen from Fig. 4a, the resistance increases nonlinearly with the magnetic field strength followed by a plateau-like phase. One should note that the plateau-like phase in Fig. 4b disappears at higher temperatures. One possible explanation is the augmented sublattice spin-splitting due to the high surface-impurity concentration of the graphene layer 18. The origin of the nonlinear magnetoresistance increment behaviour is the splitting of Landau level that gives rise to a bandgap opening at the zero energy level 32-34. In our measurements, we fit our results to an analytical approximation for the non-linear resistance , where is the Boltzmann constant. We found that our results are in good agreement with this equation. These considerations explain qualitatively why the nonlinear resistance increases with the magnetic field.Fig. 5 shows the resistance of bilayer graphene as a function of electric field (E) under different magnetic fields. The dependent characteristics are symmetric due to the chirality of graphene electrons when an applied electric field changes from E to E. The normalized resistance curve describes the response under the applied magnetic field in the range of B=0T to B=12T and the temperatures of 2-340K. The results demonstrate that when the magnetic field increases from 0T to 12T at low temperatures (2200K) and low electric field (E), the resistance of bilayer graphene drops significantly. The larger slump in the resistance at lower temperature T=2K and low electric f ield as the increasing of electric field are due to Coulomb scattering by impurities, which is a strong function of temperature. On the other hand, at high temperatures (T 200K) and electric fields (E0.01 ), the resistance of bilayer graphene show a linear decrease. This can be explained by the scattering from thermally excited surface polar phonons of the substrate being screened by the additional top graphene layers 39. This further confirms that at high temperatures, the scattering induced by the electric field on the substrate surface polar phonons is significantly screened between top and bottom layers in bilayer graphene.In our experiment, temperature and magnetic field dependence of resistance of bilayer graphene was investigated. Intrinsic semiconductor behaviour at the range of temperature is 2K-340K was observed. The strange sharp threshold-like decrease in resistance around 200K is unexpected, and we attribute it to the presence of mesoscopic ripples between the top and bottom layer. Our results reveal that the energy gap in the bilayer graphene is thermally dependent. This potentially indicates the sublattice symmetry breaking and an energy gap formation due to Landau Level splits. The obtained results are important for the better understanding of magnetic field induced high resistance and provide indications of a theoretically predicted magnetic field induced excitonic gap.AcknowledgementsY. L would like to thank Prof. Wang and Prof. Yao for his serviceable discussions. This work was supported in part by the NRF-CRP program (Multifunctional Spintronic Materials and Devices) and the path for Science, Technology and Research (A*STAR) SERC grant (082 101 0015). The authors thank Sun Li and Li Yuanqing for their assistance in experimental measurements.Experimental sectionThe bilayer graphene samples for this study were prepared using mechanical exfoliation techniques 2 from the bulk highly point pyrolitic graphite (grade ZYA, SPI Supplies) and tra nsferred onto the surface of a lightly narcotised silicon substrate covered with a 300-nm thick layer of thermally grown , The doped silicon substrate and were use as back-gate and gate dielectric, respectively. 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