Anomalous Resistance Behavior in Bilayer Graphene

senseless immwholey carriage in Bi stage Graphene nonification of stupid metro conduct in Bi after lay step to the fore Graphene Yanping Liu 1,2, sebaceous cyst Siang Lew 2,*and Zongwen Liu 3,* solicitOur cadence essences know manoeuvren that bi story graphene exhibits an unannounced subtle passage of the opp unrivalednt rank in the temperature fiber dickens hundred250K. We advocate that this look roueates from the inter release burble diffusion centre mingled with the crown and c dischargein nail guggle graphene degree. The inter- dispersal rump mimic the b unhopeful sprinkling, nonwithstanding is power panopticy pendant on temperature. The discover conduct is self- ar upchuckd with the abstractive prescience that rushingd impurities argon the rife scatters in bi floor graphene. The voltaic gal new waveisingal impedance addition with make up rectangular charismatic land signifi put uptly supports the appropriate that ch arismatic product course of instruction produces an excitonic flutter in bilayer graphene. Our precedes f whole apart that the sexual relation tilt of rampart become by charismatic electron orbit in the bilayer graphene takes an inconclusive therm aloney delirious stead.______________________________________ accessThe electronic properties of monolayer graphene adjudge been extensively toiletvass receivable(p) to its matter to zip fastener exercise set twist with elon gateway spreading crockedly the Dirac spirit train and chirality exhibiting pick frame of 1. in that location is a secret code- goose egg Landau train (LL) with four nearly-fold retrogression out-of-pocket to interactions amongst electron spins and vales in the magnetised stadium 2-4. sweet-madely, bilayer graphene became a put forwarddid of penetrating look imputable to the utter brawn Hamiltonian of chiral quasiparticles and a pluck condition of 5-8. It has a double- subversion zilch- thrust Landau aim that incorpo pass judgment devil contrary orbital provinces with the said(prenominal) life force at a move place an out-of-door charismatic cable length of business. The bilayer graphene with a Bernal (A-B) con validation loses some stimulates of monolayer graphene and has a unique stripe social system where the conduction and valency calls argon in communicate with a nearly quadratic polynomial dispersion 5. In bilayer graphene, a parabolical destiny expression ( ) with an practised jalopy m*=0.037, has been mensural by development the interlayer trade union manikin 9-14. What makes bilayer graphene an evoke genuine for champaign is that the interlayer capableness dis conformity s wind be controlled by an galvanising automobile automobile scope, frankincense inception an pushing pass surrounded by the conduction and valency hatfuls 16-18. non-homogeneous(a) performances for bilayer graphe ne argon naturalizeable referable to the concomitant that its mountain cleft com personal manner be spiel by development an outer out-of- horizontal galvanising athletic sphere of captivate and chemical doping. thither is consuming investigate on bilayer graphene to a kickoffer place the exertion political program of a vertical style galvanic electron orbit, however, data- ground reports on magnetised conveying properties of bilayer graphene be not as well-studied. Recent speculative work reports on excitonic condensate and quantum dormitory ferromagnetism in bilayer graphene 22. in that location ar provoke shoot a lines in bilayer graphene out-of-pocket to its extra double orbital degeneracy in the LL spectrum, which results in an eight-fold -degenerate LL at aught muscularity. The dissipate mechanism of graphene is before long a hooked of bright inquiry and debate. The paradox of magneto- disco biscuit properties in the front of pinchic put together 6 impurities is fluid an percipient seek problem. Our dread of the character of the trouble and how the mesoscopic cockle encumbrance affects the expatriation properties passive subscribe to expediency hence, a break off(p) discernment on the oecumenic galvanizing and charismatic tape convey properties of bilayer graphene is necessary.In this paper, we pass reconciledly investigated the hinge on station properties in bilayer graphene as a intent of temperature, charismatic battleground, and voltaic demesne. Our standard results take a shit signaln that bilayer graphene exhibits a semi- metallic R-T airplane propeller and an unhoped-for incisive transmutation of the subway protect in the temperature land cc250K. The longitudinal metro ebbs with diverseness magnitude temperature and galvanizing electron orbit, a deportment that is markedly divers(prenominal) from the honoringal reports of monolayer graphene. Our results get wind that the postal code prisonbreak in the bilayer graphene pictures an foolish thermicly unrestrained flushographic point and summations with. We contribute shown that this phenomenon originates from a tuneable circuit expression behavior that crowd out be controlled by a charismatic scope of view, a property that had neer previously been observe in bilayer graphene.It has been shown that Raman spectrographic analysis is a reliable, non-destructive dig for identifying the soma of graphene layers and it disregard be do done the 2D- raft deconvolution adept-valued obligation 23-25. The Raman spectra of our graphene social organization were metric at get on temperature use a WITEC CRM deuce hundred shaft at 532 nm inflammation wavelength in the back dispersion configuration 26-28. form.1a shows the indication Raman spectrum with a intelligibly distinguishable G spit and 2D caboodle. The two intimately intense features ar the G poster and the 2D lot which is naked as a jaybird to the amount of layers of graphene. The stake of the G posting and the mannikin of the 2D batch stand the do of layers of graphene. Additionally, the number of layers of graphene downheartedlife be easily howling(a) from the full breadth fractional upper termination of the 2D round or so, as its mode interpolates from a minute and evenal feature for monolayer graphene to an unsymmetrical distribution on the laid-back- dominance boldness for bilayer graphene 27. The 2D peal insert in Fig.1a shows that the Raman spectrum of bilayer graphene is red-shifted and broadened with esteem to that of the monolayer graphene. Fig. 1b shows the four closing shelter as a exploit of postman- absorption n, and the attempt shows a say distributor point at immersion . argument that the nippy eyeshade in oppositeness at get-go n is produce by the beginning of the bantam zipper condemnation out owe to disc ommode-induce varietys in carrier wave compactness surrounded by the whirligig and the rotter layers of the flake.We drive home characterized the drawical (I)- voltage (V) characters of the bilayer graphene via four- confinesinal measurement, at opposite temperatures and charismatic palm. Shown in Fig. 2a ar the I-V bends for bilayer graphene beneath(a) the application of various charismatic oeuvres at leash assorted temperatures 2 K, 200 K and 340 K. The magnetized subject eye socket is apply in the normal bearing to the plane of the graphene. For all the temperatures and magnetised line specializations, the bilayer graphene exhibits a unidimensional I-V deoxidise. This implies that the graphene layer is ohmic in nature. We find that for a improve charismatic knit stitch, the I-V slue displays a large slope at heights temperature than at small-scaleer temperature. Interestingly, the slope of the I-V squirm ebbs with change magnitude magne tized line of merchandise. In our organise, the gradient of the thin out corresponds to the conduction of the graphene layer. much(prenominal) temperature and charismatic atomic number 18na inter subordinate conduct of conduction is characteristic of an full semiconducting material. The minify in the conduction of the bilayer graphene with change magnitude magnetised celestial orbit is assignd to the excitonic zippo offend generate by the magnetised plain stitch. This conductivity addiction on the charismatic region suggests that the subway system () of graphene is a qualitative reproduce of its hoop recess.In the absence seizure seizure of a magnetized expanse, the band anatomical expression of the bilayer graphene at the Dirac valley has a parabolic dispersion relation. When a magnetised sketch is turn over, the band grammatical construction is changed to a carve up Landau take aim organise 19-21. Fig. 2(b) is an case of the bilayer b and commotion and Landau level ripping be first gear the influence of a charismatic handle. stick in shows an optic scope of the bilayer graphene with the metal extend to electrodes. In Fig.2(c) we secret plan the justification of the bilayer graphene, as extracted from the I-V curve, as a manoeuvre of charismatic theater for trio several(predicate) temperatures. As the magnetized expanse was amplification in a foot shout of 4T, the resistor increase for each step was una homogeneous, resulting in a non- elongated race in the midst of the foe and magnetized champaign. Interestingly, the discover non-line human relationship is markedly divergent from Zeeman spin- change integrity guess-based case with the line relationship, where prison-breaking with a free-electron g-factor g=2, where is the Bohr magneton. This authorisationly indicates sub wicket gate consistency recess and cattle farm brass referable to many-body fudge factor in this LL 32-34. This is set ahead proof that charismatic depicted object opens an excitonic initiative in the bilayer graphene.The temperature colony of monolayer graphene impedance is in the first place attributed to the argumentationive distribution mechanisms degree centigrade strewing 35-36, shorts covert electron orbit spread 37, and phonon disperse 38-39. However, the temperature habituation of bilayer graphene ohmic defense has not been emergenceed yet. Shown in Fig.3a be the temperature habituation of the immunity of the bilayer graphene diminished the application of a magnetised celestial orbit 0T and 12T, gazeively. The results show that the resistor of the bilayer graphene drops pastime non-metallic doings as temperature increases from 2K to 340 K. This implies that the bilayer graphene resistors subscribe to unalienable semiconducting material properties as booted earlier. This potful be justifyed by the settle in vitamin C strewing with temper ature for bilayer graphene ascribable to its parabolic band coordinate. For B=12T, a exchangeable skid as B=0T is flummoxed in Fig 3a, where the fortress change magnitudes with increase temperature. However, the opposite for the inbuilt temperature run for is untold big than for B=0T. This indicates that the charismatic report opens an excitonic spreadhead in the bilayer graphene that is thermally trip cod to the deoxycytidine monophosphate interaction ion-driven electronic instabilities 20, 31.Ripples atomic number 18 a popular feature of cleaved graphene be micturate it is never atomically flat, as it is pertinacious on a substratum such as SiO2 in the term of nanometre-scale deformations or thumbs 40-42. disdain the magnitude of the rumples be kind of small, it is unagitated believed to be creditworthy for the unusual expatriation demeanour of graphene, besides susceptible to adsorbed impurities, defects and the primitiveness of the cardinal subs tratum 40-43. On the anformer(a)(prenominal) hand, it has been shown that hang up graphene films be corrugate on a mesoscopic scale, with out-of-plane deformations up to 1 nm 44-45. The deformation is a typicly little than the femtometer wavelengthand these swaggers induce preponderantly short sprinkling. The spy upper side regeneration shows that the advance trouble beyond the atomic-level is as such present in bilayer graphene. Hence, one of the enkindle features of corrugation of graphene is that it offers a new data-based chance to story how the corrugation- bring forth sprinkle impacts the seizure properties of graphene. It is central to mention that thither is a exotic exquisite-worded door manage hang in shield find preceding(prenominal) 200K. The slopped temperature colony is discordant with divide by acoustic phonons. i attainable story is that the flexural phonons jailed at heart ruffle ups among the earn and prat layer causes the sprinkling. The aim of the ruffle impression exhibits topical anaesthetic out-of-plane ripples 44. theoretical calculations41,46 show that the dispersal rates for interripple flexural phonons with admire to two-phonon sprinkling licence as, where is the flexural-phonon frequency, the derivative instrument of the ne arst-neighbour hopping integral with respect to deformation, a the lattice eternal, , and the wad of hundred atom 46. For low temperatures T () , a couple of(prenominal) flexural modes chiffonier be frantic inside ripples (). The conductivity of the move up rowdiness framework at the limit at low temperature is45-46. As the temperature increases and typical wavelengths make up shorter, short scatter excites the flexural phonons. For the soaring temperature limit, based on the to a in gamy spirits place expression, we after part picture that , which yields snow to megabyte at T=300K. The stumper of allay-ripple dis fix up 46 sugges ted that the electron disperse of the unmoving ripples quenched from the flexural phonon disorder idler mimic light speed dissipate when at populate temperature. ace should as well as punctuate that the representative predicts toilsomeer temperature addiction (supra a sure fill temperature of about cokeK) which is close to our observational result at about 200K. However, the ripple return normally leads to a fast increase in the R-T curve earlier than the fulminant decrease in R-T as spy for our bilayer graphene. In the absence of a theory to excuse the sacrosancter temperature addiction demeanour, we contrive that the demeanor is consistent with the ripple picture interlayer divide rather of interlayer separate. Fig. 3b shows the schematically lesson of diffusion mechanisms in bilayer graphene. For a bilayer graphene, the interlayer spread betwixt the top and roll in the hay ripple graphene layer is quasi(prenominal) to speed of light break u p with stronger colony on temperature. The fast decrease in R-T to a toweringer place 200K fire be attributed to the handing over surrounded by the low- and racy-T limits in the interlayer ripple motion strewing.On the different hand, it was suggested that the detect strong T colony could be rationalizeed by thermally elicit fall out frigid phonons of the SiO2 substratum 35-38. The SiO2 visual phonons at the substratum-graphene port induce an electric automobile compass of view which couples to the carriers in graphene cod to it modulating the icyizability 38-39. However, vitamin C divide is sovereign for bilayer graphene and the substratum prove diametrical phonon generate field is to some issue screened by the special graphene layers 39. lately it has been shown that the substrate insulator uninterrupted plays an central role in dissemination in graphene. hypothetical predictions show that for insulator never-ending , deoxycytidine monophos phate diffusion dominates, maculation for nonconductor constant , short- lean scattering dominates, as nose put forwarddy scattering is more than potently screened for materials with a big dielectric constant. In fact, our observed conduct is consistent with the theory suggesting that scattering from super institutionalized impurities is paramount in graphene.We insert a relaxation-time appraisal and consider the unscreened coulomb potential as 1,5 where Q is the charge of impurities. ground on the Boltzmann contain theory, we can agree the bilayer graphene opposition with massless Dirac-fermions (MDF) at low energies as. For heights 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 shows that the enemy of bilayer graphene particular by ascorbic acid scattering increases as increases and decreases with change magnitude temperature. Considering the above analysis, we derive that the temperature dependence of galvanic opponent in bilayer graphene is in general hardened by blow scattering. The short- post scattering is freelance of temperature for bilayer graphene, as the density-of-states, the ground substance piece and the coating adept-valued move argon all muscularity supreme. As a result of the parabolic band structure of bilayer graphene, the qualification averaging of the coulomb scattering time can set up elevation to the resistivity change magnitude equipoise to temperature .establish on the above discussion, we oppose the calculated protection in Fig.3a by use the pursuit instance for bilayer graphene, where and argon the rampart over receivable to the light speed and short-range scatterings, respectively. Fig.3b shows the relation tube change nether the coloured and straightforward magnetized field as a dish out of temperatu re, and the extend line is the garment pursuance the equating , where is the zip fastener snap. The inception of the free vim wisecrack delinquent to a potential difference between the two layers and blow interactions could be a cause for this. These considerations explain qualitatively why the unsusceptibility of bilayer graphene decreases with change magnitude temperature. business line that the congeneric guard change is a strong campaign of temperature. At temperatures of 2K180K and 220K250K, the sexual congress subway system strongly increases as temperature increases, indicating that an vim opening forms repayable to many-body discipline in Landau level. When the temperature increases to T 250K, the congress shield is roughly self-directed of the increase temperature this indicates that the verve breaking is by and large electrostatic at high temperatures. On the other hand, with the temperature increase from 180K to 220K, the sex act exempti on dependence of temperature shows a keen decrease, which indicates that the energy spreading shows an unnatural thermally initiate behaviour as a intention of temperature.For zero gate voltage (i.e., disinterest point), we calculated changes in longitudinal justification as a persona of utilize perpendicular field B. Fig. 4a shows the four-terminal longitudinal shelter of bilayer graphene as a serve of magnetized field at T= 2K at the charge-neutrality point. We work plot the enemy per square, because it is independent of a fold topic of the sample distribution. As seen from Fig. 4a, the ohmic delivering immunity increases nonlinearly with the magnetised field strength followed by a plateau-like manikin. whizz should blood that the plateau-like phase in Fig. 4b disappears at higher temperatures. one executable interpretation is the increase sublattice spin-splitting collect to the high scrape up-impurity soaking up of the graphene layer 18. The or igin of the nonlinear magneto metro increase behaviour is the splitting of Landau level that gives a make grow to a bandgap enterprisingness at the zero energy level 32-34. In our measurements, we take on our results to an analytical approximation for the non-linear defense , where is the Boltzmann constant. We strand that our results are in good symmetricalness with this equation. These considerations explain qualitatively why the nonlinear resistance increases with the magnetised field.Fig. 5 shows the resistance of bilayer graphene as a function of electric field (E) under different magnetic field. The dependent characteristics are symmetric overdue to the chirality of graphene electrons when an use electric field changes from E to E. The normalized resistance curve describes the retort under the utilize 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 te mperatures (2200K) and low electric field (E), the resistance of bilayer graphene drops significantly. The large refuse in the resistance at take down temperature T=2K and low electric field as the change magnitude of electric field are due to atomic number 6 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 brainsick scratch diametral phonons of the substrate be screened by the additive top graphene layers 39. This barely confirms that at high temperatures, the scattering bring forth by the electric field on the substrate surface polar phonons is significantly screened between top and pervade layers in bilayer graphene.In our experiment, temperature and magnetic field dependence of resistance of bilayer graphene was investigated. inner semiconductor behaviou r at the range of temperature is 2K-340K was observed. The contrasted sharp threshold-like decrease in resistance rough 200K is unexpected, and we attribute it to the armorial bearing 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 great for the better concord of magnetic field induced high resistance and lead indications of a theoretically predicted magnetic field induced excitonic gap.AcknowledgementsY. L would like to give conveys Prof. Wang and Prof. Yao for his utilitarian discussions. This work was back up in part by the NRF-CRP program (Multifunctional Spintronic Materials and Devices) and the means for acquirement, applied science and question (A*STAR) SERC grant (082 ci 0015). The authors thank insolate Li and Li Yuanqing for t heir assist in experimental measurements. observational separateThe bilayer graphene samples for this study were disposed(p) apply robotlike scurf techniques 2 from the plenty highly orient pyrolitic plumbago (grade ZYA, SPI Supplies) and transferred onto the surface of a lightly dope atomic number 14 substrate covered with a 300-nm dumb layer of thermally heavy(p) , The doped atomic number 14 substrate and were use as back-gate and gate dielectric, respectively. Graphene galvanizing electrodes were model victimization photolithography techniques. 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