Observation of Landau-level-like quantization at 77 K along a strained-induced graphene ridge

Abstract

Recent studies show that the electronic structures of graphene can be modified by strain and it was predicted that strain in graphene can induce peaks in the local density of states (LDOS) mimicking Landau levels (LLs) generated in the presence of a large magnetic field. Here we report scanning tunnelling spectroscopy (STS) observation of nine strain-induced peaks in LDOS at 77 K along a graphene ridge created when the graphene layer was cleaved from a sample of highly oriented pyrolytic graphite (HOPG). The energies of these peaks follow the progression of LLs of massless 'Dirac fermions' (DFs) in a magnetic field of 230 T. The results presented here suggest a possible route to realize zerofield quantum Hall-like effects at 77 K.The physics of 'Dirac fermions' (DFs) in condensedmatter has received a great deal of attention, in part because it has opened up a new area of fundamental science and also for its long-term potential applications [1][2][3][4][5][6][7]. In monolayer graphene, the DFs move as if they were massless at the Fermi velocity v F ~ 10 6 m/s. The quantumrelativistic nature of the massless DFs was obtained through the appearance of the unusual Landau levels (LLs) energy spectrum, which consists of a sequence of levels with square-root dependence on both magnetic field and level index n and a unique level n = 0 at an energy that is pinned to the Dirac point E D [5]. Upon cleaving a highly oriented pyrolytic graphite (HOPG) sample, strains can be induced in the resultant graphene layer forming foldedover structure, wrinkles, and ridges [8,9]. These surface structures provide model systems for the study of the coupling between the graphene and the underlayers [10][11][12][13][14]. Recently, it was shown that strain induced gauge field can be used to alter and tailor the electronic structure of graphene. This opens a possible avenue towards allgraphene electronics [15][16][17][18]. Defects in the form of nanobubbles are also found on chemical vapor deposited graphene layer [17]. Levy and co-authors observed three peaks in scanning tunnelling spectroscopy (STS) spectra at positive voltage bias measured at 7.5 K under zero magnetic field and show evidence that these peaks mimic LLs of massless DFs generated in the presence of large magnetic field [17]. Here, we present STS results at 77 K showing 9 distinct peaks in the tunnelling spectra along a graphene ridge on HOPG produced during the cleaving process. The energy values of these 9 peaks follows the sequence of LLs of massless DFs in a magnetic field. The deviations from the expected values of energies of the peaks are also observed. Such deviations are reasonable since these peaks are not results of Landau level quantizations in a real magentic field but the consequence of the distortion of the local density of states (LDOS) induced by strain.The scanning probe microscope (STM) system used in the experiments is an ultrahigh vacuum four-probe STM from UNISOKU. All the STM and STS measurements were carried out at liquid-nitrogen temperature in a cons...

Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer

“…The pseudomagnetic field of the strained wrinkle estimated according to the spectrum is about 100 T. The wrinkle is one of the simplest model to study the strain-induced pseudo-magnetic flux of a corrugated graphene sheet 7 . The flux of the wrinkle can be estimated by U ¼ (bh 2 /la)U 0 (here h is the height, l is the width of the wrinkle, 2obo3, a is on the order of the C-C bond length and U 0 is the flux quantum) 7,11,12 . It is unexpected that the strain-induced LL-like quantizations of the twisted graphene bilayer are identical to the Landau quantizations of the massive chiral Fermions in Bernal stacking graphene bilayer in an external magnetic field 16 .…”

“…Usually, a constant pseudomagnetic field can be achieved when the honeycomb lattice are transversely displaced from their original positions in the following way (u r ,u f ) ¼ qr 2 (sin3f,cos3f), where u r and u f are the radial and azimuthal displacements, f is the azimuthal angle, r is the distance from anbitrary origin and q is a parameter corresponding to the strength of the strain 8,[11][12][13][14] . This uniform pseudomagnetic field is not easy to realize in the strained graphene [11][12][13][14] . Our experiment also confirms that the pseudomagnetic field is not uniform along the wrinkle Supplementary Fig.…”

“…It is now well established that lattice deformations of graphene lead to the appearance of a pseudomagnetic gauge field acting on the charge carriers 2,[3][4][5][6][7][8][9][10] . The pseudomagnetic field becomes an experimental reality after the observation of Landau levels (LLs) in a strained graphene monolayer [11][12][13][14] and in strained artificial graphene 15 . The energies of these LLs follow the progression of LLs of massless Dirac Fermions, which suggest a possible route to realize zero-field quantum Hall effects in the strained graphene [11][12][13][14][15] .…”

“…The pseudomagnetic field becomes an experimental reality after the observation of Landau levels (LLs) in a strained graphene monolayer [11][12][13][14] and in strained artificial graphene 15 . The energies of these LLs follow the progression of LLs of massless Dirac Fermions, which suggest a possible route to realize zero-field quantum Hall effects in the strained graphene [11][12][13][14][15] . Compared with single-layer graphene, graphene bilayers, including AA stacked, AB stacked (Bernal) and twisted graphene bilayer, display even more complex electronic band structures and intriguing properties because of the interplay of quasiparticles between the Dirac cones on each layer [16][17][18][19][20][21][22][23][24][25][26][27][28] .…”

Modeling and Simulation of Graphene Based Polymer Nanocomposites: Advances in the Last Decade

“…The first-principles calculations show that atomic-scale defects result in both intravelley and intervalley scattering of graphene and Fermi velocity is decreased in the vicinity of the defects due to enhanced scattering [60]. The electronic properties of graphene are strongly influenced by structural defects that deform the original honeycomb lattice [61] [62].…”