Mapping Dirac quasiparticles near a single Coulomb impurity on graphene

Abstract

*These authors contributed equally to this workThe response of Dirac fermions to a Coulomb potential is predicted to differ significantly from the behavior of non-relativistic electrons seen in traditional atomic and impurity systems [1][2][3] . Surprisingly, many key theoretical predictions for this ultra-relativistic regime have yet to be tested in a laboratory [4][5][6][7][8][9][10][11][12] . This small value of g ε indicates that microscopic electron-electron interactions can contribute significantly to graphene properties.Our experiment was performed using a scanning tunneling microscope (STM) in UHV at T = 4.8K to probe back-gated devices consisting of CVD-grown graphene 17 placed on top of boron nitride (BN) flakes 18 on a SiO 2 /Si surface (see Supplementary Materials for methods).Utilization of BN substrates significantly reduces the charge inhomogeneity of graphene 19,20 , thus allowing us to probe the intrinsic graphene electronic response to individual charged impurities. The charged impurities probed in this work were cobalt trimers constructed on graphene by atomically manipulating cobalt monomers with the tip of an STM 21 (cobalt atoms were deposited via e-beam evaporation onto low temperature graphene samples).Figs.1 a-f show the process of manipulating three cobalt monomers to create a single Co trimer on graphene (the detailed interior structure of the Co trimer cannot be resolved due to its instability under high current measurement).Co trimers were used in this study because they form a robust, reproducible impurity whose charge can be toggled on and off through the use of a back-gate electrode. Co monomers (which can also be charge-toggled) were unsuitable for this study due to the fact that their charge state switches in the proximity of an STM tip 22 (thus leading to spatially inhomogeneous ionization features that mask the intrinsic graphene response to a Coulomb impurity of fixed charge). Co trimers are ideal because they can be prepared in different charge states (through back-gating) that are charge-stable in the proximity of an STM tip. This is shown in the spectroscopic data of Figs. 1g and 2. Fig. 1g shows STM spectra 3 acquired with the STM tip held directly over a single Co trimer for two different back-gate voltages (V g ). Following the analysis of Ref. 22, the Co trimer impurity state marked R is seen to lie below the Fermi level (E F ) for V g = +14V, in which case it is filled by an electron, while it lies above E F for V g = -2V, in which case the electron has been removed from the trimer. The R state arises from the local cobalt-graphene hybridization and is undetectable at distances greater than r 0 = 1.5nm from the trimer center, demonstrating that short-range cobalt-graphene interactions end at r 0 . The spectroscopic feature marked S arises due to tip-induced ionization of the trimer and thus confirms the charging nature of the impurity state R 22-25 .The gate-dependent charge states of the Co trimer were determined by performing dI/dV mapping of the surrounding grap...

Optimal traps in graphene

“…Despite the appearance of sophisticated experimental techniques for probing resonances and the modification of the density of states in the continuum [22], the search for fully confined (square-integrable) states remains a significant ongo-ing task. Efficient manipulation of the Fermi level requires the presence of a back gate in close proximity to the graphene, which makes the numerous beautiful results stemming from the long-range behavior of the bare Coulomb potential [9] somewhat far from experimental reality, as the presence of image charges in the gate material (or screening effects) makes any realistic potential fall at large distances more rapidly than 1/r [21].…”

Tailoring the Magnetism of Co Atoms on Graphene through Substrate Hybridization

“…It was proposed as a perfect spin filter between two ferromagnetic electrodes [2,3], isolated adsorbed magnetic impurities were employed to tailor its electronic [4,5] and spin transport properties [6], and it was used as a capping layer to increase the magnetic anisotropy of ultra thin films [7,8]. In addition, giant magnetic anisotropies were predicted for 3d metal atoms and dimers on graphene [9,10] or on graphene C vacancies [11], suggesting long spin relaxation times with the potential for quantum information processing in single adatoms.…”

Limit cycles in renormalization group dynamics

“…©ÂAEÂÚ ÄÐÇÛÐÇÅÑ ÊÂÓâAEÂ Ä ÅÓÂ×ÇÐÇ ÑÃÔÖÉAEÂÎÂÔß Ä ÕÇÑÓÇÕËÚÇÔÍËØ [24 ë 26] Ë àÍÔÒÇÓËÏÇÐÕÂÎßÐÞØ [27,28] ÓÂÃÑÕÂØ. ±ÑÍÂÊÂÐÑ, ÚÕÑ ÔÖÜÇÔÕÄÖÇÕ ÃÂÛÐâ "ÍÄÂÊËÓËAE-ÃÇÓÅÑÄÔÍËØ" ÔÑÔÕÑâÐËÌ Ô àÍÔÒÑÐÇÐÙËÂÎßÐÞÏ ÔÍÇÌÎËÐÅÑÏ [29].…”