Tunable Kondo effect in graphene with defects

Abstract

Graphene is a model system for the study of electrons confined to a strictly two-dimensional layer 1 and a large number of electronic phenomena have been demonstrated in graphene, from the fractional 2,3 quantum Hall effect to superconductivity 4 . However, the coupling of conduction electrons to local magnetic moments 5,6 , a central problem of condensed-matter physics, has not been realized in graphene, and, given carbon's lack of d or f electrons, magnetism in graphene would seem unlikely. Nonetheless, magnetism in graphitic carbon in the absence of transition-metal elements has been reported 7-9 , with explanations ranging from lattice defects 10 to edge structures 11 to negative curvature regions of the graphene sheet 12 . Recent experiments suggest that correlated defects in highly-ordered pyrolytic graphite (HOPG), induced by proton irradiation 8 or native to grain boundaries 7 , can give rise to ferromagnetism. Here we show that point defects (vacancies) in graphene 13 are local moments which interact strongly with the conduction electrons through the Kondo effect 6,14-16 , providing strong evidence that defects in graphene are indeed magnetic. The Kondo temperature T K is tunable with carrier density from 30 to 90 K; the high T K is a direct consequence of strong coupling of defects to conduction electrons in a Dirac material 16 .We previously reported the resistivity of graphene with vacancies induced by ion irradiation in ultra-high vacuum (UHV; ref. 13). Here we present a detailed study of the gate voltage (V g ) and temperature (T ) dependence of the resistivity ρ(V g , T ) in similar graphene with vacancies over a wider temperature range 300 mK < T < 290 K. Apart from weak-localization (WL) corrections 17,18 , we find that ρ(V g ,T ) is explained by a temperatureindependent contribution ρ c (V g ) due to non-magnetic disorder plus a temperature-dependent contribution ρ K (V g ,T ), not present in as-prepared graphene 13 , which follows the universal temperature dependence expected for Kondo scattering from a localized 1/2-spin with a single scaling parameter T K .Graphene with vacancies is prepared as described in ref. 13. After irradiation, the devices were annealed overnight at 490 K in UHV, and then exposed to air during transfer to a 3 He samplein-vacuum cryostat. Figure 1a shows σ (V g ) measured at 17 K for a graphene device (sample Q6) before irradiation, immediately after irradiation, and measured at 300 mK after annealing and transfer to the 3 He cryostat. V g is applied to the Si substrate to tune the carrier density n = c g V g /e, where c g = 1.15×10 −8 F cm −2 is the gate capacitance, and e the elementary charge. The mobility of the device is approximately 4000, 300, and 2000 cm 2 V −1 s −1 , respectively, for these three measurements; the conductivity and mobility recover significantly after annealing and air exposure, consistent with our previous study 13 . From the post-annealing mobility we estimate that this device has a defect density, n imp , of approximately 3×10 11 cm −2 , alt...

Atomic defect states in monolayers of MoS2 and WS2

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Simulation of high-energy ion collisions with graphene fragments

“…Ion irradiation can be used to introduce structural defects in graphene and other carbon allotropes 16 , and provides a versatile tool for manipulating their physical properties 7,[17][18][19][20][21][22] For this purpose, proton irradiation, in particular, attracts much interest due to the observed irradiation-induced magnetism in graphite and graphene [23][24][25][26][27][28][29] , which was attributed to defects, e.g., vacancies and H species 24 . However, an atomic-resolved determination, e.g.…”

A non-perturbative treatment of quantum impurity problems in real lattices

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