Tunable Kondo effect in graphene with defects

Nature Physics, Apr 2011

Graphene is a model system for the study of electrons confined to a strictly two-dimensional layer1 and a large number of electronic phenomena have been demonstrated in graphene, from the fractional2,3 quantum Hall effect to superconductivity4. However, the coupling of conduction electrons to local magnetic moments5,6, 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 reported7,8,9, with explanations ranging from lattice defects10 to edge structures11 to negative curvature regions of the graphene sheet12. Recent experiments suggest that correlated defects in highly-ordered pyrolytic graphite (HOPG), induced by proton irradiation8 or native to grain boundaries7, can give rise to ferromagnetism. Here we show that point defects (vacancies) in graphene13 are local moments which interact strongly with the conduction electrons through the Kondo effect6,14,15,16, providing strong evidence that defects in graphene are indeed magnetic. The Kondo temperature TK is tunable with carrier density from 30 to 90 K; the high TK is a direct consequence of strong coupling of defects to conduction electrons in a Dirac material16.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://www.nature.com/articles/nphys1962.pdf

Tunable Kondo effect in graphene with defects

Abstract Graphene is a model system for the study of electrons confined to a strictly two-dimensional layer1 and a large number of electronic phenomena have been demonstrated in graphene, from the fractional2,3 quantum Hall effect to superconductivity4. However, the coupling of conduction electrons to local magnetic moments5,6, 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 reported7,8,9, with explanations ranging from lattice defects10 to edge structures11 to negative curvature regions of the graphene sheet12. Recent experiments suggest that correlated defects in highly-ordered pyrolytic graphite (HOPG), induced by proton irradiation8 or native to grain boundaries7, can give rise to ferromagnetism. Here we show that point defects (vacancies) in graphene13 are local moments which interact strongly with the conduction electrons through the Kondo effect6,14,15,16, providing strong evidence that defects in graphene are indeed magnetic. The Kondo temperature TK is tunable with carrier density from 30 to 90 K; the high TK is a direct consequence of strong coupling of defects to conduction electrons in a Dirac material16. Main 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 (Vg) and temperature (T) dependence of the resistivity ρ(Vg,T) in similar graphene with vacancies over a wider temperature range 300 mK<T<290 K. Apart from weak-localization (WL) corrections17,18, we find that ρ(Vg,T) is explained by a temperature-independent contribution ρc(Vg) due to non-magnetic disorder plus a temperature-dependent contribution ρK(Vg,T), not present in as-prepared graphene13, which follows the universal temperature dependence expected for Kondo scattering from a localized 1/2-spin with a single scaling parameter TK. 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 3He sample-in-vacuum cryostat. Figure 1a shows σ(Vg) 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 3He cryostat.Vg is applied to the Si substrate to tune the carrier density n=cgVg/e, where cg=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 cm2 V−1 s−1, respectively, for these three measurements; the conductivity and mobility recover significantly after annealing and air exposure, consistent with our previous study13. From the post-annealing mobility we estimate that this device has a defect density, nimp, of approximately 3×1011 cm−2, although greater understanding of the effects of annealing and ambient exposure on vacancies in graphene is needed. See Supplementary Information for the calculation of defect density and also Raman spectra of the device before and after irradiation. Slight asymmetry between electron and hole conduction in the σ(Vg) curve is also observed in the irradiated sample, which could indicate a non-zero on-site energy for the defects in graphene19. Figure 1: Gate voltage dependent conductivity σ(Vg) and magnetoresistance of the graphene sample. a, σ(Vg) of the graphene sample Q6 before (black solid line) and after (red dashed line) irradiation with 500 eV He+ at a temperature T=17 K, and after annealing at 490 K overnight in ultra-high vacuum and exposure to ambient before cooling to T=300 mK (blue short-dashed line). Magnetic field B=0 for all data. The gate voltage of minimum conductivity V g,min=−8 V, 5 V, 5.3 V for pristine, irradiated and annealed sample, respectively. b, Magnetoresistance of irradiated and annealed graphene sample for B=0–8 T at various Vg. c, Normalized detailed magnetoresistance of irradiated and annealed graphene sample from −1.2 to 1.2 T at Vg−V g,min≈−65 V. Full size image Figure 1b shows the perpendicular magnetic field dependence of the resistivity ρ(B) of the irradiated sample Q6 at T=300 mK at several different gate voltages. Negative magnetoresistance is observed at small B, indicating the dominance of weak localization arising from intervalley scattering due to lattice defects17,18. Figure 1c shows a detail of the magnetoresistance at small B, at 300 mK and at Vg−V g,min=−65 V (see Supplementary Information for the gate voltage and temperature dependent phase coherence length, which is extracted from analyzing the WL magnetoresistance). Shubnikov–de Haas (SdH) oscillations appear at high B field. To measure the resistivity without WL and SdH corrections, the WL contribution is suppressed by application of B=1 T in (...truncated)


This is a preview of a remote PDF: https://www.nature.com/articles/nphys1962.pdf

Jian-Hao Chen, Liang Li, William G. Cullen, Ellen D. Williams, Michael S. Fuhrer. Tunable Kondo effect in graphene with defects, Nature Physics, 2011, pp. 535-538, Issue: 7, DOI: 10.1038/nphys1962