Graphite as a bose metal

Yakov Kopelevich
2003 Brazilian journal of physics  
Although a considerable amount of the research work has been done on graphite, its physical properties are still not well understood, and novel phenomena such as the magnetic-field-driven metal-insulator transition (MIT), the quantum Hall effect, ferromagnetic and superconducting correlations have recently been revealed. Theoretical analysis suggests that the MIT in graphite is the condensed-matter realization of the magnetic catalysis phenomenon known in relativistic theories of (2 + 1)
more » ... s of (2 + 1) -dimensional Dirac fermions (DF), i. e. that the applied field opens an insulating gap in the spectrum of DF, associated with the electron-hole pairing. On the other hand, we demonstrate in this paper that a two parameter scaling analysis proposed by Das and Doniach [D. Das and S. Doniach, Phys. Rev. B 64, 134511 (2001)] to characterize the magnetic-field-tuned Bose metal -insulator transition can be well applied to the MIT observed in graphite. We discuss the possibility that the MIT in graphite is associated with the transition between Bose metal and excitonic insulator states. The apparent metal-insulator transition (MIT) in twodimensional (2D) electron (hole) systems which takes place either varying carrier concentration or applying a magnetic field H has attracted a broad research interest [1]. Recently, a similar MIT driven by a magnetic field applied perpendicular to basal planes has been reported for graphite [2 -5], and attributed to the metal -excitonic insulator transition [6] [7] [8] . In this paper we demonstrate that the MIT in graphite can also be understood as a Bose metal -insultor transition (BM-IT). In particular, it is found that the two parameter scaling analysis proposed by Das and Doniach [9] to characterize the BM-IT in 2D systems can be well applied to the MIT measured in graphite. We speculate that the MIT in graphite is associated with the transition between Bose metal and excitonic insulator states. Magnetotransport measurements have been performed on several well-characterized [4, 5] quasi-2D highly oriented pyrolitic graphite (HOPG) samples obtained from the Research Institute "Graphite" (Moscow) and the Union Carbide Co. Here, we present the results of the basalplane resistance R b (H, T ) measurements obtained on two HOPG samples with the room temperature, zero-field outof-plane/basal-plane resistivity ratio ρ c /ρ b = 5 × 10 4 and ρ b (T = 300K) = 3µΩcm and ρ b (T = 300K) = 5µΩcm for the samples labeled respectively as HOPG-UC and HOPG-3. Low-frequency (f = 1 Hz) and dc standard fourprobe magnetoresistance measurements were performed on samples with dimensions 4 × 4 × 1.2mm 3 (HOPG-3) and 5 × 5 × 1mm 3 (HOPG-UC) in the temperature interval 2K ≤ T ≤ 300K using different 9 T-magnet He-cryostats. For the measurements, silver past electrodes were placed on the sample surface, while the resistivity values were obtained in a geometry with an uniform current distribution through the sample cross section. All resistance measure-ments were performed in the Ohmic regime in both H caxis and H ⊥ c-axis applied magnetic field configurations. The transition from metallic-(dR b /dT > 0) to insulator-like (dR b /dT < 0) behavior of the basal-plane resistance R b (T, H) driven by a magnetic field applied perpendicular to the graphene planes has been observed for all studied graphite samples. Fig. 1 presents R b (T, H) measured for the HOPG-UC sample. As can be seen from Fig. 1 , R b (T ) has a metallic character at zero or low enough fields. As the applied field exceeds H ∼ 0.5 . . . 1 kOe, R b (T ) becomes insulating-like, suggesting the occurrence of MIT driven by the magnetic field. Fig. 1 shows that R b (T ) goes through a shallow minimum at the field-dependent temperature T min (H > H c ), where H c is a threshold field below which the metallic state of graphite is preserved, and Fig. 2 gives a detailed view of the resistance minimum. It has been demonstrated [5, 10] that the magnetic field component perpendicular to basal graphite planes solely drives the MIT imposing certain constrains on theoretical approaches to the MIT. The characteristic feature of the band structure of a single graphene layer is that there are two isolated points in the first Brillouin zone where the band dispersion is linear E(k) = v|k| (v = v F ∼ 10 6 m/s is the Fermi velocity), so that the electronic states can be described in terms of Dirac equations in two dimensions similar to, for instance, quasiparticles near the gap nodes in superconducting cuprates. The theoretical analysis [6 -8] suggests that the MIT in graphite is the condensed-matter realization of the magnetic catalysis (MC) phenomenon known in relativistic theories of (2 + 1) -dimensional Dirac fermions. According to the theory, the magnetic field applied perpendicular to the graphene planes opens an insulating gap in the spectrum of Dirac fermions, associated with an electron-hole pairing, leading
doi:10.1590/s0103-97332003000400020 fatcat:hm5qrkuzwzbwpgehm3ivhur57i