Field and temperature dependence of intrinsic diamagnetism in graphene: Theory and experiment

Intrinsic diamagnetism of graphene is studied both theoretically and experimentally, to unravel the magnetic response of chiral massless fermions. Comprehensive formulas predicting the variation of graphene magnetization with magnetic field and temperature are developed. Graphene magnetization $M$ at low temperatures is particularly large and $M\propto -\sqrt{B}$, intrinsically different from normal materials. The quantum Berry phase of $\pi$ and linear energy dispersion are responsible for this intriguing macroscopic behavior. The temperature dependence of magnetization is successfully formulated by a Langevin-like function. The de Haas–van Alphen oscillations are predicted in the case of doping. Correspondingly, experiments at different temperatures are conducted on highly pure, mass-produced graphene flakes derived from SiC single crystals, which exhibit very strong diamagnetism. The measured results agree well with the theoretical ones in both magnitude and trend.

Figure 1

(a) A $10\times 10\times 0.3{\text{mm}}^3$ piece of graphene sample produced from SiC is levitated by 1 mm above NdFeB magnets. (b) The scanning electron microscope (SEM) image of the graphene. (c) The magnetization curve of graphene and graphite ($T=10$ K), and typical paramagnetic materials (schematic). (d) Raman spectra for graphene and graphite samples. The wavelength of the excitation laser is 532 nm.

Figure 2

(a) The band structure (BS) of graphene near the Fermi level. Electrons filled the energy levels up to the Dirac point. (b) Unevenly spaced Landau levels (LLs) in magnetic field. The zeroth Landau level is half filled. The dashed lines show how the electrons coalesce into the LLs. (c) The density of states (DOS) of the LLs is in the form of a Dirac comb with uneven energy spacing.

Figure 3

(a) Calculated and (b) measured magnetization $M$ as a function of magnetic field $B$ at different temperatures. (c) Calculated and (d) measured magnetization $M$ as a function of temperature $T$ in different magnetic fields. Note that in the theoretical part [(a) and (c)], the numerical results are plotted as a series of markers, and analytical approximations as continuous lines, while the experimental results [(b) and (d)] are represented by markers joined by lines.

Figure 4

The calculated magnetic properties of doped graphene. (a), (c) Dependence of grand potential and magnetization on the chemical potential at different temperatures. (b), (d) Dependence of magnetization on magnetic field and temperature at different doping levels.