Department of Physics, Indian Institute of Technology-Kanpur, Kanpur 208 016, India.
J Phys Condens Matter. 2011 Nov 9;23(44):445502. doi: 10.1088/0953-8984/23/44/445502. Epub 2011 Oct 18.
The effect of magnetic modulation on thermodynamic properties of a graphene monolayer in the presence of a constant perpendicular magnetic field is reported here. One-dimensional spatial electric or magnetic modulation lifts the degeneracy of the Landau levels and converts into bands and their bandwidth oscillates with magnetic field, leading to Weiss-type oscillations in the thermodynamic properties. The effect of magnetic modulation on the thermodynamic properties of a graphene sheet is studied and then compared with electrically modulated graphene and magnetically modulated conventional two-dimensional electron gas (2DEG). We observe Weiss-type and de Haas-van Alphen oscillations at low and high magnetic fields, respectively. There is a definite phase difference in Weiss-type oscillations in thermodynamic quantities of magnetically modulated graphene compared to electrically modulated graphene. On the other hand, the phase remains the same and the amplitude of the oscillation is large when compared with the magnetically modulated two-dimensional electron gas (2DEG). Explicit asymptotic expressions of the density of states and the Helmholtz free energy are provided to understand the phase and amplitude of the Weiss-type oscillations qualitatively. We also study thermodynamic properties when both electric and magnetic modulations are present. The Weiss-type oscillations still exist when the modulations are out-of-phase.
本文报道了在恒定垂直磁场存在下，磁场调制对单层石墨烯热力学性质的影响。一维空间电场或磁场调制消除了朗道能级的简并性，转化为能带，其带宽随磁场振荡，导致热力学性质中出现魏泽型振荡。研究了磁场调制对石墨烯片热力学性质的影响，然后将其与电调制石墨烯和磁调制传统二维电子气（2DEG）进行了比较。我们在低磁场和高磁场下分别观察到魏泽型和德哈斯-范阿尔芬振荡。与电调制石墨烯相比，磁场调制石墨烯中热力学量的魏泽型振荡存在确定的相位差。另一方面，与磁调制二维电子气（2DEG）相比，相位相同，振荡幅度较大。提供了态密度和亥姆霍兹自由能的显式渐近表达式，以定性地理解魏泽型振荡的相位和幅度。我们还研究了当同时存在电和磁场调制时的热力学性质。当调制失相时，魏泽型振荡仍然存在。
