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Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene

机译：广义Landau能级表示：静态筛选在石墨烯的量子霍尔效应中的作用

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摘要

By making use of the generalized Landau level representation (GLLR) for the quasiparticle propagator, we study the effect of screening on the properties of the quantum Hall states with integer filling factors in graphene. The analysis is performed in the low-energy Dirac model in the mean-field approximation, in which the long-range Coulomb interaction is modified by the one-loop static screening effects in the presence of a background magnetic field. By utilizing a rather general ansatz for the propagator, in which all dynamical parameters are running functions of the Landau level index n, we derive a self-consistent set of the Schwinger-Dyson (gap) equations and solve them numerically. The explicit solutions demonstrate that static screening leads to a substantial suppression of the gap parameters in the quantum Hall states with a broken U(4) flavor symmetry. The temperature dependence of the energy gaps is also studied. The corresponding results mimic well the temperature dependence of the activation energies measured in experiment. It is also argued that, in principle, the Landau level running of the quasiparticle dynamical parameters could be measured via optical studies of the integer quantum Hall states.
机译：通过使用准粒子传播子的广义Landau能级表示（GLLR），我们研究了屏蔽对石墨烯中具有整数填充因子的量子霍尔态性质的影响。该分析是在低能量Dirac模型中以均值场近似进行的，其中在背景磁场存在下，通过单环静态屏蔽效应来修正远程库仑相互作用。通过将一个相当普通的ansatz用于传播器，其中所有动力学参数都是Landau级指数n的运行函数，我们导出了Schwinger-Dyson（gap）方程的一个自洽集合，并对其进行了数值求解。明确的解决方案表明，静态筛选导致具有破坏的U（4）风味对称性的量子霍尔态中的间隙参数得到了显着抑制。还研究了能隙的温度依赖性。相应的结果很好地模拟了实验中测得的活化能的温度依赖性。也有人认为，原则上，可以通过对整数量子霍尔态的光学研究来测量准粒子动力学参数的Landau能级运行。

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  • 来源
    《Physical review》 |2016年第3期|035454.1-035454.15|共15页
  • 作者

    Igor A. Shovkovy; Lifang Xia;

  • 作者单位

    College of Letters and Sciences, Arizona State University, Mesa, Arizona 85212, USA;

    Department of Physics, Arizona State University, Tempe, Arizona 85287, USA;

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