Study of the Shubnikov-de Haas Effect. Determination of the Fermi Surfaces in Graphite
Study of the Shubnikov-de Haas Effect. Determination of the Fermi Surfaces in Graphite
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舒布尼科夫-德哈斯效应的研究。
DOI：
10.1103/physrev.134.a453
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发表时间：
1964
期刊：
影响因子：
--
通讯作者：
L. B. Smith
中科院分区：
文献类型：
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作者：
D. E. Soule;J. W. Mcclure;L. B. Smith
本文测量了高质量石墨单晶在磁场与c轴夹角为θ，磁场强度为24 kG，温度为1.22 ~ 4.22K时的振荡磁电阻。结果进行了分析，通过最小二乘法拟合到一个广义的朗道公式。由于电子振荡观察到所有的方向（包括H c，其中的幅度下降了10 - 5倍），证明电子费米面是封闭的。虽然在θ = 84以后没有观察到空穴引起的振荡，但间接的论证表明空穴费米面也是闭合的。电子和空穴表面都沿c轴沿着伸长，各向异性比分别为12.1±1.4和约17。电子表面近似为椭圆形，而空穴表面类似，除了延伸的末端使其具有钻石状形状。结果与关于c轴的中等程度的三角不对称性是一致的。从电子费米面的体积发现的电子密度和先前确定的非振荡电流磁数据之间的比较证实了理论预测，有四个电子费米面的布里渊区。更多的间接论证表明存在两个孔曲面。考虑这些表面的大小和位置沿着平行于c轴的六个带边缘，导致带参数的新确定Δ E − 0.12 eV，它代表石墨晶格中两种类型原子位置之间的电势差。通过分析温度和磁场对振荡振幅的影响，得到了基底面的有效质量值为（0.039±0. 001）。0 0 1）m0和（0 0 5 7 ±0. 0 0 2）m 0为孔。这些质量显示出与导出的费米表面各向异性的取向依赖性是一致的。亚当斯和荷尔斯泰因的理论准确地描述了在1.26和4.22 K时测量的H ε c的大幅度和非对称形状的磁导率振荡。然而，在总的磁导率有一个无法解释的单调变化与磁场。由碰撞增宽引起的有效温度变化Δ T比由电导弛豫时间估计的温度变化大5倍左右。定性地解释了Δ T的这种差异，并与Berlincourt和Steele的数据建立的事实直接相关，即在同一样品上，从磁阻振荡中发现的Δ T大于从磁化率振荡中发现的Δ T。
Measurements of the oscillatory magnetoresistance of a high-quality graphite single crystal were made for all angles θ between the magnetic field and the c axis, for magnetic fields up to 24 kG, and for temperatures from 1.22 to 4.22 K. The results were analyzed by a least-squares fitting to a generalized Landau formula. Oscillations due to electrons were observed for all orientations (including H⊥ c, where the amplitude dropped by a factor 10 5), proving that the electron Fermi surfaces are closed. Although oscillations due to holes were not observed beyond θ≃ 84, indirect arguments show that the hole Fermi surfaces are also closed. Both electron and hole surfaces are elongated along the c axis and have anisotropy ratios of 12.1±1.4 and about 17, respectively. The electron surface is approximately ellipsoidal, whereas the hole surface is similar except for extended ends giving it a diamond-like shape. The results are consistent with a moderate degree of trigonal asymmetry about the c axis. Comparison between the electron density found from the volume of the electron Fermi surfaces and that determined previously from the nonoscillatory galvanomagnetic data confirms the theoretical prediction that there are four electron Fermi surfaces in the Brillouin zone. More indirect arguments show that there are two hole surfaces. Consideration of the size and location of these surfaces along the six zone edges parallel to the c axis leads to a new determination of Δ≃− 0.12 eV for the band parameter which represents the difference of potential between the two types of atomic sites in the graphite lattice. Analysis of the temperature and magnetic field dependence of the oscillatory amplitude yields effective mass values in the basal plane of (0.039±0. 0 0 1) m 0 for electrons and (0.057±0. 0 0 2) m 0 for holes. These masses show an orientation dependence that is consistent with the derived Fermi surface anisotropies. The large amplitude and asymmetric shape of the oscillations in the magnetoconductivity, measured for H∥ c at 1.26 and 4.22 K, are accurately described by the theory of Adams and Holstein. However, there is an unexplained monotonic variation with magnetic field in the total magnetoconductivity. The effective change in temperature due to collision broadening Δ T is about 5 times greater than that estimated from the conductivity relaxation time. This discrepancy in Δ T is qualitatively explained and is related directly to the fact, established from the data of Berlincourt and Steele, that the Δ T found from magnetoresistance oscillations is greater than that found from susceptibility oscillations on the same sample.