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arXiv 1907.09153cond-mat.str-el
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量子极限下三维半金属的基态图谱

Ground-state atlas of a three-dimensional semimetal in the quantum limit

Zhiming Pan, Ryuichi Shindou

摘要:

在强磁场作用下,三维半金属中电子关联和朗道量子化降维的相互作用产生了奇异的电子相。利用无偏的理论方法,我们首次阐明了在量子极限下具有一对电子和空穴口袋的三维半金属的全面的基态相图。对于电子相互作用,我们考虑屏蔽库仑排斥相互作用或由屏蔽电子-声子耦合介导的吸引电子-电子相互作用,其中屏蔽长度通常由无量纲常数乘以磁长度$l$给出。通过数值求解parquet RG方程和采用平均场参数,我们构建了这两种情况下量子极限下半金属的全面基态相图,作为费米波长和屏蔽长度的函数(均由$l$归一化)。在排斥相互作用的情况下,基态要么是强屏蔽区的激子绝缘体(EI),要么是弱屏蔽区的Ising型自旋密度波。在吸引相互作用的情况下,基态是破坏平移对称性的EI(强屏蔽区)、拓扑EI、电荷维格纳晶体(中间屏蔽区)、普通电荷密度波或可能的非费米液体(弱屏蔽区)。我们证明了拓扑EI在其侧面支持一个无质量狄拉克费米子的单拷贝,从而在面内表面输运中表现出$\sqrt{H_{\perp}}$型表面Shubnikov-de Haas(SdH)振荡作为倾斜磁场$H_{\perp}$的函数。有了这些理论知识,我们讨论了最近的高场下石墨输运实验的影响。

英文摘要:

An interplay between electron correlation and reduced dimensionality due to the Landau quantization gives rise to exotic electronic phases in three-dimensional semimetals under high magnetic field. Using an unbiased theoretical method, we clarify for the first time comprehensive ground-state phase diagrams of a three-dimensional semimetal with a pair of electron and hole pockets in the quantum limit. For the electron interaction, we consider either screened Coulomb repulsive interaction or an attractive electron-electron interaction mediated by a screened electron-phonon coupling, where a screening length is generally given by a dimensionless constant times magnetic length $l$. By solving the parquet RG equation numerically and employing a mean-field argument, we construct comprehensive ground-state phase diagrams of the semimetal in the quantum limit for these two cases, as a function of the Fermi wave length and the screening length (both normalized by $l$). In the repulsive interaction case, the ground state is either excitonic insulator (EI) in strong screening regime or Ising-type spin density wave in weak screening regime. In the attractive interaction case, the ground state is either EI that breaks the translational symmetries (strong screening regime), topological EI, charge Wigner crystal (intermediate screening regime), plain charge density wave or possible non-Fermi liquid (weak screening regime). We show that the topological EI supports a single copy of massless Dirac fermion at its side surface, and thereby exhibit a $\sqrt{H_{\perp}}$-type surface Shubnikov-de Haas (SdH) oscillation in in-plane surface transports as a function of a canted magnetic field $H_{\perp}$. Armed with these theoretical knowledge, we discuss implications of recent transport experiments on graphite under the high field.

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