The Impact of Electric and Magnetic Fields on the Quantum Capacitance of Monolayer Germanene

IF 0.9 4区 物理与天体物理 Q4 PHYSICS, CONDENSED MATTER
Do Muoi
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Abstract

In this work, we present the theory of quantum capacitance in two-dimensional buckled germanene. Germanene is a material with a natural bandgap and strong spin–orbit interaction, offering significant advantages over graphene. The results of this study reveal the behavior of the quantum capacitance in response to variations in the spin–orbit interaction and electric field. The capacitance in each valley can be adjusted with the electric field, shifting from a minimum to a maximum as the external gate voltage is applied. The total capacitance, derived from both the K and K ′ valleys, shows a tunable band gap at \({{E}_{{\text{F}}}} = 0\). When the electric field energy \({{\Delta }_{z}} = 2{{{{\lambda }}}_{{{\text{so}}}}}\), the capacitance is zero at \({{E}_{{\text{F}}}} = 0\), whereas the electric field energy \({{\Delta }_{z}} = {{{{\lambda }}}_{{{\text{so}}}}}\), the capacitance reaches maximum with a single peak at \({{E}_{{\text{F}}}} = 0\) and electron–hole symmetric spectrum. As the electric field affects the band structure, the spin-up states retain their energy gap, whereas the spin-down states converge. Shubnikov–de Haas oscillations in quantum capacitance are also observed, showing a be-ating pattern at low magnetic fields that disappears as the electric field dominates. At higher magnetic fields, the splitting of the oscillations becomes evident. The disappearance of beating pattern and subsequent oscillation splitting are attributed to the interplay between the spin–orbit interaction, electric field, and magnetic field.

Abstract Image

电场和磁场对单层锗烯量子电容的影响
在这项工作中,我们提出了二维屈曲锗烯的量子电容理论。日耳曼烯是一种具有天然带隙和强自旋轨道相互作用的材料,与石墨烯相比具有显著的优势。研究结果揭示了量子电容对自旋轨道相互作用和电场变化的响应行为。每个谷中的电容可以随电场调节,在外加栅极电压时从最小值变为最大值。从K和K '谷得出的总电容在\({{E}_{{\text{F}}}} = 0\)处显示出可调谐的带隙。当电场能量为\({{\Delta }_{z}} = 2{{{{\lambda }}}_{{{\text{so}}}}}\)时,电容在\({{E}_{{\text{F}}}} = 0\)处为零,而电场能量为\({{\Delta }_{z}} = {{{{\lambda }}}_{{{\text{so}}}}}\)时,电容在\({{E}_{{\text{F}}}} = 0\)处达到最大值,出现单峰,并形成电子空穴对称谱。当电场影响带结构时,自旋向上的态保持其能隙,而自旋向下的态收敛。量子电容中的舒布尼科夫-德哈斯振荡也被观察到,在低磁场下显示出一种减弱模式,当电场占主导地位时消失。在较高的磁场中,振荡的分裂变得明显。振荡模式的消失和随后的振荡分裂是自旋轨道相互作用、电场和磁场相互作用的结果。
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来源期刊
Physics of the Solid State
Physics of the Solid State 物理-物理:凝聚态物理
CiteScore
1.70
自引率
0.00%
发文量
60
审稿时长
2-4 weeks
期刊介绍: Presents the latest results from Russia’s leading researchers in condensed matter physics at the Russian Academy of Sciences and other prestigious institutions. Covers all areas of solid state physics including solid state optics, solid state acoustics, electronic and vibrational spectra, phase transitions, ferroelectricity, magnetism, and superconductivity. Also presents review papers on the most important problems in solid state physics.
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