Suppression of the Berezinskii-Kosterlitz-Thouless and quantum phase transitions in two-dimensional superconductors by finite-size effects
Suppression of the Berezinskii-Kosterlitz-Thouless and quantum phase transitions in two-dimensional superconductors by finite-size effects
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有限尺寸效应对二维超导体中 Berezinskii-Kosterlitz-Thouless 和量子相变的抑制
DOI：
10.1103/physrevb.90.064501
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
S. Weyeneth
中科院分区：
文献类型：
--
作者：
T. Schneider;S. Weyeneth
在存在和不存在垂直于系统的磁场的情况下，我们对Bi膜和{\mathm{LaAlO}}_{3}/{\mathm{SrTiO}}_{3}界面的方阻进行了详细的有限尺寸标度分析。我们的主要目的是探索Berezinskii-Kosterlitz-Thouless(BKT)的发生和有限尺寸下的量子相变行为，这是由均匀磁区或磁场的有限范围引起的。此外，我们还探讨了它的含义。在由厚度$d$、栅极电压${V}_{g}$或磁场$H$调制的外推BKT转变温度之上，我们确定了发生BKT行为的温度范围。它的范围由相关的极限长度控制，而极限长度是由均匀磁区或磁场的范围设置的。外推的BKT相变线${T}_{c}(d，{V}_{g}，H)$与量子相变的发生相容，其中${T}_{c}({d}_{c}，{V}_{gc}，{H}_{c})=0$。然而，各自的极限长度的一个基本含义是，外推的相变线${T}_{c}(d，{V}_{g}，H)$是无法获得的。因此，在有限的极限长度下，BKT和量子相变不会发生。然而，BKT和量子临界行为是可以观察到的，受相关极限长度的程度控制。其他结果和启示包括：磁场诱导的有限尺寸效应在0$极限下产生平坦化，而在零场下它表现出一种特征的温度依赖关系，并且只在$T=0$时消失。前者的预测在Bi膜和{\mathm{LaAlO}}_3}/{\mathm{SrTiO}}_{3}界面中都得到了证实，也得到了前人的研究。后者与{{\mathm{LaAlO}}_{3}/{\mathm{SrTiO}}_{3}}界面数据相一致，而Bi膜表现出平坦化。
We perform a detailed finite-size scaling analysis of the sheet resistance in Bi films and the ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ interface in the presence and absence of a magnetic field applied perpendicular to the system. Our main aim is to explore the occurrence of Berezinskii-Kosterlitz-Thouless (BKT) and quantum phase transition behavior in the presence of limited size, stemming from the finite extent of the homogeneous domains or the magnetic field. Moreover we explore the implications thereof. Above an extrapolated BKT transition temperature, modulated by the thickness $d$, gate voltage ${V}_{g}$, or magnetic field $H$, we identify a temperature range where BKT behavior occurs. Its range is controlled by the relevant limiting lengths, which are set by the extent of the homogeneous domains or the magnetic field. The extrapolated BKT transition lines ${T}_{c}(d,{V}_{g},H)$ uncover compatibility with the occurrence of a quantum phase transition where ${T}_{c}({d}_{c},{V}_{gc},{H}_{c})=0$. However, an essential implication of the respective limiting length is that the extrapolated phase transition lines ${T}_{c}(d,{V}_{g},H)$ are unattainable. Consequently, given a finite limiting length, BKT and quantum phase transitions do not occur. Nevertheless, BKT and quantum critical behavior is observable, controlled by the extent of the relevant limiting length. Additional results and implications include: the magnetic-field-induced finite-size effect generates a flattening out of the sheet resistance in the $T\ensuremath{\rightarrow}0$ limit, while in zero field it exhibits a characteristic temperature dependence and vanishes at $T=0$ only. The former prediction is confirmed in both the Bi films and the ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ interface as well as in previous studies. The latter is consistent with the ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ interface data, while the Bi films exhibit a flattening out.