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Since the discovery of two-dimensional electron gas with high mobility at the LaAlO3/SrTiO3 heterointerface, many physical properties such as two-dimensional superconductivity, magnetism and spin-orbit coupling have been widely studied. The origin of the transition from quantum superconductor to metal at zero temperature in two-dimensional superconductor is still an open problem, which has been discussed intensely. According to the conventional theory, when the temperature is close to zero, the superconductor-insulator transition can be observed by applying a magnetic field or magnetic field effect of disorder, and the ground state should be superconducting or insulating. However, when Jaeger et al. (Jaeger H M, Haviland D B, Orr B G, Goldman A M 1989 Phys. Rev. B 40 182 ) studied the relationship between superconductivity evolution and thickness and temperature in a superconducting granular film, they found that there exists an intermediate metal state that can destroy the direct transition between superconducting and insulating. The intermediate metal state is characterized by the existence of saturation resistance at superconducting transition temperature, and the corresponding ground state is called anomalous metallic state. In addition to the saturation of resistance at low temperature, the characteristics of an anomalous metallic state also include the linear current-voltage (I-V) characteristics in the low current range, the giant positive magnetoresistance (MR), the vanishing of Hall resistance (Rxy), and the tuning capability adjusted by changing a variety of parameters including degree of disorder, gate voltage and magnetic field.In this work, we systematically investigate the electrical transport properties of LaAlO3/SrTiO3 (001) heterointerface in a perpendicular magnetic field at low temperature. The R-T curves and the I-V characteristics in zero magnetic field show that LaAlO3/SrTiO3 (001) heterointerface is in a superconducting state. However, after a small magnetic field is applied, the LaAlO3/SrTiO3 (001) heterointerface has the characteristics of resistance saturation at low temperature, linear I-V characteristics, giant positive MR, abnormal Hall response, indicating the clear characteristics of an anomalous metallic state. The sample undergoes a transition from quantum superconductor to metal at temperatures approaching to zero. In addition, we observe that the anomalous metallic state in an unusually large region under the action of magnetic field, and our main observations are summarized in the H-T phase diagram. By analyzing the relationship between the resistance of the anomalous metallic regime and the magnetic field, and the vanish of Hall resistance, we infer that the anomalous metallic state observed in LaAlO3/SrTiO3 (001) heterointerface can be explained by Bose metal model. According to our findings, the magnetic field regulated LaAlO3/SrTiO3 (001) heterointerface appears as a special platform to study the details of anomalous metallic state in a controllable way. -
Keywords:
- LaAlO3/SrTiO3 heterointerface /
- anomalous metallic state /
- saturation resistance /
- Bose metal
[1] Tinkham M 2004 Introduction to Superconductivity (New York: Courier Corporation) p110
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[4] Jaeger H M, Haviland D B, Orr B G, Goldman A M 1989 Phys. Rev. B 40 182
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[5] Kapitulnik A, Kivelson S A, Spivak B 2019 Rev. Mod. Phys. 91 011002
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图 1 (a) 无外加磁场时LaAlO3/SrTiO3(001)异质界面的R-T曲线, 左上角插图是R-T曲线在高温区的放大图, 右下角插图展示了和温度相关的上临界场
$H_{{\text{c}}2}^{50\% }$ 与$ T/{T_{\text{c}}} $ 的依赖关系; (b) 不同垂直磁场下的R-T曲线Figure 1. (a) R-T curves of LaAlO3/SrTiO3 (001) heterointerface in zero magnetic field. Inset in upper left corner is an enlarged view of R-T curve in high temperature region. Inset in lower right corner shows dependency relationship between temperature-dependent upper critical fields
$H_{{\text{c}}2}^{50\% }$ and$ T/{T_{\text{c}}} $ ; (b) R-T curves in different perpendicular magnetic fields.
图 2 T = 50 mK时, 不同垂直磁场下的I-V曲线, 插图是局域放大图, 其中黑色实线是对数据的线性拟合
Figure 2. I-V curves in different perpendicular magnetic fields at T = 50 mK. Inset is a magnification, black lines are linear fitting.
图 3 (a) 不同磁场下的Arrhenius曲线; (b) 不同磁场下Arrhenius曲线的高温区局域放大图 (彩色实线是利用(2)式对数据进行的拟合); (c) 热激活能
$U/{k_{\text{B}}}$ 与$\ln H$ 的关系 (红色实线是利用(3)式对数据进行的拟合)Figure 3. (a) Arrhenius curves in different magnetic fields; (b) magnification of Arrhenius curves in high temperature region in the different magnetic fields (Color lines are linear fitting by Eq. (2)); (c) relationship between activation energy
$U/{k_{\text{B}}}$ and$\ln H$ (Red line is empirical fit by Eq. (3)).
图 4 (a) 不同温度下的Rxx-H曲线, 插图是MR曲线; (b) 不同温度下的lgR-lg(H–Hc0)曲线, 其中黑色实线是利用(4)式对数据进行的拟合, 插图是2
${\nu _0}$ 随温度的变化关系Figure 4. (a) Rxx-H curves at different temperatures, and inset is MR curves; (b) lgR-lg(H–Hc0) curves at different temperatures. Black lines are fitting curves by Eq. (4), and inset shows 2
${\nu _0}$ vs. T.
图 5 (a) T = 50 mK下的霍尔电阻Rxy与外加磁场的变化关系, 插图是低磁场下的局域放大图; (b) T = 50 mK下的纵向电阻Rxx与外加磁场的变化关系, 插图是低磁场下的局域放大图.
Figure 5. (a) Hall resistance Rxy as a function of magnetic field at T = 50 mK, and inset is a magnification of low magnetic field; (b) longitudinal resistance Rxx as a function of magnetic field at T = 50 mK, and inset is a magnification of low magnetic field.
图 6 LaAlO3/SrTiO3(001)体系的H-T相图, 背景是不同磁场下R-T曲线的二维彩图. 缩写分别表示样品处于SC, 超导态; AM, 反常金属态; NORMAL, 正常态; TAFF, 热激活磁通流区
Figure 6. H-T phase diagram of LaAlO3/SrTiO3 (001) system, and the background is a 2D color plot of R-T curves at differential magnetic field. Abbreviations indicate that sample is in SC, superconducting state; AM, anomalous metal state; NORMAL, normal state; TAFF, thermally activated flux flow regime.
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[1] Tinkham M 2004 Introduction to Superconductivity (New York: Courier Corporation) p110
[2] Phillips P, Dalidovich D 2003 Science 302 243
Google Scholar
[3] Goldman A M 2010 Int. J. Mod. Phys. B 24 4081
Google Scholar
[4] Jaeger H M, Haviland D B, Orr B G, Goldman A M 1989 Phys. Rev. B 40 182
Google Scholar
[5] Kapitulnik A, Kivelson S A, Spivak B 2019 Rev. Mod. Phys. 91 011002
Google Scholar
[6] He Z H, Tu H Y, Gao K H, Yu G L, Li Z Q 2020 Phys. Rev. B 102 224502
Google Scholar
[7] Ephron D, Yazdani A, Kapitulnik A, Beasley M R 1996 Phys. Rev. Lett. 76 1529
Google Scholar
[8] Mason N, Kapitulnik A 1999 Phys. Rev. Lett. 82 5341
Google Scholar
[9] Mason N, Kapitulnik A 2002 Phys. Rev. B 65 220505
Google Scholar
[10] Breznay N P, Kapitulnik A 2017 Sci. Adv. 3 e1700612
Google Scholar
[11] Tsen A W, Hunt B, Kim Y D, Yuan Z J, Jia S, Cava R J, Hone J, Kim P, Dean C R, Pasupathy A N 2016 Nat. Phys. 12 208
Google Scholar
[12] Saito Y, Kasahara Y, Ye J, Iwasa Y, Nojima T 2015 Science 350 409
Google Scholar
[13] Li L, Chen C, Watanabe K, Taniguchi T, Zheng Y, Xu Z, Pereira V M, Loh K P, Neto A H C 2019 Nano Lett. 19 4126
Google Scholar
[14] Han Z, Allain A, Arjmandi-Tash H, Tikhonov K, Feigel’man M, Sacépé B, Bouchiat V 2014 Nat. Phys. 10 380
Google Scholar
[15] Bøttcher C G L, Nichele F, Kjaergaard M, Suominen H J, Shabani J, Palmstrøm C J, Marcus C M 2018 Nat. Phys. 14 1138
Google Scholar
[16] Chen Z, Liu Y, Zhang H, Liu Z R, Tian H, Sun Y Q, Zhang M, Zhou Y, Sun J R, Xie Y W 2021 Science 372 721
Google Scholar
[17] Chen Z Y, Adrian G, Swartz A G, Yoon H, Inoue H, Merz T A, Lu D, Xie Y W, Yuan H T, Hikita Y, Raghu S, Hwang H Y 2018 Nat. Commun. 9 4008
Google Scholar
[18] Chen Z Y, Wang B Y, Swartz A G, Yoon H, Hikita Y, Raghu S, Hwang H Y 2021 npj Quantum Mater. 6 15
Google Scholar
[19] Das D, Doniach S 1999 Phys. Rev. B 60 1621
Google Scholar
[20] Das D, Doniach S 2001 Phys. Rev. B 64 134511
Google Scholar
[21] Shimshoni E, Auerbach A, Kapitulnik A 1998 Phys. Rev. Lett. 80 3352
Google Scholar
[22] Galitski V M, Refael G, Fisher M P A, Senthil T 2005 Phys. Rev. Lett. 95 077002
Google Scholar
[23] Wang P J, Huang K, Sun J, Hu J J, Fu H L, Lin X 2019 Appl. Phys. Lett. 90 023905
Google Scholar
[24] Saito Y, Nakamura Y, Bahramy M S, Kohama Y, Ye J, Kasahara Y, Nakagawa Y, Onga M, Tokunaga M, Nojima T, Yanase Y, Iwasa Y 2016 Nat. Phys. 12 144
Google Scholar
[25] Kozuka Y, Kim M, Bell C, Kim B G, Hikita Y, Hwang H Y 2009 Nature 462 487
Google Scholar
[26] Reyren N, Thiel S, Caviglia A D, Fitting Kourkoutis L, Hammerl G, Richter C, Schneider C W, Kopp T, Rüetschi A S, Jaccard D, Gabay M, Muller D A, Triscone J M, Mannhart J 2007 Science 317 1196
Google Scholar
[27] Yang C, Liu Y, Wang Y, Feng L, He Q M, Sun J, Tang Y, Wu C C, Xiong J, Zhang W L, Lin X, Yao H, Liu H W, Fernandes G, Xu J, Valles J M, Wang J, Li Y R 2019 Science 366 1505
Google Scholar
[28] Feigel’man M V, Geshkenbein V B, Larkin A I 1990 Physica C 167 177
Google Scholar
-
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