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SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 48, Issue 8: 087406(2018) https://doi.org/10.1360/SSPMA2018-00100

High-temperature superconductivity and quantum Griffith singularity in two-dimensional crystal

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  • ReceivedApr 2, 2018
  • AcceptedMay 14, 2018
  • PublishedJul 11, 2018
PACS numbers

Abstract

Superconductors have become one of the most important directions in condensed matter physics and materials science due to their unique properties incuding zero-resistance and perfect diamagnetism. With the development of the fabrication technique of two-dimensional (2D) single crystals, 2D superconductors have recently come to be a new research frontier, in which novel physics phenomena, such as high-temperature superconductivity and quantum phase transitions, have emerged and received wide attention. In this artcle, we first briefly review the research background and basic properties of 2D superconductors. Then, focusing on two important classes of phenomena—high-temperature superconductivity and quantum phase transitions, the article is organized into two parts. In the first part, we introduce a typical example of high-temperature superconductivity in 2D systems, the ultrathin FeSe films grown on SrTiO3 (STO) substrate, including the experimental properties and mechanism discussions. In the second part, as an example of quantum phase transitions in 2D systems, an overview of the theories and experiments of the newly-discovered quantum Griffiths singularity in 2D crystalline superconductors is given. In the end, we summary the high-temperature superconductivity and quantum Griffiths singularity in 2D crystals and provide an outlook of the future development in the relevant frontiers.


Funded by

国家重大科学研究计划(2018YFA0305604,2017YFA0303302)

国家自然科学基金(批准号:,11774008)

中国科学院卓越创新中心项目(XDPB08-2)

低维量子物理国家重点实验室开放研究基金(KF201703)


Acknowledgment

感谢成文过程之中刘超飞, 陈澄, 刘易, 邢颖, 刘海文等人的有益探讨和帮助.


Contributions statement

同等贡献


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  • Figure 1

    (Color online) FeSe samples grown on SiC substrates[26]. (a), (b) A series of normalized tunneling conductance spectra on 8 unit cell (UC) (a) and 2 UC FeSe films (b). Insets: Temperature-dependent zero bias conductance (ZBC) for 8 UC and 2 UC FeSe films. (c) Superconducting transition temperature Tc vs the inverse of the film thickness d. (d) Crystal structure of β-FeSe. From Ref. [26].

  • Figure 2

    (Color online) (a) STM topography of the 1-UC-thick FeSe film on STO(001). Grain boundaries appear as trenches along the ⟨100⟩ or ⟨010⟩ direction. (b) Schematic structure (side-view) of the FeSe films on the STO substrate along the 𝑐c-axis. (c) Tunneling spectrum taken on the 1-UC-thick FeSe film on STO(001) at 4.2 K revealing the appearance of superconducting gap. (d) Tunneling spectrum taken on the 2-UC-thick FeSe film reveals a non-superconductive behavior. (e) The dI/dV tunneling spectra of 1 UC FeSe on the Se-etched STO(001) surface at different temperatures. From Ref. [7].

  • Figure 3

    (Color online) (a) The temperature dependence of resistance of 1-UC FeSe/STO in zero field. The inset shows a schematic structure for the transport measurements in the heterostructure of 30 nm amorphous Si/(10-UC) FeTe/(1-UC) FeSe/STO. (b) The magnetic susceptibility of the 1-UC FeSe film. Temperature dependence of magnetic susceptibility for 𝐻H=1000 Oe parallel to the film shows a sharp drop around 25 K. The inset shows the typical magnetic hysteresis behavior measured at 2 K. (c) Schematic diagram of the four-point probe transport measurement set-up. (d) Temperature dependence of the resistance obtained from a linear fit to the I-V curves. The inset shows the temperature dependence of resistance taken on a bare STO surface. (a), (b) from Ref. [29]; (c), (d) from Ref. [32].

  • Figure 4

    (Color online) (a) Magnetoresistance of 1 UC FeSe measured in perpendicular magnetic field by utilizing pulsed magnetic field up to 52 T. (b) Magnetoresistance measured in parallel magnetic field. (c) V(I) curves measured at temperatures ranging from 2 to 50 K for 𝐵B=0 T. (d) Jc calculated from Ic at various temperatures and perpendicular magnetic fields. (e) The variation of exponent 𝛼as a function of temperature, extracting from the power-law, showing that TBKT=23.1 K where α=3. (f) The 𝑇curve plotted with the (dln(R)/dT)−2/3 scale. The dashed line shows the fitting to the Halprin-Nelson formula with TBKT=23.0 K. From Ref. [29].

  • Figure 5

    (Color online) ARPES measurements on FeSe/STO superconductors. (a) Fermi surface mapping of 1 UC FeSe measured at 20 K that consists only of the electron-like Fermi-surface sheet around M point. (b) Band structure crossing the Γ point (left panel) and crossing the M point (right panel). The pink dashed line in the left panel shows schematically a hole-like band near the Γ point with its top at 80 meV below the Fermi level. (c) Typical photoemission images along the momentum cut near the M point (blue line in (d)) measured at different temperatures. (d) Location of the momentum cut near M point (blue line). (e) Temperature dependence of the superconducting gap. The dashed line is a BCS gap form that gives a gap size of 15 meV at zero temperature. From Ref. [57].

  • Figure 6

    (Color online) The transport measurement of FeSe/STO(110). (a) The temperature denpendence of the resistance of the 10UC-FeTe/1UC-FeSe/STO(110) system. Inset is the schematic diagram of the divice. The right figure is the result of measurement at another spot, showing the same superconducting transition. (b) The functions of upper critical field versus temperature using two kinds of STO substrate, where the solid circles suggest the result of the pulsed magnetic field measurement from ref. [29] and the empty circles suggest the static field measurement. The inset is theR(T) curve in different magnetic field. (c) The relationship of α and T, obtained from the fitting of VIα under different temperatures, where α=3 stands for the BKT transition temperature. (d) According to Halperin-Nelson formula R(T)=Rexp[b(TTBKT1)12], (dln(R)/dT)−2/3 changes linearly with temperature. The fitted BKT transition temperature is TBKT=24.1 K. From Ref. [58].

  • Figure 7

    (Color online) The 2×1 reconstruction on the surface of FeSe/STO. (a) The crystal structure and lattice constant of the FeSe layer without oxygen atoms vacancies. (b) With the presence of the oxygen atoms vacancies, the FeSe layers will pair in two, forming the 2×1 reconstruction shown in (c). (c) STM image of 1 UC FeSe on the STO (001) surface. (d) The charge-density difference obtained by subtracting the valence charge densities of the isolated FeSe layer and SrTiO3 substrate from that of the combined system. A charge transfer from the top TiO2 layer to the FeSe layer can be clearly seen. From Ref. [52].

  • Figure 8

    (Color online) The copied energy band. (a)–(c) The energy bands around Γ point of samples with different thicknesses. Only in the single-layer sample the “replica” energy band can be seen. (d)–(f) The energy bands around M point of samples with different thicknesses. Again only in the single-layer sample the “replica” energy band can be seen. (g)–(j) Similar results in varied temperatures. The phenomenon suvives after the gap closing (90 K). From Ref. [59].

  • Figure 9

    (Color online) The theoretical explanation of the copied energy band. (a) The oscillation mode of oxygen atoms on top of STO. (b) The electron-phonon interaction. The additive Hamiltonian is k,σΦ(q,0)ψk+q,σ+ψk,σ. From Ref. [61].

  • Figure 10

    (Color online) The superconductivity of the FeSe/STO samples with different annealing conditions. (a) R(T) curves of samples with different annealing time. The curves are renormalized using tbe resistance at 60 K. (b) The Hall measurement of samples with different annealing time. The temperature where the Hall coefficient changes sign varies among samples with different annealing time. (c) The superconducting critical temperatures and the the dominant-carrier-type transition temperatures of samples with different annealing time. From Ref. [62].

  • Figure 11

    (Color online) The influence of electron doping on the superconductivity of FeSe. (a) A schematic diagram of electric double-layer transistor (EDLT). The electrodes are made of Pt. The green half circle suggests the ion liquid. Below is the FeSe sample on insulating substrate. (b) Comparison of the Tc with and without the applied electric field, where the former one is obviously enhanced. The Tc of the FeSe with electric field is obviously enhanced. (c) The symmetrized ARPES spectra of the K decorated triple-layer FeSe sample, with maximum energy gap at effective doping level ne=0.11. (d) The energy band dipersion of the K decorated triple-layer FeSe sample at effective doping level ne=0.11, with an obvious gap at 13 K and gapless at 71 K. (e) The crystal structure of (Li1−xFexOH)FeSe can be constructed by inserting Li1−xFexOH layers into the layered compound FeSe. (f) The magnetic susceptibility measurement of the (Li1−xFexOH)FeSe samples shows a sharp decline near 40 K, which is the evidence for the Meissner effect in superconductors. The inset is the close-up view of the transition area. (a), (b) from Ref. [63]; (c), (d) from Ref. [67]; (e), (f) from Ref. [23].

  • Figure 12

    (Color online) FeSe/STO with different annealing time. (a)–(g) Density of state measured by ARPES, with increasing annealing time from the left to the right. There appears an obvious superconducting gap in (g). The white line in (h) manifests the line measured in the momentum space in (a)–(g). (i) The overall phase diagram, with the horizontal axis representing the effective doping level. The pink area stands for insulating while the blue area stands for superconducting phase. The single-layer FeSe/STO turns from an insulator to a superconductor with incresing doping level. From Ref. [77].

  • Figure 13

    (Color online) Fine structures of the fermi surfaces of the FeSe/STO in the Brillouin zone. (a) The order parameter of s wave has the same sign on different Fermi surfaces. (b) Nodeless d wave has order parameter that changes sign on different ellipse Fermi surfaces. (c) The s± wave parity with opposite sign on the outer flower-shaped Fermi surfaces and the inner fermi surfaces.

  • Figure 14

    (Color online) Atoms deposited FeSe/STO surface. (a) The map of a single Mn atom deposited FeSe/STO surface; (b) the map of a single Zn atom deposited FeSe/STO surface; (c) spatially resolved STS after the Mn atom deposition with weakened superconductivity; (d) spatially resolved STS after the Zn atom deposition with maintained superconductivity. From Ref. [90].

  • Figure 15

    The phase diagram of diluted Ising ferromagnet. Here p suggests the occupation possibility of the magnetic atom, and T is the temperature. The solid line indicates Tc(p) while the dotted line isTc(1) [6].

  • Figure 16

    (Color online) The magnetic-field-induced superconductor-insulator quantum phase transition in interface superconductor LaTiO3-SrTiO3. (a) The temperature dependence of the sheet resistance of the sample with the perpendicular magnetic field from 0 to 0.3 T. Inset: The superconductivity critical temperature and 2D electrical conductance Gs of the sample versus gate voltage VG. (b) Close up of the data in (a) around characteristic magnetic field Bx. The critical resistance Rs is constant between 0.12–0.22 K. (c) The data in (a) around characteristic magnetic field Bc in detail. The critical resistance Rs is constant as the temperature approaches 0 K. From Ref. [122].

  • Figure 17

    (Color online) The finite-size scaling (FSS) results of the sample under 80 V gate voltage. (a) The magnetoresistance curves in the temperature regime of 0.1–0.2 K. The crossing point (critical point) is (Bx=0.185 T, Rc=372.4 Ω). (b) FSS analysis of the data in (a). The resistances in different temperature collapse into a universal function of |BBx|t, where t=(T/T0)−1/. Inset: critical exponent =0.66 obtained by linearly fitting the T-t curve in logarithmic coordinate. (c) The magnetoresistance at different temperature from 0.04 to 0.07 K. The crossing point is (Bc=0.235 T, Rc=376.6 Ω). (d) FSS analysis of the data in (c). The curves at different temperatures collapse. Inset: critical exponent =1.5 obtained by linearly fitting the T-t curve in logarithmic coordinate. From Ref. [122].

  • Figure 18

    (Color online) The observed superconductivity in Ga thin film. (a) The resistance versus temperature of the Ga thin film sample in zero magnetic field. The zero-resistane Tc is 3.62 K. Inset shows the configuration of the Ga thin film and its protecting layers grown on Si substrate. (b) The resistance versus temperature of the Ga thin film sample under different magnetic field (0–3.000 T). (c) The magnetoresistance curve of the sample under different temperatures (1.90–10 K). Inset: Close-up of the same data in the crossing area around Bc=(2.235±0.125) T. (d) The I-V characteristics in various temperatures plotted on a logarithmic scale ranging from 2.00 to 8.00 K at B=0 T. Inset: The slopes of I-V curves in the logarithmic coordinate in various temperatures, with the two dashed lines corresponding to VI and VI3. TBKT=3.72 K is defined by VI3. From Ref. [5].

  • Figure 19

    (Color online) Griffiths Singularity in the Ga thin film. (a) Detailed measurement of the Ga thin film’s magnetoresistance in the crossing area. Inset is the temperature dependence of the critical magnetic field. There is an up-turn of Bc appraoching the zero temperature. (b) The critical exponent versus magnatic field near the critical point Bc*=2.639 T, showing a power law divergence. The solid line is the theroretical fitting of the experiment result[130]. (c) The phase diagram of the type-II superconductor-metal phase transition, with B1, B2 indicating the upper and lower critical field of the superconductor. When temperature is above TM, the system manifests a clean QPT at B2. When temperature decreases to T<TM, however, quenched disorder overtakes thermal fluctuation and gives rise to a vortex glass-like phase, as shown in the “tail” region. Such a vortex glass-like phase disappears at the infinite-randomness QCP Bc* From Ref. [5].

  • 图 20

    (网络版彩图)LAO-STO体系中的界面处两种不同的可能排列情况. (a), (b)分别为(LaO)+和(TiO2)0相接和(AlO2)和(SrO)0相接的情况. 前者的界面是n型载流子导电, 也是人们普遍研究的一种, 后者在界面处是绝缘体.引自文献[132]

  • Figure 21

    (Color online) Magnetic field induced superconductor-metal phase transition in LAO-STO. (a) The resistance versus temperature in the absence of magnetic field, with onset and zero-resistance critical temperature approximately 0.711 and 0.123 K, respectively. (b) Isomagnetic R(T) curves measured at different magnetic field (0.347–0.997 T). (c) The magnetoresistance of the sample in different temperatures, showing a crossing area around 0.2–0.45 T. From Ref. [92].

  • Figure 22

    (Color online) Griffiths Singularity in the SMT of LAO-STO interface. (a) The isothermal magnetoresistance in various temperatures ranging from 0.095 to 0.650 K of the same sample in Figure 21. The crossing point of the curves with adjacent temperatures slowly moves as the temperature changing. Inset: The relationship of critical magnetic field and temperature shows good linearlity. (b) The magnetic field dependence of the critical exponent . diverges while B approaching Bc*=0.428 T, in a power law manner which can be well described by =0.06(Bc*B)−0.6 according to the activated scaling theory. (c) The magnetoresistance in different temperatures. The hysteresis suggests the existence of magnetic order, and the intensity of the peak depends on the speed of scanning, indicating its magnetohydrodynamics origin. From Ref. [92].

  • Figure 23

    (Color online) Ising superconductivity and Griffiths Singularity in monolayer NbSe2. (a) The temperature dependence of the sheet resistance of the monolayer NbSe2 sample in different perpendicular magnetic field ranging from 0 to 15.50 T. The onset superconducting critical temperature in zero magnetic field is 6.61 K (inset). With increasing magnetic field, the sample appears SMT in low temperature regime. (b) Temperature dependence of the perpendicular and parallel upper critical magnetic field fitted by Bc(T)1T/Tc and Bc(T)(1T/Tc)1/2. The extrapolation to zero temperature gives Bc(0) and Bc(0) 2.16 T and 32.42 T respectively, with Bc(0) far beyond the Pauli limit Bp=6.37 T. The inset is the schematic diagram of the measuring configuration. (c) The dynamics exponents zν versus magnetic field obtained by FSS analysis shows diversing behavior when the magnetic field approaching the critical magnetic field Bc*≈2.639 T, indicating the Griffiths singularity. The inset is the atomically resolved STM topography of the sample. (d) The relationship of the crossing magnetic field and temperature, where Bc shows an anomalous upturn deviating from linearity near the zero temperature, as the Ga thin film. From Ref. [112].

  • Figure 24

    (Color online) The observed Quantum metal states and Griffiths singularity of ZrNCl and MoS2. (a) The schematic crystal structures of monolayer ZrNCl and MoS2. (b) The temperature dependence of the sheet resistance of the ZrNCl under 6 V gate voltage in different perpendicular magnetic field ranging from 0 T to 9.0 T. (c) The FSS analysis of the data in (b). (d) and (e) are the comparisons of the mean-fieldly calculated upper critical magnetic field BcMF, the “critical” magnetic field and “critical” temperature of the Griffiths states of ZrNCl and MoS2, respectively. Here the definition of “critical’ magnetic field is the magnetic field at the crossing point of the two R-T curves in adjacent temperatures, and the “critical” temperature is defined as the temperature where dRdT=0 in some fixed magnetic field. From Ref. [113].

  • Figure 25

    (Color online) (a) The diagram of quantum Griffiths state; (b) the diagram of quantum metal state; (c) the quantum phase diagram of ion-gated 2D crystalline superconuctors. In low temperature and low magnetic field (blue) the system is in the quantum metal state, while in low temperature and high magnetic field (yellow) it changes to the quantum Griffiths state as shown in (a). Around TBKT in low magnetic field (rose), the system manifests the crystal vortex state (b) with finite resistance caused by thermo-activated vortex creeping[154]. By increasing the tempreature the system turns into the vortex liquid state. From Ref. [113].

  • Table 1   The dependence of with tensile strain in 1-UC FeSe films on different substrates with various in-plane lattice constants

    衬底

    面内的晶格常数 (Å)

    晶格失配度 (%)

    Tc (K)

    Nb:BaTiO3/KTaO3 (Rotated lattice)

    3.78

    0.4

    ~70[79]

    3-UC Nb:STO/LaAlO3

    3.79

    0.7

    ~55[82]

    5-UC Nb:STO/LaAlO3

    3.81

    1.2

    ~62[82]

    Nb:STO

    3.91

    3.9

    ~65[8,9]

    Nb:STO/KTaO3

    3.99

    6.0

    ~70[83]

    Nb:BaTiO3/KTaO3 (Unrotated lattice)

    3.99

    6.0

    ~75[79]

  • Table 2   Critical exponents and their physical meanings. In the table, is the relative temperature (−)/, and is the relative external field (−)/, , , , and are critical exponents of the specific heat capacity, order parameter, magnetic susceptibility, isothermo-magnatization and correlation length near the critical point, respectively. , are the exponent of the correlation length and correlation function, and are the dynamical exponent in quantum critical transitions and the active dynamical exponent in Griffiths Singularity, respectively. From Ref.

    指数

    定义

    条件

    热容

    α

    c|r|α

    r→0, h=0

    序参量

    β

    m(r)β

    r→0, h=0

    磁化系数

    γ

    χ|r|γ

    r→0, h=0

    等温磁化

    δ

    h|m|δsign(m)

    h→0, r=0

    关联长度

    ν

    ξ|r|υ

    r→0, h=0

    关联函数

    Η

    G(x)|x|d+2η

    r=0, h=0

    动力学指数

    z

    ξtξz

    r→0, h=0

    激活动力学指数

    ψ

    lnξtξψ

    r→0, h=0

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