모트 금속-절연체 전이(Metal-Insulator Transition: MIT) 현상은 간접 전이(Indirect transition)이며 불순 물이 존재할 때 절연체에서 금속으로 금속에서 절연체로 전이가 일어나는 것이다. 이 모트 MIT 현상이 superconducting energy gap을 정의한다. D-wave 전자구조는 45° 135° 225° 315°를 노드(Node)라고 하는 곳에서 에너지 갭이 존재하지 않으며 그 반면 0° 90° 180° 270°를 Anti-node라고 하는 곳에서 초전도 갭을 갖는 크로바 모양을 뜻하며, 이 구조가 d-wave superconductor의 특징이다. 그림 11(b)는 1993년에 발표된 d-wave superconducting gap을 증명하기 위하여 an underdoped Bi2Sr2CaCu2O8+δ (BSCCO)crystal에서 측정된 각도 분해 광전자 분광 (Angle Resolved Photoemission Spectroscopy: ARPES) 데이터 이다.1) 이것을 ARPES spectra라고 한다. 이 데이터는 초전도 임계온도 Tc 위와 아래에서 측정된
그림 11. Previous data on pairing symmetry. (a) The definition of the dx2-y2 -wave gap. (b) ARPES data measured in an underdoped Bi2Sr2CaCu2O8+δ crystal. The shapes of the curves measured at B (node) above and below Tc are similar. In particular, the superconducting gap is not seen at B below Tc, which has been put forward as evidence of d-wave symmetry (taken from Shen et al.1). (c) ARPES data measured in a high-resolution system in an optimally doped Bi2Sr2CaCu2O8+δ crystal, showing the obvious superconducting node gap at 40K (taken from Kaminski et al.3). Data at 15K was measured in a low resolution system. (d) A nodal superconducting gap, measured in an optimally doped YBa2Cu3O7-d crystal by a laser ARPES, was clearly seen (taken from Okawa et al.4). (e) Top view of an image of the half-flux quantum measured by a SQUID microscope for a superconducting ring made from an underdoped YBa2Cu3O7-d film on the tricrystal point of a substrate (taken from Tsuei et al.6). (f) A flux image measured in a superconducting ring for an overdoped Tl2Ba2CuO6+d film (taken from Tsuei et al.8); in the case of Fo, the colour tone is uniform, which is evidence of s-wave symmetry.
The dull colour image on the tricrystal point represents anisotropy.
결정으로 측정된 ARPES Curve는 Node에서 Tc 이하에서 선명한 초전도 에너지 갭을 보여준다 (그림 11c)2). 이것은 2000년도에 측정된 것과 완전히 다른 결과와 해석을 준다. 이것은 d-wave pairing symmetry를 부정하는 결과이며 s-wave symmetry를 증명하는 증거가 되었다. 그리고 2005년 an 2) A. Kaminski, J. Mesot, H. Fretwell, J. Campuzano, M. Norman, M. Randeria, H. Ding, T. Sato, T.
Takahashi, T. Mochiku, et al., “Quasiparticles in the superconducting state of Bi2Sr2CaCu2O8+δ,” Physical review letters, vol. 84, no. 8, p. 1788, 2000.
optimally doped YBa2Cu3O7−δ crystal로 Laser-ARPES로 측정된 실험데이터는 Node에 12meV 초전도 pairing symmetry를 증명하는 것으로 해석될 수 없다. 그리고 an overdoped Tl2Ba2CuO6+δ film으로 초 전도 링을 만들어서 magnetic flux를 측정한 결과 거의 완전한 Ring 타입의 isotropic image가 얻어졌다 (그림 11f)5). 이것은 cuprate superconductor가 s-wave pairing symmetry라는 것을 증명하는 증거이다.
그리고 pairing symmetry의 대표적인 실험 데이터로 Electronic Raman Spectrum (ERS) 가 있다. 이론 Superconducting gap을 보여준다. 이런 결과들은 d-wave symmetry를 부정하며 오히려 s-wave symmetry 의 증거가 된다.
Bhushan, “Pairing symmetry in single-layer tetragonal T l2Ba2CuOβ+δ superconductors,” Science, vol. 271, no.
5247, pp. 329–332, 1996.
그림 12. Analysis of the electronic Raman spectrum. (a) The B2g mode measured at the node area using polarised ERS at 35 K for an underdoped YBa2Cu3O6.5 single crystal with Tc » 61 K.
Linear behaviour is shown below 150 cm-1 and a superconducting gap is observed near 250 cm-1. This curve was redrawn from the original data.13 (b) The B2g mode measured by ERS at 10 K for an underdoped Bi2Sr2CaCu2O8+d single crystal with Tc » 68 K. Linear behaviour is shown below 300 cm-1 and a superconducting gap is exhibited near 380 cm-1. This curve was redrawn from the original data.14 In both types of crystals, the d-wave superconducting gap in the B1g
mode of the antinode was not observed.13,14 (c) The B1g mode measured at the antinode area using ERS at 4 K in an underdoped Pr2-xCexCuO4-d (x=0.135) single crystal with Tc » 16.5 K.
The d-wave superconducting gap is not shown. The insets display the presence of two phases in the measurement region for the two-phase model and the measurement areas in k-space of the B1g and B2g modes. (d) The B2g mode measured using ERS under the same conditions as for the crystal used in Fig. 1c. The pink curve was measured in the normal state; the green and black curves were decomposed by the pink curve. The blue curve measured at 4 K shows linear behaviour and a superconducting gap. The violet curve (red star) shows the fitting of the intrinsic superconducting curve (shown in orange) obtained by subtracting the incoherent part (black), giving the final result shown here. The small background is shown. (e) The B2g mode measured using ERS for an optimal doped Pr2-xCexCuO4-d (x=0.147) single crystal with Tc » 23.5 K. The pink curve was measured in the normal state; the green and black curves were decomposed by the pink curve. The blue curve measured at 4 K includes a superconducting gap.
The intrinsic superconducting curve (orange) was obtained by subtracting the incoherent part (black). Figs. 2 (c, d, and e) were redrawn using data extracted from original data.12
2) (국제공동연구)Nano-scale optical phenomena for metal-insulator transition in VOx
국제 공동연구를 통해 Photoinduced insulator-metal transition을 Si substrate위에 성장된 VO2를에서 측 정하였다. 국제 공동연구팀에서는 near-field infrared microscopy와 transport measurements를 이용하여 photoresponse에 의해 일어나는 저항값 변화를 공간적으로 측정하였다. 이때 사용한 레이저는 5 mW, 633 nm HeNe Laser를 사용하였다.
그림 13 Summary of systematic studies of photoresponse VOx/doped Si samples using a combination of transport and nano-optical experiments. Panel 13a: 2-probe transport measurements of the resistance of films with various Si substrate doping levels in dark and light (5 mW, 633 nm red light) settings. Panel 13b: 2-probe transport measurements of the resistance of films with various Si substrate doping levels in dark and light (5 mW, 10 µm infrared light) settings. Panel 1c: Normalized near-field contrast for Si (n=1018 cm-3) sample in dark setting (top row), illuminated under 5 mW green light setting (middle row), and the contrast change [(NFlight-NFdark)/NFdark] between the dark and illuminated images (bottom row). Panel 1d:
Normalized near-field contrast for Si (n=1017 cm-3) sample in dark setting (top row), illuminated under 10 mW green light setting (middle row), and the contrast change [(NFlight-NFdark)/NFdark] between the dark and illuminated images (bottom row).
’
국제 공동연구팀에서는 그림 13의 a와 같이 HeNe Laser를 이용하여 5 mW, 633nm에서의 샘플의 resistance photoresponse 측정을 진행하였다. 이러한 측정을 통해 carrier concentration이 1018cm-3 인 Si 웨이퍼 위어서 성장된 VO2의 경우 최대 25.70%의 photoresponse에 의한 저항이 줄어든 것을 확인할 수 있었다. 또한 동일한 실험을 5 mW, 10 um의 CO2 레이저를 통해 실험해 본 결과 그림 13b와 같다. 그림 13b를 보면 photoresponse에 의한 resistance를 보면 값의 변화가 거의 없다는 것을 확인할 수 있다. 즉,
최대 0.63%의 photoresponse resistance가 줄어든 것을 확인할 수 있는데, 이는 near-field probe에 의하 여 photoresponse가 excite 되지 않는다는 것을 의미하다. 즉, 10 um Laser에 의한 반응은 없는 것으로 확인도니다. 공동연구에서는 pho-susceptible sample에서 power 의존성을 측정을 진행하였고, 이를 통해 resistance photoreponse를 power P에 관하여 측정을 진행하였다. 이를 통해 ln(1/P)의 의존성을 가지고 있는 것을 확인할 수 있었다.
앞의 연구 결과를 확장하기 위해 nano-optical phenomena를 near-field measurements를 통해 측정하 였다. 그러나 공동연구팀에서 측정할 수 있는 최대 파워인 10 mW에서 측정하였을 때에도 near-field contast가 매우 작은 것을 확인할 수 있었다. 공동연구팀이 소유하고 있는 10 nm green light laser와, 10um CO2 laser를 이용하여 near-field reponse를 측정한 결과는 그림 13c, 그림 13d와 같다. 이를 보면 5 mW 와 10 mW에서 모두 거의 contrast가 거의 없는 것을 확인할 수 있었다.
3) Metal Insulator Transition in thin and ultra-thin epitaxial
Vanadium dioxide (VO2) is a canonical material with strong electron-electron correlations and an abrupt reversible phase transition characteristic at the critical temperature Tc ≈ 340 K in a bulk and bulk-like state (Fig. 1). By rising the temperature, an electrical insulator-metal transition (IMT) and structural phase transition (SPT) occur resulting in a transformation from the low-temperature (< 340 K) monoclinic insulating phase with dimerized V-V atoms along the aM1-axis to the high-temperature (> 340 K) rutile metallic phase with undimerized V-V atoms along the cR(≡aM1)-axis (insets in Fig. 1 4).
그림 14 Electrical insulator-metal and structural monoclinic-rutile (insets) phase transitions at temperature ~ 340 K in a bulk-like VO2 sample. Here, red and black curves describe resistance changes of VO2 on heating and cooling, respectively. Blue and yellow circles show the position of V and O atoms, respectively, in M1 and R phases
Because the atomic lattice influences the correlation strength in VO2, the material is an ideal platform for investigating the interconnection between structural and electronic systems. The effective way to tune the electrical properties of the VO2 sample is by applying strain. Here we investigate the phase transition characteristics in strained thin and ultrathin VO2 films.
Fig. 15a shows the temperature dependences of the resistance of the following samples: red curve – 100 nm VO2 film on AlN/Si substrate, black curve – 100 nm VO2 film on r-plane Al2O3 substrate, blue curve – 5 nm VO2 film on TiO2 [001] substrate, cyan curve – 10 nm VO2 film on TiO2 [001]
substrate, green curve – 30 nm VO2 film on TiO2 [001] substrate.
Fig. 15b shows the derivatives of the lnR(T) for all of the five samples presented in Fig. 14a with the determined Tc values by Gaussian fitting. It can be seen that depending on the substrate type, the values of the Tc of the VO2 films can be changed as much as 58 K with the lowest value of 291.5 K for the VO2/TiO2-3 sample and the highest value of 349.7 K for the VO2/AlN/Si sample (the value of Tc ≈ 341.3 K for VO2/Al2O3 is the most close to the bulk one of 340÷341 K). This difference in the Tc values of the VO2 films is caused by the substrate induced strain. To understand its nature, we have performed the further structural measurements of the samples with the two threshold values of Tc.
그림 15 (a) Resistance vs temperature curves for the VO2 films on different substrates: AlN, Al2O3 and TiO2. (b) Derivatives of the lnR(T) for the samples shown in (a) with determined Tc values.
Fig. 16 shows the X-ray diffraction scans obtained from the VO2/AlN/Si and VO2/TiO2-3 samples at room temperature. Note that at this temperature the VO2 film on AlN/Si is in its monoclinic insulating state, while the VO2 film on TiO2 substrate is in its rutile metallic state (see Fig. 16a).
그림 16 θ-2θ XRD scans of the VO2/AlN/Si and VO2/TiO2-3 samples
From Fig. 12 it is seen that on the AlN layer the monoclinic VO2 film grows epitaxially with the in-plane relation of VO2 (010)∥AlN (0001), while on the TiO2 substrate the rutile VO2 film grows epitaxially with the in-plane relation of VO2 (002)∥ TiO2 (002).
그림 17 (a) Schematic arrangement (top view) of Al/N atoms (blue balls) in the AlN layer having the hexagonal structure with the in-plane lattice parameters aALN = bAlN = 3.069 Å (cALN is the out-of-plane direction). (b) Schematic arrangement (top view) of Ti atoms (light blue balls) in the TiO2 substrate having the rutile tetragonal structure with the in-plane lattice parameters aTiO2 = bTiO2 = 4.594 Å (cTiO2 is the out-of-plane direction).
A cross-sectional modeling of the alignment of the VO2 film on AlN layer and the VO2 film on TiO2 substrate is shown on Fig. 5a and b, respectively.
그림 18 (a) Modeling of the VO2/AlN cross section in [101] view direction for monoclinic VO2 and [100] view direction for AlN. (b) Modeling of the VO2/TiO2 cross section in [110] view directions for rutile VO2 and TiO2. Red rectangles mark film-substrate interface region with corresponding lattice parameters and, thus, define strain in the film.
From Fig. 18a,b it is seen that for both samples VO2 films are under tensile in-plane and compressive out-of-plane strain at the interface with the substrates (denoted by red rectangles).
Considering the crystallographic alignment of the films with respect to the substrates, in case of the VO2/AlN sample, the aM1 axis with the dimerized chain of V-atoms lies in-plane and, thus, it experiences tensile strain. As a result of the strain, the distance between V4+ and V4+ in the dimers increases, which induces smaller overlap of the 3d electronic orbits and, thus, shifts Tc to the higher values for almost 10 K with respect to the typical bulk or bulk-like value of 340 K. In case of the VO2 film on TiO2 substrate it can be seen that lattice mismatch at their interface is much smaller, less than 1 %, when VO2 is in its rutile phase. Thus, already at room temperature the ultrathin VO2 film is already in its metallic state. Further we examine whether shift of the critical temperature of the electronic phase transition effects on structural system or not.
Fig. 19 shows the temperature dependence of the XRD peaks of the VO2 films on AlN and TiO2 substrates.
그림 19 Changes in XRD patterns on heating of the VO2 films on AlN (a) and TiO2 (b) substrates
In Fig. 19a a diffraction peak at 2θ ≈ 39.66° from the monoclinic VO2 (020)M1 is seen near the room temperature ~ 300 K. As temperature increased, a gradual shift to the smaller 2θ values is observed with the final structural phase transition to the rutile phase at 375-384 K revealed by the VO2 (200)R peak at 2θ ≈ 39.58°. Note that registered temperature of the SPT of the VO2 film on AlN/Si substrate is much higher than typical values of 340 K for bulk or bulk-like samples that is caused by strained state of the film.
As for the VO2 film on TiO2 substrate, it is characterized by the rutile structure already in the vicinity of the room temperature of 293-297 K revealed by the VO2 (200)R peak at 2θ ≈ 65.58°.
The film undergoes SPT to the rutile phase at 291 K shown by lower shift of the XRD peak to the 2 θ ≈ 65.52°. It is a very unique behavior, so we investigated the dynamics of the insulator-metal transition of the VO2 film on TiO2 substrate on the nanoscale.
Prior to that it is important to confirm that the film possesses a clean and smooth surface. It was performed by imaging of the sample by optical microscopy (OM), scanning electron microscopy (SEM) and atomic force microscopy (AFM). Obtained images are shown on Fig. 7a, b and c, respectively.
그림 20 Surface images of the 30 nm VO2 film on TiO2 substrate obtained by OM (a), SEM (b) and AFM (c).
From Fig. 20b,c it is seen that the VO2 film has a very clean and smooth surface with the root mean square roughness Rq ~ 0.1 nm. However, OM image (Fig. 7a) reveals cracks in the film due strain relaxation (film thickness ~ 30 nm). To avoid this and obtain homogeneously strained VO2 film on TiO2 substrate, we have imaged the thinner VO2 film – 10 nm thick (cyan curve on Fig. 2a). Fig.
8 shows the OM image of the 10 nm VO2 film on TiO2 demonstrating that the film is in homogeneously strained state.
그림 21 OM image of the 10 nm VO2 film on TiO2 substrate
This 10 nm film is perfect for a nanoscale imaging of the thermally driven IMT in VO2, which was performed by the technique of AFM-based scattering-type scanning near-field infrared microscopy (s-SNIM) utilizing a table-top quantum cascade laser (QCL) with wavelength of 10.3 μm and demodulating the higher harmonic (S3) of the tip scattered signal (Fig. 32).
그림 22 Schematic of the s-SNIM technique
Fig. 23 shows the S-SNIM images obtained in the same spatial region on heating run through the phase changing regime of the 10 nm VO2 film on TiO2 substrate.
그림 23 s-SNIM images of the same region of the 10 nm VO2 film on TiO2 at different temperatures are displayed. Yellow-colored amplitude corresponds to metallic regions, while blue-colored signals correspond to insulating regions.
From Fig. 14 it can be seen that the images are fully insulating at temperature ≤ 306.5 K. Then,
at 307.5 K, nanoscale metallic domains start to nucleate and gradually spread until the film completely transforms to the metallic state at the temperature ≥ 310 K. The temperature scale is in a good agreement with the R-T data shown in Fig. 2a (cyan curve).
Thus, the ultrathin VO2 films undergo percolative IMT at the reduced transition temperature. This feature along with the excellent quality of the films is important for the in-depth investigation of the dynamics of the electronic and structural phase transitions in VO2, as well as to broaden its application scope.
4) Decopling of IMT and SPT for Mott transition in strained VO2 films on AlN/Si
이산화 바나듐(VO2)은 상온인 대략 340 K에서 상전이를 하는 물질로서 이 특이한 성질로 인해 전세계 의 많은 연구자들로하여금 많은 관심을 이끌어내고 있으며 또한 상온에서 전이를 일으키는 성질은 앞으 로도 많은 활용도를 가지는 디바이스로서 큰 잠재력을 갖는 물질이다. 특히 적기적 혹은 광학적 고속 스위칭, 적외선 감지, 전계효과 트랜지스터(FET) 등에 사용될 수 있으며 이뿐만 아니라 에너지 세이빙
이산화 바나듐(VO2)은 상온인 대략 340 K에서 상전이를 하는 물질로서 이 특이한 성질로 인해 전세계 의 많은 연구자들로하여금 많은 관심을 이끌어내고 있으며 또한 상온에서 전이를 일으키는 성질은 앞으 로도 많은 활용도를 가지는 디바이스로서 큰 잠재력을 갖는 물질이다. 특히 적기적 혹은 광학적 고속 스위칭, 적외선 감지, 전계효과 트랜지스터(FET) 등에 사용될 수 있으며 이뿐만 아니라 에너지 세이빙