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Scanning tunneling spectroscopy studies on vortices in YBa2Cu3Oy single crystals
Physica C 392–396 (2003) 323–327 www.elsevier.com/locate/physc
Scanning tunneling spectroscopy studies on vortices in YBa2Cu3Oy single crystals Kenji Shibata b
a,*
, Makoto Maki a, Terukazu Nishizaki a, Norio Kobayashi
a,b
a Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan Center for Low Temperature Science, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
Received 13 November 2002; accepted 2 December 2002
Abstract Low-temperature scanning tunneling spectroscopy (STS) has been performed on YBa2 Cu3 Oy (YBCO) in the magnetic field l0 H ¼ 1 T. Clear vortex images are obtained on the surface chemically etched with 1% Br-ethanol. We measured on the twinned crystals and directly observed the effect of twin boundary on the vortex arrangement. Vortices close to the twin boundary align themselves parallel to it, suggesting that vortices are effectively trapped by the twin boundary. The vortices very close to the twin boundary form almost square lattice. Such tendency decreases with increasing distance and the vortices form a hexagonal lattice in the region far from the twin boundary. However, the orientation of hexagonal lattice is not consistent with the previous reports. Possible origins of such disagreement are described in this paper. We also show spectra observed in the scan region and discuss their features. 2003 Elsevier B.V. All rights reserved. PACS: 74.60.G; 74.80 Keywords: Scanning tunneling spectroscopy; Vortex state; YBa2 Cu3 Oy
1. Introduction In high temperature superconductors (HTSC), it has been believed that superconducting order parameter has dx2 y 2 anisotropy. Many studies have been done trying to detect the dx2 y 2 nature of the superconductivity in the vortex structure of the mixed states. The electronic state of vortex core in HTSC has attracted much attention and been studied a lot.
*
Corresponding author. Tel./fax: +81-3-5452-6235. E-mail address: [email protected] (K. Shibata).
First scanning tunneling spectroscopy (STS) imaging of vortex core in HTSC was carried out in YBa2 Cu3 Oy (YBCO) [1] and double-peak in the tunneling spectrum was observed inside the vortex core, which were attributed to the discrete bound states. Recently, similar vortex core states were also observed in Bi2 Sr2 CaCu2 O8þd (Bi2212) [2]. Although many theoretical studies have been carried out to explain observed bound states [3–6], the experimental information is insufficient and more detailed experimental studies for the electronic states of vortex core are necessary to clarify the mechanism of such bound states. On the other hand, the vortex lattice structure in d-wave HTSC has also attracted much attention.
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01056-6
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K. Shibata et al. / Physica C 392–396 (2003) 323–327
It is expected that vortex system reveals the fourfold symmetry in high magnetic field [7,8]. Recently, such an evidence of square vortex lattice was detected by small angle neutron scattering (SANS) for La1:83 Sr0:17 CuO4þd [9]. But in other HTSC compounds, it has not been obviously observed yet and more experimental studies are necessary as well. STS can detect real space modulation of local density of states (LDOS) and reveal the vortex core structure. Such a study has already done for Bi2212 [10]. Thus STS is the powerful tool which can investigate all the above mentioned subjects of vortex states in HTSC. In this paper, we show results of STM spectroscopic studies of YBCO single crystals. The vortex arrangements near and far from the twin boundary are displayed and the effect of twin boundary on the symmetry and orientation of vortex system is discussed along with the spectroscopic features.
2. Experimental YBCO single crystals were grown by self-flux method using Y2 O3 crucible. Slightly overdoped crystals (Tc 90 K, DTc 1:5 K) prepared by annealing in 1 bar oxygen at 450 C were used in this study. The post-annealed samples were cleaved and followed by the wet chemical etching with 1% Br in ethanol for 1 min. Then rinsed in ethanol, immediately transferred into the loadlock chamber to be high vacuum condition to minimize the exposure time to air. STM/STS measurements were carried out in UHV condition (1010 Torr) in l0 H ¼ 1 T (field cooled) applied parallel to the c-axis. Tip used in this study was mechanically sharpened Pt/Ir wire, mounted perpendicularly to the (0 0 1) surface of YBCO. Typical tunneling parameters for STS were I ¼ 0:1 nA, Vsample ¼ 0:03 V, giving the tunneling resistance of 0.3 GX. At zero magnetic field, clear superconducting energy gap was observed for entire scan region of over 1 lm square field. To obtain vortex images, we first divided scan field into typically 128 · 128 regions and I–V curve was taken at each point, which took about 20 h. After all the measurements, each I–V
curve was numerically calculated into the differential conductance dI=dV curve. dI=dV is proportional to the LDOS at the measured position and the two dimensional plot of dI=dV value at bias voltage Vsample construct LDOS map at Vsample . All vortex images shown in this paper were obtained as a ratio of the LDOS map of Vsample ¼ 20 mV to 0 mV. We confirmed that the relative position between the tip and sample doesnÕt change during the STS measurements by taking the STM images before and after the STS measurements and comparing the two images.
3. Results and discussion Fig. 1(a) shows topographic image taken on 260 nm square region. In the figure, we observe straight line running almost diagonally from the middle left to the upper right direction, as shown by an arrow. The line has its width of 2.5 nm. The surface is enough flat and we cannot observe any other structures within our experimental res height. Fig. 1(b) shows olution of less than 1 A vortex image taken on the same position as Fig. 1(a). Clear straight line anomaly is presented at the same position of the image in Fig. 1(a) along with the vortices. The spacing between the vortices is about 50 nm and well agrees with the expected value for applied magnetic field of l0 H ¼ 1 T. In the figure, vortices positioned near the straight line are about 50 nm apart from it and align themselves parallel to it. From these results, it is strongly suggested that the straight line in Fig. 1(a) and (b) shows twin boundary, trapping the vortices in it. It is well known that twin boundary effectively pins vortices [11] and disturb the formation of vortex lattice. Certainly, vortex arrangement is influenced very close to the twin boundary. Vortices of first and second row apart from the twin boundary forms almost square lattice. But the influence becomes weaker with increasing distance and vortices form a hexagonal lattice. These results suggest that the influence of twin boundary is limited to the region very close to it and vortex lattice structure in the region far from the twin boundary is expected to be the same as that in twin-free sample.
K. Shibata et al. / Physica C 392–396 (2003) 323–327
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Fig. 2. Typical spectra observed in the scan region shown in Fig. 1. We observed three types of spectra, that is, superconducting spectrum (bottom), vortex core spectrum (middle) and spectrum at twin boundary (top). The curves are offset by 1.5 nS for clarity.
Fig. 1. (a) Topographic image taken on 260 nm square region (Vsample ¼ 0:5 V, I ¼ 0:1 nA). (b) Vortex image taken on the same area as (a). The dark dot regions represent vortices. Both images are taken at T ¼ 30 K, l0 H ¼ 1 T. The arrows show the position of twin boundary.
In Fig. 2, typical three types of spectra observed in the scan region of Fig. 1 are shown. The bottom spectrum shows a superconducting gap-like structure. The spectrum has a coherence peak at Vsample 20 mV and a remaining zero bias conductance, which is almost the same as typically observed spectrum in zero magnetic field. The
spectrum shown in the middle part of Fig. 2 is the spectrum inside the vortex core. The spectrum is characterized by the suppression of the coherence peak and bound states at bias voltage Vsample 5 mV, almost the same features reported previously [1]. The origin of such bound states in the vortex core spectrum have been theoretically discussed [3–6]. Particularly from our result, it should be noted that vortex core spectrum has almost the same features between those in 1 and 6 T [1], i.e. this result suggests that the bound states in the vortex core cannot be explained by the magnetic field dependent mechanism as suggested by Yasui and Kita [5]. The topmost spectrum shows that on the twin boundary, which shows gap-like structure at the Fermi energy but does not show the superconducting coherence peak and the dI=dV curve shows steeper increase at large bias voltage region than the others. Thus the spectrum is quite different from those in vortex core and superconducting region. To our knowledge, this is the first report of spectrum at twin boundary as well as the vortex
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K. Shibata et al. / Physica C 392–396 (2003) 323–327
core spectrum at low magnetic field region of l0 H ¼ 1 T. The clear difference of the electronic states at twin boundary (the absence of coherence peak) leads to the effective vortex pinning at the twin boundary. In Fig. 1(b), we suggested that vortex arrangement far from the twin boundary, would coincide with that of the twin-free sample. Now we will investigate the vortex behavior far from twin boundary. Fig. 3(a) shows vortex image at T ¼ 4:5 K in magnetic field of l0 H ¼ 1 T taken on 200 nm square region. It is confirmed that the center of scan region is at least 240 nm apart form the twin boundary. Fig. 3(b) shows two-dimensional power spectrum of vortex image in Fig. 3(a). The spots in Fig. 3(b) show distorted hexagonal pattern. SANS studies for untwinned YBCO showed that SANS pattern of flux-line lattice forms a hexagonal pattern of six spots distorted by the a–b anisotropy and orients with the axis of the atomic lattice when magnetic field is applied parallel to the c-axis [12]. Our results is the same as neither that of SANS nor previous STS results [1], i.e. power spectrum spots show nearly hexagonal pattern and it does not orient with the crystalline axis. Besides, the hexagonal spots elongate to nearly {1 1 0} direction. We now consider the origin of such a difference. First, the effect of twin boundary should be taken into consideration. We detected just one twin boundary in the maximum scan length of more than 1 lm and its density can be considered to be enough dilute but the effect on the vortex system can be significant, especially in its orientation. As shown in Fig. 1(b), the effect of twin boundary on the symmetry of vortex lattice disappears in the region far from it. But we cannot say that the effect on the orientation always vanish rapidly as well. The elongation of hexagonal spots to nearly {1 1 0} direction implies the validity of this scenario. Next possible origin is the effect of vortex pinning by the local impurity or defects in the sample. It is well known that random point disorder such as oxygen deficiencies effectively pin the vortices in YBCO [13]. We observed quasiparticle scattering resonances which appear as single peak in the spectrum taken on the same surface of YBCO [14]. Vortices can be influenced by such a scatterer and a little distorted, resulting in the
Fig. 3. (a) Vortex image taken on 200 nm square field of view. The scanned field locates at least 240 nm far from twin boundary. (b) Two-dimensional power spectrum image of (a). The arrows show crystalline axis in real space determined from the direction of twin boundary.
formation of spots in Fig. 3(b). Theoretically, it is predicted that triangular vortex lattice in low magnetic field changes its symmetry into square lattice in high magnetic field [7,8]. It may become the last possible origin of our results that we observed vortex states in the intermediate magnetic
K. Shibata et al. / Physica C 392–396 (2003) 323–327
field of such a transformation in vortex system. We cannot show quantitative estimation about the strength of above mentioned twin boundary or pinning effects in our STM/STS studies. But it will be helpful if we obtain vortex image of much wider scan region and distinguish the local distortion of vortices from the entire vortex lattice arrangement. Our vortex observation is limited to the narrow scan region far less than 1 lm in the present condition of STM/STS apparatus. The measurements for twin-free samples and improvements of measurement system will be necessary to clarify this problem.
4. Summary We have carried out STS studies on the vortex states of YBCO single crystals. We show topographic and vortex images around a twin boundary in magnetic field. The twin boundary appears as the straight dark line in both topographic and vortex images. Vortices close to the twin boundary are distorted to form a nearly square structure but relax with increasing distance from it to form a hexagonal lattice. The result implies that the twin boundary influences the vortex symmetry just in the very narrow region close to it. Vortex states far from twin boundary show distorted hexagonal lattice but its orientation does not agree with the SANS result for untwinned crystal and theoretical studies. The origin of such a disagreement remains
327
open. Effect of twin boundary, local quasiparticle scatterer and d-wave anisotropy will be the possible origins.
References [1] I. Maggio-Aprile, Ch. Renner, A. Erb, E. Walker, O. Fischer, Phys. Rev. Lett. 75 (1995) 2754. [2] S.H. Pan, E.W. Hudson, A.K. Gupta, K.-W. Ng, H. Eisaki, S. Uchida, J.C. Davis, Phys. Rev. Lett. 85 (2000) 1536. [3] A. Himeda, M. Ogata, Y. Tanaka, S. Kashiwaya, J. Phys. Soc. Jpn. 66 (1997) 3367. [4] M. Franz, Z. Tesanovic, Phys. Rev. Lett. 80 (1998) 4763. [5] K. Yasui, T. Kita, Phys. Rev. Lett. 83 (1999) 4168. [6] M. Ogata, Int. J. Mod. Phys. B 13 (1999) 3560. [7] J. Shiraishi, M. Kohmoto, K. Maki, Phys. Rev. B 59 (1999) 4497. [8] M. Ichioka, A. Hasegawa, K. Machida, Phys. Rev. B 59 (1999) 8902. [9] R. Gilardi, J. Mesot, A. Drew, U. Divakar, S.L. Lee, E.M. Forgan, O. Zaharko, K. Conder, V.K. Aswal, C.D. Dewhurst, R. Cubitt, N. Momono, M. Oda, Phys. Rev. Lett. 88 (2002) 217003. [10] J.E. Hoffman, E.W. Hudson, K.M. Lang, V. Madhavan, H. Eisaki, S. Uchida, J.C. Davis, Science 295 (2002) 466. [11] W.K. Kwok, U. Welp, G.W. Crabtree, K.G. Vandervoort, R. Hulscher, J.Z. Liu, Phys. Rev. Lett. 64 (1990) 966. [12] S.T. Johnson, E.M. Forgan, S.H. Lloyd, C.M. Aegerter, S.L. Lee, R. Cubitt, P.G. Kealey, C. Ager, S. Tajima, A. Rykov, D.McK. Paul, Phys. Rev. Lett. 82 (1999) 2792. [13] T. Nishizaki, N. Kobayashi, Supercond. Sci. Technol. 13 (2000) 1. [14] K. Shibata, M. Maki, T. Nishizaki, N. Kobayashi, Physica C 388–389 (2003) 277.
Scanning tunneling spectroscopy studies on vortices in YBa2Cu3Oy single crystals Kenji Shibata b
a,*
, Makoto Maki a, Terukazu Nishizaki a, Norio Kobayashi
a,b
a Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan Center for Low Temperature Science, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan
Received 13 November 2002; accepted 2 December 2002
Abstract Low-temperature scanning tunneling spectroscopy (STS) has been performed on YBa2 Cu3 Oy (YBCO) in the magnetic field l0 H ¼ 1 T. Clear vortex images are obtained on the surface chemically etched with 1% Br-ethanol. We measured on the twinned crystals and directly observed the effect of twin boundary on the vortex arrangement. Vortices close to the twin boundary align themselves parallel to it, suggesting that vortices are effectively trapped by the twin boundary. The vortices very close to the twin boundary form almost square lattice. Such tendency decreases with increasing distance and the vortices form a hexagonal lattice in the region far from the twin boundary. However, the orientation of hexagonal lattice is not consistent with the previous reports. Possible origins of such disagreement are described in this paper. We also show spectra observed in the scan region and discuss their features. 2003 Elsevier B.V. All rights reserved. PACS: 74.60.G; 74.80 Keywords: Scanning tunneling spectroscopy; Vortex state; YBa2 Cu3 Oy
1. Introduction In high temperature superconductors (HTSC), it has been believed that superconducting order parameter has dx2 y 2 anisotropy. Many studies have been done trying to detect the dx2 y 2 nature of the superconductivity in the vortex structure of the mixed states. The electronic state of vortex core in HTSC has attracted much attention and been studied a lot.
*
Corresponding author. Tel./fax: +81-3-5452-6235. E-mail address: [email protected] (K. Shibata).
First scanning tunneling spectroscopy (STS) imaging of vortex core in HTSC was carried out in YBa2 Cu3 Oy (YBCO) [1] and double-peak in the tunneling spectrum was observed inside the vortex core, which were attributed to the discrete bound states. Recently, similar vortex core states were also observed in Bi2 Sr2 CaCu2 O8þd (Bi2212) [2]. Although many theoretical studies have been carried out to explain observed bound states [3–6], the experimental information is insufficient and more detailed experimental studies for the electronic states of vortex core are necessary to clarify the mechanism of such bound states. On the other hand, the vortex lattice structure in d-wave HTSC has also attracted much attention.
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01056-6
324
K. Shibata et al. / Physica C 392–396 (2003) 323–327
It is expected that vortex system reveals the fourfold symmetry in high magnetic field [7,8]. Recently, such an evidence of square vortex lattice was detected by small angle neutron scattering (SANS) for La1:83 Sr0:17 CuO4þd [9]. But in other HTSC compounds, it has not been obviously observed yet and more experimental studies are necessary as well. STS can detect real space modulation of local density of states (LDOS) and reveal the vortex core structure. Such a study has already done for Bi2212 [10]. Thus STS is the powerful tool which can investigate all the above mentioned subjects of vortex states in HTSC. In this paper, we show results of STM spectroscopic studies of YBCO single crystals. The vortex arrangements near and far from the twin boundary are displayed and the effect of twin boundary on the symmetry and orientation of vortex system is discussed along with the spectroscopic features.
2. Experimental YBCO single crystals were grown by self-flux method using Y2 O3 crucible. Slightly overdoped crystals (Tc 90 K, DTc 1:5 K) prepared by annealing in 1 bar oxygen at 450 C were used in this study. The post-annealed samples were cleaved and followed by the wet chemical etching with 1% Br in ethanol for 1 min. Then rinsed in ethanol, immediately transferred into the loadlock chamber to be high vacuum condition to minimize the exposure time to air. STM/STS measurements were carried out in UHV condition (1010 Torr) in l0 H ¼ 1 T (field cooled) applied parallel to the c-axis. Tip used in this study was mechanically sharpened Pt/Ir wire, mounted perpendicularly to the (0 0 1) surface of YBCO. Typical tunneling parameters for STS were I ¼ 0:1 nA, Vsample ¼ 0:03 V, giving the tunneling resistance of 0.3 GX. At zero magnetic field, clear superconducting energy gap was observed for entire scan region of over 1 lm square field. To obtain vortex images, we first divided scan field into typically 128 · 128 regions and I–V curve was taken at each point, which took about 20 h. After all the measurements, each I–V
curve was numerically calculated into the differential conductance dI=dV curve. dI=dV is proportional to the LDOS at the measured position and the two dimensional plot of dI=dV value at bias voltage Vsample construct LDOS map at Vsample . All vortex images shown in this paper were obtained as a ratio of the LDOS map of Vsample ¼ 20 mV to 0 mV. We confirmed that the relative position between the tip and sample doesnÕt change during the STS measurements by taking the STM images before and after the STS measurements and comparing the two images.
3. Results and discussion Fig. 1(a) shows topographic image taken on 260 nm square region. In the figure, we observe straight line running almost diagonally from the middle left to the upper right direction, as shown by an arrow. The line has its width of 2.5 nm. The surface is enough flat and we cannot observe any other structures within our experimental res height. Fig. 1(b) shows olution of less than 1 A vortex image taken on the same position as Fig. 1(a). Clear straight line anomaly is presented at the same position of the image in Fig. 1(a) along with the vortices. The spacing between the vortices is about 50 nm and well agrees with the expected value for applied magnetic field of l0 H ¼ 1 T. In the figure, vortices positioned near the straight line are about 50 nm apart from it and align themselves parallel to it. From these results, it is strongly suggested that the straight line in Fig. 1(a) and (b) shows twin boundary, trapping the vortices in it. It is well known that twin boundary effectively pins vortices [11] and disturb the formation of vortex lattice. Certainly, vortex arrangement is influenced very close to the twin boundary. Vortices of first and second row apart from the twin boundary forms almost square lattice. But the influence becomes weaker with increasing distance and vortices form a hexagonal lattice. These results suggest that the influence of twin boundary is limited to the region very close to it and vortex lattice structure in the region far from the twin boundary is expected to be the same as that in twin-free sample.
K. Shibata et al. / Physica C 392–396 (2003) 323–327
325
Fig. 2. Typical spectra observed in the scan region shown in Fig. 1. We observed three types of spectra, that is, superconducting spectrum (bottom), vortex core spectrum (middle) and spectrum at twin boundary (top). The curves are offset by 1.5 nS for clarity.
Fig. 1. (a) Topographic image taken on 260 nm square region (Vsample ¼ 0:5 V, I ¼ 0:1 nA). (b) Vortex image taken on the same area as (a). The dark dot regions represent vortices. Both images are taken at T ¼ 30 K, l0 H ¼ 1 T. The arrows show the position of twin boundary.
In Fig. 2, typical three types of spectra observed in the scan region of Fig. 1 are shown. The bottom spectrum shows a superconducting gap-like structure. The spectrum has a coherence peak at Vsample 20 mV and a remaining zero bias conductance, which is almost the same as typically observed spectrum in zero magnetic field. The
spectrum shown in the middle part of Fig. 2 is the spectrum inside the vortex core. The spectrum is characterized by the suppression of the coherence peak and bound states at bias voltage Vsample 5 mV, almost the same features reported previously [1]. The origin of such bound states in the vortex core spectrum have been theoretically discussed [3–6]. Particularly from our result, it should be noted that vortex core spectrum has almost the same features between those in 1 and 6 T [1], i.e. this result suggests that the bound states in the vortex core cannot be explained by the magnetic field dependent mechanism as suggested by Yasui and Kita [5]. The topmost spectrum shows that on the twin boundary, which shows gap-like structure at the Fermi energy but does not show the superconducting coherence peak and the dI=dV curve shows steeper increase at large bias voltage region than the others. Thus the spectrum is quite different from those in vortex core and superconducting region. To our knowledge, this is the first report of spectrum at twin boundary as well as the vortex
326
K. Shibata et al. / Physica C 392–396 (2003) 323–327
core spectrum at low magnetic field region of l0 H ¼ 1 T. The clear difference of the electronic states at twin boundary (the absence of coherence peak) leads to the effective vortex pinning at the twin boundary. In Fig. 1(b), we suggested that vortex arrangement far from the twin boundary, would coincide with that of the twin-free sample. Now we will investigate the vortex behavior far from twin boundary. Fig. 3(a) shows vortex image at T ¼ 4:5 K in magnetic field of l0 H ¼ 1 T taken on 200 nm square region. It is confirmed that the center of scan region is at least 240 nm apart form the twin boundary. Fig. 3(b) shows two-dimensional power spectrum of vortex image in Fig. 3(a). The spots in Fig. 3(b) show distorted hexagonal pattern. SANS studies for untwinned YBCO showed that SANS pattern of flux-line lattice forms a hexagonal pattern of six spots distorted by the a–b anisotropy and orients with the axis of the atomic lattice when magnetic field is applied parallel to the c-axis [12]. Our results is the same as neither that of SANS nor previous STS results [1], i.e. power spectrum spots show nearly hexagonal pattern and it does not orient with the crystalline axis. Besides, the hexagonal spots elongate to nearly {1 1 0} direction. We now consider the origin of such a difference. First, the effect of twin boundary should be taken into consideration. We detected just one twin boundary in the maximum scan length of more than 1 lm and its density can be considered to be enough dilute but the effect on the vortex system can be significant, especially in its orientation. As shown in Fig. 1(b), the effect of twin boundary on the symmetry of vortex lattice disappears in the region far from it. But we cannot say that the effect on the orientation always vanish rapidly as well. The elongation of hexagonal spots to nearly {1 1 0} direction implies the validity of this scenario. Next possible origin is the effect of vortex pinning by the local impurity or defects in the sample. It is well known that random point disorder such as oxygen deficiencies effectively pin the vortices in YBCO [13]. We observed quasiparticle scattering resonances which appear as single peak in the spectrum taken on the same surface of YBCO [14]. Vortices can be influenced by such a scatterer and a little distorted, resulting in the
Fig. 3. (a) Vortex image taken on 200 nm square field of view. The scanned field locates at least 240 nm far from twin boundary. (b) Two-dimensional power spectrum image of (a). The arrows show crystalline axis in real space determined from the direction of twin boundary.
formation of spots in Fig. 3(b). Theoretically, it is predicted that triangular vortex lattice in low magnetic field changes its symmetry into square lattice in high magnetic field [7,8]. It may become the last possible origin of our results that we observed vortex states in the intermediate magnetic
K. Shibata et al. / Physica C 392–396 (2003) 323–327
field of such a transformation in vortex system. We cannot show quantitative estimation about the strength of above mentioned twin boundary or pinning effects in our STM/STS studies. But it will be helpful if we obtain vortex image of much wider scan region and distinguish the local distortion of vortices from the entire vortex lattice arrangement. Our vortex observation is limited to the narrow scan region far less than 1 lm in the present condition of STM/STS apparatus. The measurements for twin-free samples and improvements of measurement system will be necessary to clarify this problem.
4. Summary We have carried out STS studies on the vortex states of YBCO single crystals. We show topographic and vortex images around a twin boundary in magnetic field. The twin boundary appears as the straight dark line in both topographic and vortex images. Vortices close to the twin boundary are distorted to form a nearly square structure but relax with increasing distance from it to form a hexagonal lattice. The result implies that the twin boundary influences the vortex symmetry just in the very narrow region close to it. Vortex states far from twin boundary show distorted hexagonal lattice but its orientation does not agree with the SANS result for untwinned crystal and theoretical studies. The origin of such a disagreement remains
327
open. Effect of twin boundary, local quasiparticle scatterer and d-wave anisotropy will be the possible origins.
References [1] I. Maggio-Aprile, Ch. Renner, A. Erb, E. Walker, O. Fischer, Phys. Rev. Lett. 75 (1995) 2754. [2] S.H. Pan, E.W. Hudson, A.K. Gupta, K.-W. Ng, H. Eisaki, S. Uchida, J.C. Davis, Phys. Rev. Lett. 85 (2000) 1536. [3] A. Himeda, M. Ogata, Y. Tanaka, S. Kashiwaya, J. Phys. Soc. Jpn. 66 (1997) 3367. [4] M. Franz, Z. Tesanovic, Phys. Rev. Lett. 80 (1998) 4763. [5] K. Yasui, T. Kita, Phys. Rev. Lett. 83 (1999) 4168. [6] M. Ogata, Int. J. Mod. Phys. B 13 (1999) 3560. [7] J. Shiraishi, M. Kohmoto, K. Maki, Phys. Rev. B 59 (1999) 4497. [8] M. Ichioka, A. Hasegawa, K. Machida, Phys. Rev. B 59 (1999) 8902. [9] R. Gilardi, J. Mesot, A. Drew, U. Divakar, S.L. Lee, E.M. Forgan, O. Zaharko, K. Conder, V.K. Aswal, C.D. Dewhurst, R. Cubitt, N. Momono, M. Oda, Phys. Rev. Lett. 88 (2002) 217003. [10] J.E. Hoffman, E.W. Hudson, K.M. Lang, V. Madhavan, H. Eisaki, S. Uchida, J.C. Davis, Science 295 (2002) 466. [11] W.K. Kwok, U. Welp, G.W. Crabtree, K.G. Vandervoort, R. Hulscher, J.Z. Liu, Phys. Rev. Lett. 64 (1990) 966. [12] S.T. Johnson, E.M. Forgan, S.H. Lloyd, C.M. Aegerter, S.L. Lee, R. Cubitt, P.G. Kealey, C. Ager, S. Tajima, A. Rykov, D.McK. Paul, Phys. Rev. Lett. 82 (1999) 2792. [13] T. Nishizaki, N. Kobayashi, Supercond. Sci. Technol. 13 (2000) 1. [14] K. Shibata, M. Maki, T. Nishizaki, N. Kobayashi, Physica C 388–389 (2003) 277.