Before 1982, the type of atomic or electronic patterns that could arise on sub-micron length scales was mainly a theoretician's fantasy. But thanks to the invention of the Scanning Tunneling Microscope (STM) by Binnig and Rohrer [1] that such patterns down to atomic scales can be observed easily today. An atomic resolution STM image actually reflects patterns of surface electrons due to the underlying atoms.

On the other hand, the surface image of an electronically homogeneous surface reflects its topography. At times, it is difficult to distinguish between electronic and topographic features for an unknown surface. While various topographic patterns on such scales can be conceived easily, the electronic patterns of sub-micron length scale mainly arise from chemical inhomogenieties (e.g. impurities), lattice deformation (strain), strong correlation effects (e.g., charge density waves) or quantum effects (interference or confinement).

In our laboratory, we have explored a few such patterns using a homemade STM based on our own design [2]. This design makes STM quite compact in size and compatible for high vacuum and low temperature applications. Fig.1 shows a photograph of this STM together with some atomic resolution images and an image where acronym IITK has been written by making pits on a graphite crystal using STM itself.

       Fig.1: The left photograph shows the homemade STM in our lab. On the right the gray image is atomic resolution on graphite, the blue one is the charge density wave in NbSe₂ crystal at 8K, here every third atomic spot is brighter than the others. The lower one is the acronym IITK written with the STM on a graphite crystal.

Graphite has been studied quite extensively with the STM due to the ease with which an atomically flat surface can be prepared because of its layered structure. A number of anomalous STM images on graphite have been reported. One such commonly seen pattern is a hexagonal pattern with a periodicity 10-100 times larger than that of graphite's in-plane lattice constant [3]. This arises from the Moiré pattern due to a small rotation of the topmost graphite layer with respect to the underlying layers. Such a Moiré pattern is shown in Fig.2 where a large-scale hexagonal periodic pattern is visible by superimposing two hexagonal lattices with slight rotation between them. The pattern seen by STM is actually the electronic pattern arising from different local atomic structure.

The central image in Fig.3 shows an image of graphite surface taken with our STM where we see a pattern confined between the fiber-1 and fiber-2 on a terrace defined by step-1 and step-2. This structure was found on a fresh cleaved graphite surface, presumably created during crystal growth. More interesting is the variation in the pattern as we move to the right where the 2-D pattern's periodicity increases and after the end of fiber-1 it evolves into 1-D fringes that bend towards step-2. The left and right images in Fig.3 focus on two areas of this image with a fixed periodicity on left and a changing periodicity on the right. This is also demonstrated by the fast Fourier transform  (FFT) of the two images shown in the insets. Detailed tunneling

Fig.3: The middle STM image shows the pattern due to a spatially varying Moiré rotation in the portion of the graphite layer confined between fiber-1 and fiber-2 and on the terrace defined by step-1 and step-2. The left and right images highlight the marked portion of the central image. The inset in these two images is the FFT of the respective images showing no lattice variation in left image, and significant lattice variation in the right image.

spectra and tunneling conductance images of this region show that this is due to the changes in the electron density and not due to topographic deformation. In fact the bright spots in the hexagonal super-lattice are found to be more metallic than the dark regions pertaining to different local arrangements of the carbon atoms. We also found that repeated imaging of this area etched away the fiber-1 slowly and 1-D to 2-D transition point moved with this fiber end and the whole pattern evolved accordingly.

We attribute this pattern to spatially varying Moiré rotation [4]. The two fibers are constraining a portion of this layer to a particular rotation angle (2.3 degrees) and at the end of the fiber the layer relaxes to no rotation with a shear strain near the fiber end. However, the detailed pattern, and in particular the 1-D pattern, is far from obvious even with the Moiré rotation hypothesis. We have developed a model giving us a better insight into the large-scale variations in these spatially varying Moire patterns. Using this model we have calculated the 1-D fringes as well as the spatially varying 2-D pattern. Such a calculated image is shown in Fig.4 together with the STM image. The qualitative resemblance of the two, particularly in the 2-D fringe region, is remarkable. The 1-D fringes, from this model, are found to be very sensitive to the details of the spatial variation of the Moiré rotation angle, while in the modeled image below we have taken a relatively simple function for modeling for the variation in this angle.

Fig.4: Comparison of a STM image (left) with an modeled image using spatially varying Moiré rotation.

In conclusion, we have observed spatially varying periodic patterns on graphite that we attribute to the shear strain in the graphite layer. We have modeled these patterns using spatially varying Moiré rotation hypothesis and qualitatively we find a good agreement with the observed pattern. In fact this mathematical model is quite insightful regarding the details of the pattern and we are still working to understand these patterns better. We have also observed other large-scale patterns on graphite that are still under investigation.

References:

1. G. Binning, H Rohrer, C. Gerber, and E. Weibel, Phys. Rev. Lett. 49, 57 (1982).
2. S. K. Choudhary, Rupali Nagar, and A. K. Gupta, Proc. of DAE S. S. Symp. (Amritsar), (2004); A. K. Gupta and K.-W. Ng, Rev. Sci. Instrum. 72, 3552 (2001).
3. W. T. Pong and C. Durkan, Jap. J. Appl. Phys. Part 1 44 (7B), 5443 (2005); M. Kuwabara, D. R. Clarke, and D. A. Smith, Appl. Phys. Lett. 56, 2396 (1990); J. Xhie, K. Sattler, G. Me, N. Venkateswaran Phys. Rev. B 47 (1993), p. 15835; Zhao Y. Rong and Pieter Kuiper Phys. Rev. B 48, 17427 (1993).
4. S. K. Choudhary and A. K. Gupta, in preparation.

Professor Anjan K Gupta
Department of Physics
    eMail: anjankg@iitk.ac.in
    URL: http://home.iitk.ac.in/~anjankg/