JERUSALEM, Feb. 13 (Xinhua) -- Israeli and German researchers have discovered unique properties of four-dimensional (4D) crystals, the Israel Institute of Technology (Technion) said Thursday.

The study, published in the journal Science, was conducted by creating a special wave pattern on a quasiperiodic surface with advanced techniques such as near-field scanning optical microscopy, said Technion in a statement.

Quasiperiodic crystals, ordered but not periodic, were first discovered by Technion researcher Dan Shechtman in 1982, which earned him the Nobel Prize in Chemistry in 2011.

Over the years, scientists found that quasiperiodic crystals exist in higher dimensions beyond the conventional three. This higher-dimensional structure determines their mechanical and topological properties.

The new study showed that despite differences in appearance, two quasiperiodic patterns shared the same topological properties, distinguishable only through their higher-dimensional structure.

It also showed that two surface wave patterns appear identical when measured in attoseconds, which can be explained by the balance between the crystal's topological and energetic properties. An attosecond is a very short period of time and is equal to one quintillionth of a second

The researchers said their findings may help scientists better understand quasiperiodic crystals and lead to new applications in quantum computing and data transmission. Enditem

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