Unformatted text preview: x,y ) about an axis through the origin that forms an angle φ with the xaxis. Show that the matrix form of this operation is cos(2 φ ) sin(2 φ ) sin(2 φ )cos(2 φ ) ! Hint: An eﬃcient way of ﬁnding the matrix consists in rotating the lattice such that the reﬂection axis coincides with the xaxis, performing the reﬂection, and rotating back! Problem 3: Allowed rotation axes (15 points, Marder  Problem 1.4) Prove that the only allowed rotation axis in a twodimensional Bravais lattice are twofold, threefold, fourfold, and sixfold! To this end, consider the images of the lattice point ( a, 0) under rotations around the origin by angles φ andφ . Both must be in the Bravais lattice! From these conditions derive a simple expression that implicitly speciﬁes all possible φ ....
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 Spring '11
 ThomasVojta
 Physics, Work, Rotation, Condensed matter physics, lattice point, Marder, honeycomb lattice

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