Consider a two-dimensional triangular lattice with a lattice constant a, as shown in the figure below.(a) What are the primitive lattice vectors 𝐚1 and 𝐚2 in the Cartesian coordinates?(b) What is the area of the primitive unit cell?(c) Draw the Wigner-Seitz cell for the triangular lattice? And what is its volume?(d) Construct the reciprocal lattice vectors for the triangular lattice.(Hint: For a 2D lattice, use 𝐚i ·𝐛j = 2πδij)(e) Draw the first Brillouin zone.(f) If a point 𝐤 = (kx, ky) in
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