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Equation 5 · Part 4 · A Strained Crystal Is a Designer Spacetime

Symbol W

H=vF σ⋅(k−b)+vF W(x) k⋅1H = v_F\,\boldsymbol{\sigma}\cdot(\mathbf{k}-\mathbf{b}) + v_F\,W(x)\,\mathbf{k}\cdot\mathbb{1}
WW

What this part means

W is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

W is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…statement as a single Hamiltonian, fixing the Fermi velocity vFv_F , the Pauli matrices σ\boldsymbol{\sigma} acting on the electron’s internal degree of freedom, the momentum-space shift b\mathbf{b} , and the tilt vector W(x) : H=vF σ⋅(k−b)+vF W(x) k⋅1H = v_F\,\boldsymbol{\sigma}\cdot(\mathbf{k}-\mathbf{b}) + v_F\,W(x)\,\mathbf{k}\cdot\mathbb{1}. The first term is ordinary tilted-free Weyl physics, shifted by the strain-induced gauge field. The second term is the one that matters here: it multiplies the momentum by the tilt and by the identity matrix, so it does not distinguish between the electron’s two internal…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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