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Equation 5 · Part 3 · A Strained Crystal Is a Designer Spacetime

Symbol boldsymbolσ

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}
σ\boldsymbol{\sigma}

What this part means

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

Its job in the formula

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

The passage around this formula

…into a black hole, with the tilt itself playing the role of the metric’s off-diagonal, “flow” components. The paper writes the whole 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…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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