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Equation 5 · Part 2 · A Strained Crystal Is a Designer Spacetime

Symbol v_F

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}
vFv_F

What this part means

the fixing the fermi velocity.

Its job in the formula

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

Where the article explains it

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 passage around this formula

…an object falling 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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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