TY - JOUR

T1 - Quantised hall conductance in a perfect crystal

AU - Dana, Itzhack

AU - Avron, Yosi

AU - Zak, J.

PY - 1985/8/10

Y1 - 1985/8/10

N2 - Using magnetic translation symmetry, the Hall conductance of an isolated magnetic band in units of e2/h is shown to satisfy the Diophantine equation p σ +qm=1, where p and q are relatively prime integers giving the number of flux quanta per unit cell area, φ=p/q, and m is an integer. This equation holds for a general periodic Schrodinger Hamiltonian with an arbitrary magnetic field and is a direct consequence of the q-fold degeneracy of magnetic bands. Extension to general real phi gives the equation φσH-ρ =integer with σH the Hall conductance and ρ the number of electrons per unit cell, from which sσH is uniquely determined once rho, phi and the gap structure are given.

AB - Using magnetic translation symmetry, the Hall conductance of an isolated magnetic band in units of e2/h is shown to satisfy the Diophantine equation p σ +qm=1, where p and q are relatively prime integers giving the number of flux quanta per unit cell area, φ=p/q, and m is an integer. This equation holds for a general periodic Schrodinger Hamiltonian with an arbitrary magnetic field and is a direct consequence of the q-fold degeneracy of magnetic bands. Extension to general real phi gives the equation φσH-ρ =integer with σH the Hall conductance and ρ the number of electrons per unit cell, from which sσH is uniquely determined once rho, phi and the gap structure are given.

UR - http://www.scopus.com/inward/record.url?scp=0039675161&partnerID=8YFLogxK

U2 - 10.1088/0022-3719/18/22/004

DO - 10.1088/0022-3719/18/22/004

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AN - SCOPUS:0039675161

SN - 0022-3719

VL - 18

SP - L679-L683

JO - Journal of Physics C: Solid State Physics

JF - Journal of Physics C: Solid State Physics

IS - 22

ER -