TY - JOUR

T1 - Electronic structure of periodic curved surfaces

T2 - Topological band structure

AU - Aoki, H.

AU - Koshino, M.

AU - Takeda, D.

AU - Morise, H.

AU - Kuroki, K.

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 2002/1/15

Y1 - 2002/1/15

N2 - The electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerenes. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wave function interferes on a multiply connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet transformation (such as Schwarz's P and D surfaces) possess one-to-one correspondence in their band energies at Brillouin-zone boundaries.

AB - The electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerenes. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wave function interferes on a multiply connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet transformation (such as Schwarz's P and D surfaces) possess one-to-one correspondence in their band energies at Brillouin-zone boundaries.

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U2 - 10.1103/PhysRevB.65.035102

DO - 10.1103/PhysRevB.65.035102

M3 - Article

AN - SCOPUS:0037080603

VL - 65

SP - 351021

EP - 351028

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 0163-1829

IS - 3

M1 - 035102

ER -