%0 Generic %1 fang2012topological %A Fang, Chen %A Gilbert, Matthew J. %A Bernevig, B. Andrei %D 2012 %K Hall %T Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators %U http://arxiv.org/abs/1207.5767 %X We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that: (i) the Chern number of a $C_n$-invariant insulator can be determined, up to a multiple of $n$, by evaluating the eigenvalues of symmetry operators at high-symmetry points in the Brillouin zone; (ii) the Chern number of a $C_n$-invariant insulator is also determined, up to a multiple of $n$, by the $C_n$ eigenvalue of the Slater determinant of a noninteracting many-body system and (iii) the Chern number vanishes in insulators with dihedral point groups $D_n$, and the quantized electric polarization is a topological invariant for these insulators. In three-dimensional insulators, we show that: (i) only insulators with point groups $C_n$, $C_nh$ and $S_n$ PGS can have nonzero 3D quantum Hall coefficient and (ii) only insulators with improper rotation symmetries can have quantized magnetoelectric polarization $P_3$ in the term $P_3E\cdotB$, the axion term in the electrodynamics of the insulator (medium).

@misc{fang2012topological, abstract = {We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that: (i) the Chern number of a $C_n$-invariant insulator can be determined, up to a multiple of $n$, by evaluating the eigenvalues of symmetry operators at high-symmetry points in the Brillouin zone; (ii) the Chern number of a $C_n$-invariant insulator is also determined, up to a multiple of $n$, by the $C_n$ eigenvalue of the Slater determinant of a noninteracting many-body system and (iii) the Chern number vanishes in insulators with dihedral point groups $D_n$, and the quantized electric polarization is a topological invariant for these insulators. In three-dimensional insulators, we show that: (i) only insulators with point groups $C_n$, $C_{nh}$ and $S_n$ PGS can have nonzero 3D quantum Hall coefficient and (ii) only insulators with improper rotation symmetries can have quantized magnetoelectric polarization $P_3$ in the term $P_3\mathbf{E}\cdot\mathbf{B}$, the axion term in the electrodynamics of the insulator (medium).}, added-at = {2012-07-25T22:46:35.000+0200}, author = {Fang, Chen and Gilbert, Matthew J. and Bernevig, B. Andrei}, biburl = {https://www.bibsonomy.org/bibtex/2597f0c5cc510caabe145c9f4ca9ef8a8/vakaryuk}, description = {Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators}, interhash = {b97e814d946bb2af6e9fba9530550c4f}, intrahash = {597f0c5cc510caabe145c9f4ca9ef8a8}, keywords = {Hall}, note = {cite arxiv:1207.5767 Comment: 14 pages for main text, 6 pages for appendices, three figures and one table}, timestamp = {2012-07-25T22:46:35.000+0200}, title = {Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators}, url = {http://arxiv.org/abs/1207.5767}, year = 2012 }