Format

Send to

Choose Destination
Phys Rev Lett. 2018 Mar 2;120(9):096401. doi: 10.1103/PhysRevLett.120.096401.

Space-Time Crystal and Space-Time Group.

Xu S1,2, Wu C1.

Author information

1
Department of Physics, University of California, San Diego, California 92093, USA.
2
Condensed Matter Theory Center and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.

Abstract

Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in D+1 dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed a "space-time" group is constructed to describe the discrete symmetries of a space-time crystal. Compared to space and magnetic groups, the space-time group is augmented by "time-screw" rotations and "time-glide" reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in one-plus-one dimensions (1+1D) is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, nonsymmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semimetal states. We provide a general framework for further studying topological properties of the (D+1)-dimensional space-time crystal.

Supplemental Content

Full text links

Icon for American Physical Society
Loading ...
Support Center