English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The quantum spin Hall effect arises due to band inversion in topologicalinsulators, and has the defining characteristic that it hosts helical edgechannels at zero magnetic field, leading to a finite spin Hall conductivity.The spin Hall conductivity is understood as the difference of the contributionsof two spin states. In the effective four-band BHZ model, these two spin statesappear as two uncoupled blocks in the Hamiltonian matrix. However, this ideabreaks down if additional degrees of freedom are considered. The two blockscannot be identified by proper spin $S_z$ or total angular momentum $J_z$, bothnot conserved quantum numbers. In this work, we discuss a notion of blockstructure for the more general k.p model, defined by a conserved quantum numberthat we call isoparity, a combination of parity $z\to-z$ and spin. Isoparityremains a conserved quantity under a wide range of conditions, in particular inpresence of a perpendicular external magnetic field. From point-groupconsiderations, isoparity is fundamentally defined as the action of $z\to-z$ onthe spatial and spinorial degrees of freedom. Since time reversal anticommuteswith isoparity, the two blocks act as Kramers partners. The combination ofconductivity and isoparity defines spin conductivity. This generalized notionof spin Hall conductivity uncovers the meaning of 'spin': It is not the properspin $S_z$, but a crystal symmetry that is realized by a spinorialrepresentation.

Parity symmetry as the origin of 'spin' in the quantum spin Hall effect