Probing helicity and the topological origins of helicity via non-local Hanbury-Brown and Twiss correlations

Arjun Mani,Colin Benjamin

doi:10.1038/s41598-017-06820-w

Arjun Mani, Colin Benjamin

Open Access

https://doi.org/10.1038/s41598-017-06820-w

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Abstract

Quantum Hall edge modes are chiral while quantum spin Hall edge modes are helical. However, unlike chiral edge modes which always occur in topological systems, quasi-helical edge modes may arise in a trivial insulator too. These trivial quasi-helical edge modes are not topologically protected and therefore need to be distinguished from helical edge modes arising due to topological reasons. Earlier conductance measurements were used to identify these helical states, in this work we report on the advantage of using the non local shot noise as a probe for the helical nature of these states as also their topological or otherwise origin and compare them with chiral quantum Hall states. We see that in similar set-ups affected by same degree of disorder and inelastic scattering, non local shot noise “HBT” correlations can be positive for helical edge modes but are always negative for the chiral quantum Hall edge modes. Further, while trivial quasi-helical edge modes exhibit negative non-local”HBT” charge correlations, topological helical edge modes can show positive non-local “HBT” charge correlation. We also study the non-local spin correlations and Fano factor for clues as regards both the distinction between chirality/helicity as well as the topological/trivial dichotomy for helical edge modes.

Highlights

In presence of magnetic field and at low temperatures, chiral quantum Hall (QH) edge modes appear in a 2DEG1, 2
We find in this paper that while there is no distinction between charge and spin noise correlations for topological helical edge modes, they are completely different for trivial quasi-helical edge modes enabling an effective discrimination between the topological or trivial origins of these edge modes
We focus on the topological helical quantum spin Hall (QSH) case, we distinguish between the non-local charge and spin correlations

Summary

All probe disorder

Charge Fano factor sub-Poissonian, no sign change sub-Poissonian, changes sign spin Fano factor absent sub-Poissonian. Modes and second between topological and trivial origins of QSH edge modes in two Tables 1 and 2. Our story is not yet complete, the trivial phase we have assumed to have spin-momentum locked edge modes in absence of non-magnetic disorder but there is overwhelming evidence regarding this it is not cent percent guaranteed[4]. In the sub-section we address this what-if regarding the trivial phase. What if the trivial quasi-helical phase does not have any spin-momentum locking, even in absence of non-magnetic disorder? Its quite probable that the trivial phase in case of QSH systems is dominated by transport via quasi-helical spin-momentum locked edge modes in absence of non-magnetic What if the trivial quasi-helical phase does not have any spin-momentum locking, even in absence of non-magnetic disorder? its quite probable that the trivial phase in case of QSH systems is dominated by transport via quasi-helical spin-momentum locked edge modes in absence of non-magnetic

Spin Fano factor positive but small

Trivial Ballistic turn completely negative turn completely positive

Conclusion

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