Non-conservation of the valley density and its implications for the observation of the valley Hall effect

Abstract

We show that the conservation of the valley density in multivalley insulators is broken in an unexpected way by the electric field that drives the valley Hall effect. This implies that time-reversal-invariant fully gapped insulators, in which no bulk or edge state crosses the Fermi level, can support a valley Hall current in the bulk and yet show no valley density accumulation at the edges. Thus, the valley Hall effect cannot be observed in such systems. If the system is not fully gapped then valley density accumulation at the edges is possible. The accumulation has no contribution from undergap states and can be expressed as a Fermi surface average, for which we derive an explicit formula. We demonstrate the theory by calculating the valley density accumulations in an archetypical valley-Hall insulator: a gapped graphene nanoribbon. Surprisingly, we discover that a net valley density polarization is dynamically generated for certain edge terminations.

5 pages with 3 figures + 12 pages of supplemental material with 1 figure

References in corpus (10)

• The Valley Hall Effect in MoS2 Transistors
• Detecting Topological Currents in Graphene Superlattices
• On A Proper Definition of Spin Current
• Magneto-Optical Detection of the Orbital Hall Effect in Chromium
• Orbital Hall effect as an alternative to valley Hall effect in gapped graphene
• Edge currents shunt the insulating bulk in gapped graphene
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• Non-identical moiré twins in bilayer graphene

Cited by in corpus (8)

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• Orbital Edelstein effect of electronic itinerant orbital motion at edges
• Absence of Parity Anomaly in Massive Dirac Fermions on a Lattice
• Orbital Hall effect in spin-3/2 hole-doped semiconductors and its implications for orbitronics
• Ge as an orbitronic platform: giant in-plane orbital magneto-electric effect in a 2-dimensional hole gas