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.

arXiv comment5 pages with 3 figures + 12 pages of supplemental material with 1 figure

References in corpus (18)

• Valley contrasting physics in graphene: magnetic moment and topological transport
• The Valley Hall Effect in MoS2 Transistors
• Detecting Topological Currents in Graphene Superlattices
• Electrical control of the valley Hall effect in bilayer MoS2 transistors
• Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene
• On A Proper Definition of Spin Current
• Gate-tunable Topological Valley Transport in Bilayer Graphene
• Magneto-Optical Detection of the Orbital Hall Effect in Chromium
• Orbital Hall effect as an alternative to valley Hall effect in gapped graphene
• Topological Valley Currents in Gapped Dirac Materials
• Edge currents shunt the insulating bulk in gapped graphene
• Origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride: Fermi surface edge currents rather than Fermi sea topological valley currents
• Orbital magnetoelectric effect in zigzag nanoribbons of p-band systems
• Topological Valley Currents in Bilayer Graphene/Hexagonal Boron Nitride Superlattices
• Nonlocal topological valley transport at large valley Hall angles
• Valley Hall Effect and Non-Local Resistance in Locally Gapped Graphene
• Non-identical moiré twins in bilayer graphene
• Low-dissipation edge currents without edge states

Cited by in corpus (8)

• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Orbital Hall Responses in Disordered Topological Materials
• Quantum correction to the orbital Hall effect
• Intrinsic torque on the orbital angular momentum in an electric field
• 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