Blurring the boundaries between topological and non-topological phenomena in dots

Abstract

We investigate the electronic and transport properties of topological and trivial InAs${}_{1-x}$Bi${}_x$ quantum dots (QDs). By considering the rapid band gap change within valence band anticrossing theory for InAs${}_{1-x}$Bi${}_x$, we predicted that Bi-alloyed quantum wells become $\sim 30$meV gapped 2D topological insulators for well widths $d>6.9$nm $(x=0.15)$ and obtain the $\mathbf{k}.\mathbf{p}$ parameters of the corresponding Bernevig-Hughes-Zhang (BHZ) model. We analytically solve this model for cylindrical confinement via modified Bessel functions. For non-topological dots we find "geometrically protected" discrete helical edge-like states, i.e., Kramers pairs with spin-angular-momentum locking, in stark contrast with ordinary InAs QDs. For a conduction window with four edge states, we find that the two-terminal conductance $\mathcal{G}$ vs. the QD radius $R$ and the gate $V_g$ controlling its levels shows a double peak at $2e^2/h$ for both topological and trivial QDs. In contrast, when bulk and edge-state Kramers pairs coexist and are degenerate, a single-peak resonance emerges. Our results blur the boundaries between topological and non-topological phenomena for conductance measurements in small systems such as QDs. Bi-based BHZ QDs should also prove important as hosts to edge spin qubits.

arXiv commentMain text (4 pages + 3 figures) and Supplemental Material

References in corpus (35)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Spins in few-electron quantum dots
• Time-dependent transport in interacting and non-interacting mesoscopic systems
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks
• Tunable Fano effect in parallel-coupled double quantum dot system
• Fingerprint of Different Spin-Orbit Terms for Spin Transport in HgTe Quantum Wells
• Interface-induced Topological Insulator Transition in GaAs/Ge/GaAs Quantum Wells
• Edge Transport in the Trivial Phase of InAs/GaSb
• Helical Quantum States in HgTe Quantum Dots with Inverted Band Structures
• Intersubband-induced spin-orbit interaction in quantum wells
• Fano resonance in electron transport through parallel double quantum dots in the Kondo regime
• Magnetically Defined Qubits on 3D Topological Insulators
• Hyperfine-phonon spin relaxation in a single-electron GaAs quantum dot
• Topological Insulating States in Laterally Patterned Ordinary Semiconductors
• Spin-orbit interaction in GaAs wells: From one to two subbands
• Strain tuning of topological band order in cubic semiconductors
• Persistent Skyrmion Lattice of Noninteracting Electrons with Spin-Orbit Coupling
• A 3D topological insulator quantum dot for optically controlled quantum memory and quantum computing
• Energy spectrum and broken spin-surface locking in topological insulator quantum dots
• Spin-orbit-induced circulating currents in a semiconductor nanostructure
• Confinement and Fermion Doubling Problem in Dirac-like Hamiltonians
• Helical edge states in multiple topological mass domains
• Spin-orbit induced hole spin relaxation in InAs and GaAs quantum dots
• Probing Majorana-like states in quantum dots and quantum rings
• An all electron topological insulator in InAs double wells
• Gate-defined coupled quantum dots in topological insulators
• Geometric and compositional influences on spin-orbit induced circulating currents in nanostructures
• Electrically controlled crossing of energy levels in quantum dots in two-dimensional topological insulators

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• Dual topological insulator with mirror symmetry protected helical edge states
• Massive and massless two-dimensional Dirac particles in electric quantum dots
• Transport of Majorana Bound State in the presence of telegraph noise
• Higher-order topological insulator in cubic semiconductor quantum wells