Engineering topological phases in triple HgTe/CdTe quantum wells

Abstract

Quantum wells formed by layers of HgTe between Hg${}_{1-x}$Cd${}_x$Te barriers lead to two-dimensional (2D) topological insulators, as predicted by the BHZ model. Here, we theoretically and experimentally investigate the characteristics of triple HgTe quantum wells. We describe such heterostructure with a three dimensional $8\times 8$ Kane model, and use its eigenstates to derive an effective 2D Hamiltonian for the system. From these we obtain a phase diagram as a function of the well and barrier widths and we identify the different topological phases composed by zero, one, two, and three sets of edge states hybridized along the quantum wells. The phase transitions are characterized by a change of the spin Chern numbers and their corresponding band inversions. Complementary, transport measurements are experimentally investigated on a sample close to the transition line between the phases with one and two sets of edges states. Accordingly, for this sample we predict a gapless spectrum with low energy bulk conduction bands given by one parabolic and one Dirac band, and with edge states immersed in the bulk valance bands. Consequently, we show that under these conditions, local and non-local transport measurements are inconclusive to characterize a sole edge state conductivity due to bulk conductivity. On the other hand, Shubnikov-de Haas (SdH) oscillations show an excellent agreement with our theory. Particularly, we show that the measured SdH oscillation frequencies agrees with our model and show clear signatures of the coexistence of a parabolic and Dirac bands.

arXiv comment15 pages, 5 figures

References in corpus (69)

• Topological Insulators
• Topological insulators and superconductors
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• 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
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Weyl Semimetal in a Topological Insulator Multilayer
• Quantum Spin Hall Effect
• Topological Materials: Weyl Semimetals
• Topological Insulator Materials
• Unconventional Integer Quantum Hall effect in graphene
• Kwant: a software package for quantum transport
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• The quantum spin Hall effect and topological insulators
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Catalogue of Topological Electronic Materials
• Nonlocal edge state transport in the quantum spin Hall state
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se
• Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe
• Weyl semimetal with broken time reversal and inversion symmetries
• Time-reversal invariant realization of the Weyl semimetal phase
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations
• Helical edge resistance introduced by charge puddles
• Topological Surface States and Dirac point tuning in ternary Bi2Te2Se class of topological insulators
• Berry phase of non-ideal Dirac fermions in topological insulators
• High-Field Shubnikov-de Haas Oscillations in the Topological Insulator Bi${}_2$Te${}_2$Se
• Quantum Oscillations in a Topological Insulator Bi${}_2$Te${}_2$Se with Large Bulk Resistivity (6 $\Omega$cm)
• Fingerprint of Different Spin-Orbit Terms for Spin Transport in HgTe Quantum Wells
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations II: transport properties
• Quantized Conductance and Field-Effect Topological Quantum Transistor in Silicene Nanoribbons
• Theoretical possibilities for flat-band superconductivity
• Pressure and temperature driven phase transitions in HgTe quantum wells
• Stretchable persistent spin helices in GaAs quantum wells
• Persistence of two-dimensional topological insulator state in wide HgTe quantum well
• Temperature-induced topological phase transition in HgTe quantum wells
• Electric field driven quantum phase transition between band insulator and topological insulator
• Phase transitions in two tunnel-coupled HgTe quantum wells. Bilayer graphene analogy and beyond
• Nonlocal resistance and its fluctuations in microstructures of band-inverted HgTe/(Hg,Cd)Te quantum wells
• Large gap quantum spin Hall insulator, massless Dirac fermions and bilayer graphene analogue in InAs/Ga(In)Sb heterostructures
• Devices with electrically tunable topological insulating phases
• Coexisting edge states and gapless bulk in topological states of matter
• Tunable quantum spin Hall effect in double quantum wells
• Helical Liquids in Semiconductors
• Realistic picture of helical edge states in HgTe quantum wells
• Anomalous magneto-oscillations in two-dimensional systems
• Emergent quantum Hall effects below $50$ mT in a two-dimensional topological insulator
• Topologically confined states at corrugations of gated bilayer graphene
• Mesoscopic transport in two-dimensional topological insulators
• Topological insulators based on HgTe
• Topological excitonic corner states and nodal phase in bilayer quantum spin Hall insulators
• Layertronic control of topological states in multilayer metal-organic frameworks
• Robust helical edge transport at $\nu =0$ quantum Hall state
• Two-dimensional topological insulator state in double HgTe quantum well
• Paradoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system
• Pedagogical introduction to equilibrium Green's functions: condensed matter examples with numerical implementations
• An all electron topological insulator in InAs double wells
• Blurring the boundaries between topological and non-topological phenomena in dots
• Disorder-induced phase transition in Dirac systems beyond the linear approximation
• Massive and topological surface states in tensile strained HgTe
• Existence of nontrivial topologically protected states at grain boundaries in bilayer graphene: signatures and electrical switching
• Non-trivial quantum oscillation geometric phase shift in a trivial band
• Multiple crossing of Landau levels of two-dimensional fermions in double HgTe quantum wells
• Effect of Berry Phase on Nonlinear Response of Two-dimensional Fermions
• Electrical tuning of helical edge states in topological multilayers
• Bias-Voltage-Induced Topological Phase Transition in Finite Size Quantum Spin Hall Systems in the Presence of a Transverse Electric Field

Cited by in corpus (7)

• Direct observation of topological surface state in the topological superconductor 2M-WS2
• Energy states of Rydberg excitons in finite crystals: From weak to strong confinement
• Quantum oscillations in 2D electron gases with spin-orbit and Zeeman interactions
• Unconventional quantum oscillations and evidence of nonparabolic electronic states in quasi-two-dimensional electron system at complex oxide interfaces
• Interaction-controlled transport in a two-dimensional massless-massive Dirac system: Transition from degenerate to nondegenerate regimes
• Tunable Competing Electronic Orders in Double Quantum Spin Hall Superlattices
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators