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Register a new userPerfect transmission and Aharanov-Bohm oscillations in topological insulator nanowires with nonuniform cross section
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Added by
Jens Hjorleifur Bardarson
Publication date
2017
fields
Physics
and research's language is
English
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Topological insulator nanowires with uniform cross section, combined with a magnetic flux, can host both a perfectly transmitted mode and Majorana zero modes. Here we consider nanowires with rippled surfaces---specifically, wires with a circular cross section with a radius varying along its axis---and calculate their transport properties. At zero doping, chiral symmetry places the clean wires (no impurities) in the AIII symmetry class, which results in a $mathbb{Z}$ topological classification. A magnetic flux threading the wire tunes between the topologically distinct insulating phases, with perfect transmission obtained at the phase transition. We derive an analytical expression for the exact flux value at the transition. Both doping and disorder breaks the chiral symmetry and the perfect transmission. At finite doping, the interplay of surface ripples and disorder with the magnetic flux modifies quantum interference such that the amplitude of Aharonov-Bohm oscillations reduces with increasing flux, in contrast to wires with uniform surfaces where it is flux-independent.
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A direct signature of electron transport at the metallic surface of a topological insulator is the Aharonov-Bohm oscillation observed in a recent study of Bi_2Se_3 nanowires [Peng et al., Nature Mater. 9, 225 (2010)] where conductance was found to oscillate as a function of magnetic flux $phi$ through the wire, with a period of one flux quantum $phi_0=h/e$ and maximum conductance at zero flux. This seemingly agrees neither with diffusive theory, which would predict a period of half a flux quantum, nor with ballistic theory, which in the simplest form predicts a period of $phi_0$ but a minimum at zero flux due to a nontrivial Berry phase in topological insulators. We show how h/e and h/2e flux oscillations of the conductance depend on doping and disorder strength, provide a possible explanation for the experiments, and discuss further experiments that could verify the theory.
In three-dimensional topological insulators (3D TI) nanowires, transport occurs via gapless surface states where the spin is fixed perpendicular to the momentum[1-6]. Carriers encircling the surface thus acquire a pi Berry phase, which is predicted to open up a gap in the lowest-energy 1D surface subband. Inserting a magnetic flux ({Phi}) of h/2e through the nanowire should cancel the Berry phase and restore the gapless 1D mode[7-8]. However, this signature has been missing in transport experiments reported to date[9-11]. Here, we report measurements of mechanically-exfoliated 3D TI nanowires which exhibit Aharonov-Bohm oscillations consistent with topological surface transport. The use of low-doped, quasi-ballistic devices allows us to observe a minimum conductance at {Phi} = 0 and a maximum conductance reaching e^2/h at {Phi} = h/2e near the lowest subband (i.e. the Dirac point), as well as the carrier density dependence of the transport.
The electron spectrum in a uniform nanowire with a hexagonal cross-section is calculated by means of a numerical diagonalization of the effective-mass Hamiltonian. Two basis sets are utilized. The wave-functions of low-lying states are calculated and visualized. The approach has an advantage over mesh methods based on finite-differences (or finite-elements) schemes: non-physical solutions do not arise. Our scheme can be easily generalized to the case of multi-band (Luttinger or Kane) ${bf k}cdot{bf p}$ Hamiltonians. The external fields (electrical, magnetic or strain) can be consistently introduced into the problem as well.
Snake states and Aharonov-Bohm interferences are examples of magnetoconductance oscillations that can be observed in a graphene p-n junction. Even though they have already been reported in suspended and encapsulated devices including different geometries, a direct comparison remains challenging as they were observed in separate measurements. Due to the similar experimental signatures of these effects a consistent assignment is difficult, leaving us with an incomplete picture. Here we present measurements on p-n junctions in encapsulated graphene revealing several sets of magnetoconductance oscillations allowing for their direct comparison. We analysed them with respect to their charge carrier density, magnetic field, temperature and bias dependence in order to assign them to either snake states or Aharonov-Bohm oscillations. Furthermore we were able to consistently assign the various Aharonov-Bohm interferences to the corresponding area which the edge states enclose. Surprisingly, we find that snake states and Aharonov-Bohm interferences can co-exist within a limited parameter range.
In this chapter we review our work on the theory of quantum transport in topological insulator nanowires. We discuss both normal state properties and superconducting proximity effects, including the effects of magnetic fields and disorder. Throughout we assume that the bulk is insulating and inert, and work with a surface-only theory. The essential transport properties are understood in terms of three special modes: in the normal state, half a flux quantum along the length of the wire induces a perfectly transmitted mode protected by an effective time reversal symmetry; a transverse magnetic field induces chiral modes at the sides of the wire, with different chiralities residing on different sides protecting them from backscattering; and, finally, Majorana zero modes are obtained at the ends of a wire in a proximity to a superconductor, when combined with a flux along the wire. Some parts of our discussion have a small overlap with the discussion in the review [Bardarson and Moore, Rep. Prog. Phys., 76, 056501, (2013)]. We do not aim to give a complete review of the published literature, instead the focus is mainly on our own and directly related work.
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