We study experimentally the transport properties of "inverted" semiconductor HgT e-based quantum well, which is related to the two-dimensional topological insulator, in diffusive transport regime. We perform nonlocal electrical measurements in the absence of the magnetic field and observe large signal due to the edge states. It demonstrates, that the edge states can propagate over long distance ∼ 1mm, and, therefore, there is no difference between local and non local electrical measurements in topological insulator. In the presence of the in-plane magnetic field we find strong decrease of the local resistance and complete suppression of the nonlocal resistance. We attribute this observation to the transition between topological insulator and bulk metal induced by the in-plane magnetic field. Recently, a novel class of the topological state of a quantum matter has emerged, called topological insulator [1][2][3][4]. The first famous example of the two dimensional topological insulator (2DTI) is the integer quantum Hall effect (QHE) state on the resistance minima [5]. Such system represents the 2D electron gas in the presence of the strong perpendicular magnetic field, when all current is carried by the edge states, while electrons in the bulk region are localized. The number of the edge states are determined by the Landau level filling factor ν. The edge states are unidirectional because of the breaking of the time-reversal (TR) symmetry due to the magnetic field and robust against impurity scattering. Note, that disorder plays the crucial role in establishment of the Hall plateau in the finite region of the magnetic field or electron density.Another class of 2DTI is the quantum spin Hall effect state, which can be realized in 2D system with strong spin-orbit interaction in the absence of the magnetic field [1][2][3][4]. It has been shown that an "inverted" semiconductor HgTeCdTe quantum well [2,4], possess the insulating phase having the gap in the bulk electron spectrum and a single pair of counterpropagating or helical edge states for the two opposite spin polarizations. Remarkable consequence of the presence of the edge states in ballistic 2DTI is a quantized longitudinal resistance R = h/2e 2 , which has been observed in micrometer scale Hall bars [4]. The edge states are expected to be insensitive to weak, nonmagnetic impurity scattering due to destructive interference between two backscattering paths of the helical edge states ( see review [6]). It is worth noting that the backscattering does not destroy the edge states, therefore any 2DTI sample represents almost ideal natural one dimensional (1D) wire localized near the sample edge.In this letter we present an experimental study of the transport properties of "inverted" HgT e-based quantum well which possesses a pair of counter-propagating or helical edge states strongly mixed by spin flip scattering. When the Fermi level passes the bulk insulating gap, the devices revel unusual behaviour, which is characterized by high resistance R >> h/e 2 with metallic...

We investigate the magnetotransport properties of strained 80 nm thick HgTe layers featuring a high mobility of μ ∼ 4 × 10 5 cm 2 =V · s. By means of a top gate, the Fermi energy is tuned from the valence band through the Dirac-type surface states into the conduction band. Magnetotransport measurements allow us to disentangle the different contributions of conduction band electrons, holes, and Dirac electrons to the conductivity. The results are in line with previous claims that strained HgTe is a topological insulator with a bulk gap of ≈ 15 meV and gapless surface states. DOI: 10.1103/PhysRevLett.112.196801 PACS numbers: 73.25.+i, 05.60.Gg, 73.20.At, 73.43.-f The discovery of two-(2D) and three-dimensional (3D) topological insulators (TIs), a new material class with insulating bulk and topologically protected conducting surface states, has opened an exciting research field in condensed matter physics [1][2][3][4][5][6][7][8][9][10]. Although quite a number of different, especially, Bi-based materials [11][12][13][14], belong to this category, materials which combine high charge carrier mobility and insulating bulk are still scarce. This is mostly due to the fact that Bi-based 3D TIs are heavily doped alloy films with a low mobility ≈1000 cm 2 =V · s and a high bulk carrier density of 10 17 -10 19 cm −3 . HgTe-based 2D TIs, on the other hand, are characterized by very high mobilities enabling the discovery of the quantum spin Hall effect [15]. A recent analysis of the sequence of quantum Hall plateaus suggests that also strained HgTe layers constitute a 3D TI. The strain opens a gap in the gapless semimetal HgTe so that the TI properties can be explored by tuning the Fermi energy E F into the bulk gap and probing the transport properties of the gapless surface states. Although the strained HgTe film has a much higher mobility μ ¼ ð3 − 4Þ × 10 4 cm 2 =V · s, the high bulk carrier density and the absence of a top gate have complicated the detection of 3D TIs so far [16,17].The strain in HgTe layers grown by molecular beam epitaxy stems from a 0.3% lattice mismatch between HgTe and CdTe. The corresponding critical film thickness is larger than 100 nm, meaning that thinner films adopt the substrate lattice constant. Because of this strain, a small gap of ∼15 meV opens (see below) in the bulk energy spectrum of the film. Within the bulk gap, the gapless surface states reside. The charge neutrality point of the corresponding Dirac cone is located in the valence band [16].In this Letter, we report on transport properties of highmobility, 80 nm wide, strained HgTe films equipped with a gate. The low disorder manifested in high charge carrier mobilities, together with the possibility to tune E F from the valence via the gap into the conduction band, enables us to probe the 2D Dirac surface states when E F is in the bulk energy gap. Since HgTe films grown on CdTe suffer from dislocations due to the lattice mismatch, our 80 nm thick HgTe films were separated from the CdTe substrate by a 20 nm thin Cd 0.7 Hg 0.3 Te buf...

Nanowires with helical surface states represent key prerequisites for observing and exploiting phase-coherent topological conductance phenomena, such as spin-momentum locked quantum transport or topological superconductivity. We demonstrate in a joint experimental and theoretical study that gated nanowires fabricated from high-mobility strained HgTe, known as a bulk topological insulator, indeed preserve the topological nature of the surface states, that moreover extend phase-coherently across the entire wire geometry. The phase-coherence lengths are enhanced up to 5 µm when tuning the wires into the bulk gap, so as to single out topological transport. The nanowires exhibit distinct conductance oscillations, both as a function of the flux due to an axial magnetic field, and of a gate voltage. The observed h/e-periodic Aharonov-Bohm-type modulations indicate surface-mediated quasi-ballistic transport. Furthermore, an in-depth analysis of the scaling of the observed gate-dependent conductance oscillations reveals the topological nature of these surface states. To this end we combined numerical tight-binding calculations of the quantum magneto-conductance with simulations of the electrostatics, accounting for the gate-induced inhomogenous charge carrier densities around the wires. We find that helical transport prevails even for strongly inhomogeneous gating and is governed by flux-sensitive high-angular momentum surface states that extend around the entire wire circumference. arXiv:1708.07014v2 [cond-mat.mes-hall]

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