Multifractal Conductance Fluctuations of Helical Edge States.

Two-dimensional topological insulators are characterized by the bulk gap and one-dimensional helical states running along the edges. The theory predicts the topological protection of the helical transport from coherent backscattering. However, the unexpected deviations of the conductance from the quantized value and localization of the helical modes are generally observed in long samples. Moreover, at millikelvin temperatures significant mesoscopic fluctuations are developed as a function of the electron energy. Here we report the results of an experimental study of the transport in a HgTe quantum well with an inverted energy spectrum that reveal a multifractality of the conductance fluctuations in the helical edge state dominated transport regime. We attribute observed multifractality to mesoscopic fluctuations of the electron wave function or local density of states at the spin quantum Hall transition. We have shown that the mesoscopic two-dimensional topological insulator provides a highly tunable experimental system in which to explore the physics of the Anderson transition between topological states.

Engineering topological phases in triple HgTe/CdTe quantum wells.

Quantum wells formed by layers of HgTe between Hg[Formula: see text]Cd[Formula: see text]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 [Formula: see text] 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 subbands given by one parabolic and one Dirac subband, and with edge states immersed in the bulk valence subbands. 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 subbands.

Electronic thermal conductivity in 2D topological insulator in a HgTe quantum well.

We have measured the differential resistance in a two-dimensional topological insulator (2DTI) in a HgTe quantum well, as a function of the applied dc current. The transport near the charge neutrality point is characterized by a pair of counter propagating gapless edge modes. In the presence of an electric field, the energy is transported by counter propagating channels in the opposite direction. We test a hot carrier effect model and demonstrate that the energy transfer complies with the Wiedemann Franz law near the charge neutrality point in the edge transport regime.

Low field magnetoresistance in a 2D topological insulator based on wide HgTe quantum well.

Low field magnetoresistance is experimentally studied in a two-dimensional topological insulator (TI) in both diffusive and quasiballistic samples fabricated on top of a wide (14 nm) HgTe quantum well. In all cases a pronounced quasi-linear positive magnetoresistance is observed similar to that found previously in diffusive samples based on a narrow (8 nm) HgTe well. The experimental results are compared with the main existing theoretical models based on different types of disorder: sample edge roughness, nonmagnetic disorder in an otherwise coherent TI and metallic puddles due to locally trapped charges that act like local gate on the sample. The quasiballistic samples with resistance close to the expected quantized values also show a positive low-field magnetoresistance but with a pronounced admixture of mesoscopic effects.

Persistence of a two-dimensional topological insulator state in wide HgTe quantum wells.

Our experimental studies of electron transport in wide (14 nm) HgTe quantum wells confirm the persistence of a two-dimensional topological insulator state reported previously for narrower wells, where it was justified theoretically. Comparison of local and nonlocal resistance measurements indicate edge state transport in the samples of about 1 mm size at temperatures below 1 K. Temperature dependence of the resistances suggests an insulating gap of the order of a few meV. In samples with sizes smaller than 10 µm a quasiballistic transport via the edge states is observed.

Transport properties of a 3D topological insulator based on a strained high-mobility HgTe film.

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.

Nonlocal transport near charge neutrality point in a two-dimensional electron-hole system.

Nonlocal resistance is studied in a two-dimensional system with a simultaneous presence of electrons and holes in a 20 nm HgTe quantum well. A large nonlocal electric response is found near the charge neutrality point in the presence of a perpendicular magnetic field. We attribute the observed nonlocality to the edge state transport via counterpropagating chiral modes similar to the quantum spin Hall effect at a zero magnetic field and graphene near a Landau filling factor ν=0.

Quantum Hall effect near the charge neutrality point in a two-dimensional electron-hole system.

We study the transport properties of HgTe-based quantum wells containing simultaneously electrons and holes in a magnetic field B. At the charge neutrality point (CNP) with nearly equal electron and hole densities, the resistance is found to increase very strongly with B while the Hall resistivity turns to zero. This behavior results in a wide plateau in the Hall conductivity sigma(xy) approximately = 0 and in a minimum of diagonal conductivity sigma(xx) at nu = nu(p) - nu(n) = 0, where nu(n) and nu(p) are the electron and hole Landau level filling factors. We suggest that the transport at the CNP point is determined by electron-hole "snake states" propagating along the nu = 0 lines. Our observations are qualitatively similar to the quantum Hall effect in graphene as well as to the transport in a random magnetic field with a zero mean value.