A quantum anomalous Hall (QAH) insulator coupled to an s-wave superconductor is predicted to harbor chiral Majorana modes. A recent experiment interprets the half-quantized two-terminal conductance plateau as evidence for these modes in a millimeter-size QAH-niobium hybrid device. However, non-Majorana mechanisms can also generate similar signatures, especially in disordered samples. Here, we studied similar hybrid devices with a well-controlled and transparent interface between the superconductor and the QAH insulator. When the devices are in the QAH state with well-aligned magnetization, the two-terminal conductance is always half-quantized. Our experiment provides a comprehensive understanding of the superconducting proximity effect observed in QAH-superconductor hybrid devices and shows that the half-quantized conductance plateau is unlikely to be induced by chiral Majorana fermions in samples with a highly transparent interface.

We report on the scaling behavior of V-doped (Bi,Sb)_{2}Te_{3} samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a two-dimensional integer quantum Hall state, we observe a dimensional crossover to three spatial dimensions as a function of layer thickness. In the limit of a sufficiently thick layer, we find scaling behavior matching the flow diagram of two parallel conducting topological surface states of a three-dimensional topological insulator each featuring a fractional shift of 1/2e^{2}/h in the flow diagram Hall conductivity, while we recover the expected integer quantum Hall behavior for thinner layers. This constitutes the observation of a distinct type of quantum anomalous Hall effect, resulting from 1/2e^{2}/h Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of the signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.

In the quantum anomalous Hall effect, the edge states of a ferromagnetically doped topological insulator exhibit quantized Hall resistance and dissipationless transport at zero magnetic field. Up to now, however, the resistance was experimentally assessed with standard transport measurement techniques which are difficult to trace to the von-Klitzing constant RK with high precision. Here, we present a metrologically comprehensive measurement, including a full uncertainty budget, of the resistance quantization of V-doped (Bi,Sb)2Te3 devices without external magnetic field. We established as a new upper limit for a potential deviation of the quantized anomalous Hall resistance from RK a value of 0.26 ± 0.22 ppm, the smallest and most precise value reported to date. This provides another major step towards realization of the zero-field quantum resistance standard which in combination with Josephson effect will provide the universal quantum units standard in the future.Quantum standards are the backbone of the system of measurement units. Already since 1990 all electrical units are based on flux quantization in units of ℎ 2 ⁄ , realized with the Josephson effect [1,2], and conductance quantization in units of 2 ℎ ⁄ , realized with the quantized Hall effect (QHE) [3,4]. With the revision of the international system of units, SI, in near future [5,6] also the realizations of the units of mass [7,8], the kilogram, and of temperature [9,10], the Kelvin, will utilize and rely on practical electric quantum standards, realizing the vision of Maxwell [11] and Planck [12] of a truly universal system of units. Both electrical quantum standards require temperatures of 4 K or lower for their operation, but since in addition the QHE only works in a magnetic field, it is practically impossible to combine both in one system. However, in ferromagnetic topological insulators like e.g. Cr-or V-doped (Bi,Sb)2Te3, the quantum anomalous Hall effect (QAHE) provides conductance quantization without a magnetic field [13][14][15][16], giving legitimate hope for a future quantum standard where all units based on ℎ and can be realized in one measurement setup.Yet, up to now the precision of the QAHE has not been tested with precision metrology methods, and in particular no uncertainty budgets were presented with the data published [17,18]. Indeed, the fact that very low measurement currents are required makes it difficult to reach uncertainties in the parts in 10 9 range as are routinely obtained in calibrations based on GaAs or graphene QHE devices. A main reason for the limitation of current is the robustness of the ferromagnetic state, which at this stage of development still requires temperatures in the mK-regime and does not tolerate current levels

Here we report the investigation of the anomalous Hall effect in the magnetically doped topological insulator (V,Bi,Sb)2Te3. We find it contains two contributions of opposite sign. Both components are found to depend differently on carrier density, leading to a sign inversion of the total anomalous Hall effect as a function of applied gate voltage. The two contributions are found to have different magnetization reversal fields, which in combination with a temperature dependent study points towards the coexistence of two ferromagnetic orders in the system. Moreover, we find that the sign of total anomalous Hall response of the system depends on the thickness and magnetic doping density of the magnetic layer. The thickness dependence suggests that the two ferromagnetic components originate from the surface and bulk of the magnetic topological insulator film. We believe that our observations provide insight on the magnetic behavior, and thus will contribute to an eventual understanding of the origin of magnetism in this material class. In addition, our data bears a striking resemblance to anomalous Hall signals often associated with skyrmion contributions. Our analysis provides a straightforward explanation for both the magnetic field dependence of the Hall signal and the observed change in sign without needing to invoke skyrmions, and thus suggest that caution is needed when making claims of effects from skyrmion phases. arXiv:1912.02766v1 [cond-mat.mes-hall]

The influence of Sb content, substrate type and cap layers on the quantum anomalous Hall effect observed in V-doped (Bi,Sb)2Te3 magnetic topological insulators is investigated. Thin layers showing excellent quantization are reproducibly deposited by molecular beam epitaxy at growth conditions effecting a compromise between controlled layer properties and high crystalline quality. The Sb content can be reliably determined from the in-plane lattice constant measured by X-ray diffraction, even in thin layers. This is the main layer parameter to be optimized in order to approach charge neutrality. Within a narrow range at about 80% Sb content, the Hall resistivity shows a maximum of about 10 kΩ at 4 K and quantizes at mK temperatures. Under these conditions, thin layers grown on Si(111) or InP(111) and with or without a Te cap exhibit quantization. The quantization persists independently of the interfaces between cap, layer and substrate, the limited crystalline quality, and the degradation of the layer proving the robustness of the quantum anomalous Hall effect.A quantum anomalous Hall effect (QAHE), in which a Hall plateau with a resistance of h/e 2 can be observed even in the absence of a magnetic field, was predicted to occur in ferromagnetically doped topological insulators (TIs) [1][2][3][4]. The effect was first observed in 2013 in a 5 nm Cr 0.15 (Bi 0.1 Sb 0.9 ) 1.85 Te 3 layer without a cap layer, and grown on a SrTiO 3 substrate [5]. The QAHE has since been reproduced in such tetradymite-type layers with different layer thicknesses, layer compositions, magnetic dopants (Cr or V), with/without a cap layer and on various substrates [6][7][8][9][10][11]. Perfect quantization was observed in Cr-doped (Bi,Sb) 2 Te 3 layers capped by an AlO x layer on GaAs substrates, and V-doped (Bi,Sb) 2 Te 3 layers capped by Te on SrTiO 3 substrates and Si(111) substrates [6,[9][10][11]. Many authors point out that the layer properties have to be optimized to observe the QAHE, but details of the epitaxial growth conditions, the structural layer properties and the applied characterization techniques are sparse.An apparent requirement for observing the QAHE is the optimization of Sb content in order to approach charge neutrality by compensation of n-and p-type intrinsic point defects. Further, an applied gate bias is needed to tune the Fermi level into the bandgap of topological surface states (TSSs) caused by magnetization [5]. The layer thickness, ranging from about 4 to 10 nm in the literature, likely affects the hybridization of the TSSs and possibly also the mechanisms leading to the QAHE. Theoretical predictions and experiments both reveal a degradation of the surface states due to oxidation in Bi 2 Te 3 layers and shifts of the Fermi level in epitaxial tetradymite layers due to adsorbates [12][13][14][15]. The influence of the interfaces between the layer and the sub- * M. Winnerlein and S. Schreyeck contributed equally to this work.† Karl.Brunner@physik.uni-wuerzburg.de strate, as well as between the layer and either an...