Precision measurement of the quantized anomalous Hall resistance at zero magnetic field

Abstract

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

Part-per-million quantization and current-induced breakdown of the quantum anomalous Hall effect

“…After submission we became aware of work by Götz et al . reporting measurements of Hall resistance in V-doped (Bi,Sb) 2 Te 3 with similar precision and accuracy of quantization [66].…”

Intrinsic quantized anomalous Hall effect in a moiré heterostructure

“…In the absence of time reversal symmetry, nontrivial band topology manifests experimentally as a quantized Hall conductivity σ xy = C e 2 h , where C = 0 is the total Chern number of the filled bands. Motivated by fundamental questions about the nature of topological phase transitions [1] as well as possible applications in resistance metrology [2] and topological quantum computing [3], significant effort has been devoted to engineering quantum anomalous Hall (QAH) effects showing topologically protected quantized resistance in the absence of an applied magnetic field. To date, QAH effects have been observed only in a narrow class of materials consisting of transition metal doped (Bi,Sb) 2 Te 3 [4][5][6][7][8][9][10].…”

Families of magnetic semiconductors — an overview

“…This cluster extends over all spins at T = 0, implying that at T > 0 ferromagnetism co-exists with superparamagnetism produced by not percolative clusters [73] . Presumably this effect accounts for thermal instabilities of the quantum anomalous Hall effect even at T ≪ T C , and shifts below 100 mK the operation range of the potential resistance standards based on this phenomenon [74,75] .…”