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The quantized version of the anomalous Hall effect has been predicted to occur in magnetic topological insulators, but the experimental realization has been challenging. Here, we report the observation of the quantum anomalous Hall (QAH)…
An intriguing observation on the quantum anomalous Hall effect (QAHE) in magnetic topological insulators (MTIs) is the dissipative edge states, where quantized Hall resistance is accompanied by nonzero longitudinal resistance. We…
We report ultra-low temperature experiments on the obscure fractional quantum Hall effect (FQHE) at Landau level filling factor $\nu$=5/2 in a very high mobility specimen of $\mu=1.7 \times 10^7$ cm$^2$/Vs. We achieve an electron…
We report the observation of a fully developed fractional quantum Hall state at $\nu=5/2$ in GaAs/Al$_{x}$Ga$_{1-x}$As quantum wells with mobility well below $10^{7}$\thinspace cm$^{2}$/Vs. This is achieved either by strong illumination or…
We study numerically conductance fluctuations near the integer quantum Hall effect plateau transition. The system is presumed to be in a mesoscopic regime, with phase coherence length comparable to the system size. We focus on a…
We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to $2 e^2/h$ and vanishing thermal Hall conductivity. In contrast to the integer…
We have measured the temperature (0.1 < T < 15 K) and magnetic field (0 < B < 32 T) dependences of longitudinal and Hall resistivities for the p-Ge_{1-x}Si_x/Ge, x=~0.07, multilayers with different Ge layer widths 10 < d_w < 38 nm and hole…
We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy…
We report the discovery of the half-quantized mirror Hall effect, a novel quantum-anomaly induced by mirror symmetry in a strong topological insulator (TI) film. These films are known to host a pair of gapless Dirac cones associated with…
By designing a multi-channel millimeter Hall measurement configuration, we realize the carrier-density (locally) controllable measurement on the transport property in 2H MoS$_{2}$. We observe a linearly increased Hall conductivity and…
Based on very general arguments we show that for any geometry of the experiment, in the regime when the measurement leads to a quantized Hall conductivity, almost the entire current injected into the sample is carried by the bulk states.…
In QED of two space dimensions, a quantum Hall effect occurs in the absence of any magnetic field. We give a simple and transparent explanation. In solid state physics, the Hall conductivity for non-degenerate ground state is expected to be…
We have studied quantized transport in HgTe wells with inverted band structure corresponding to the two-dimensional topological insulator phase (2D TI) with locally-controlled density allowing n-p-n and n-2D TI-n junctions. The resistance…
We report on a comparison of four GaAs/AlGaAs-based quantum resistance standards using an original technique adapted from the well-known Wheatstone bridge. This work shows that the quantized Hall resistance at Landau level filling factor…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
We derive electromagnetomotive force fields for charged particles moving in a rotating Hall sample, satisfying a twofold U(1) gauge invariance principle. It is then argued that the phase coherence property of quantization of the line…
In certain backgrounds string theory exhibits quantum Hall-like behavior. These backgrounds provide an explicit realization of the effective non-commutative gauge theory description of the fractional quantum Hall effect (FQHE), and of the…
We have measured the magnetoresistance of a very low density and an extremely high quality two-dimensional hole system. With increasing magnetic field applied perpendicularly to the sample we observe the sequence of insulating, $\nu=1/3$…
The quantum Hall effect is observed in a two-dimensional electron gas formed in millimeter-scale hydrogenated graphene, with a mobility less than 10 $\mathrm{cm^{2}/V\cdot s}$ and corresponding Ioffe-Regel disorder parameter…
Quantized Hall conductance is a generic feature of two dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is…