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We study the quantum Hall effect (QHE) in the three-dimensional topological insulator HgTe, which features topological Dirac-type surface states in a bulk gap opened by strain. Despite the co-existence of multiple carrier subsystems, the…
The Hall conductivity in the mixed state of a clean ($l \gg \xi_0$) type-II s-wave superconductor is determined from a microscopic calculation within a quasiclassical approximation. We find that below the superconducting transition the…
We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the $\nu=2$ and the $\nu=1$ quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall…
Two-dimensional electron or hole systems in semiconductors offer the unique opportunity to investigate the physics of strongly interacting fermions. We have measured the 1/f resistance noise of two-dimensional hole systems in high mobility…
A microscopic calculation of the conductivity in the integer quantum Hall effect (IQHE) regime is carried out. The problem of precision of quantization is analyzed for samples of finite size. It is demonstrated that the precision of…
We have performed a metrological characterization of the quantum Hall resistance in a 1 $\mu$m wide graphene Hall-bar. The longitudinal resistivity in the center of the $\nu=\pm 2$ quantum Hall plateaus vanishes within the measurement noise…
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…
The observation of new insulating phases of two-dimensional electrons in the first excited Landau level is reported. These states, which are manifested as re-entrant integer quantized Hall effects, exist alongside well-developed…
We present measurements of transport through two tunnel-coupled quantum dots of different sizes connected in series in a strong, variable, perpendicular magnetic field. Double dot conductance was measured both as a function of magnetic…
We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT…
Quantum Hall edge states in proximity to a superconductor (SC) usually acquire a non-quantized electron-to-hole conversion probability in transport, due to non-universal SC couplings and disorders. With counter-propagating modes, we show…
We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the…
Recently unusual integer quantum Hall effect was observed in graphene in which the Hall conductivity is quantized as $\sigma_{xy}=(\pm 2, \pm 6, \pm 10, >...) \times \frac{e^2}{h}$, where $e$ is the electron charge and $h$ is the Planck…
Quantum anomalous Hall (QAH) effect in magnetic topological insulator (TI) is a novel transport phenomenon in which the Hall resistance reaches the quantum plateau in the absence of external magnetic field. Recently, this exotic effect has…
The edge states of a sample displaying the quantum Hall effect (QHE) can be described by a 1+1 dimensional (conformal) field theory of $d$ massless scalar fields taking values on a $d$-dimensional torus. It is known from the work of…
Magneto-transport measurements are performed on the two-dimensional electron system (2DES) in an AlGaAs/GaAs heterostructure. By increasing the magnetic field perpendicular to the 2DES, magnetoresistivity oscillations due to Landau…
Topological states of matter are characterized by topological invariant, which are physical quantities whose values are quantized and do not depend on details of the measured system. Of these, the easiest to probe in experiments is the…
We show that, for Galilean invariant quantum Hall states, the Hall viscosity appears in the electromagnetic response at finite wave numbers q. In particular, the leading q dependence of the Hall conductivity at small q receives a…
Fractional conductance is measured by partitioning $\nu = 1$ edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9…
We propose that a quantum anomalous Hall insulator (QAHI) can be realized in a nanopatterned two-dimensional electron gas (2DEG) with a small in-plane magnetic field and a high carrier density. The Berry curvatures originating from the…