No abstract

The three-dimensional topological insulator is a novel state of matter characterized by twodimensional metallic Dirac states on its surface. To verify the topological nature of the surface states, Bi-based chalcogenides such as Bi 2 Se 3 , Bi 2 Te 3 , Sb 2 Te 3 and their combined/mixed compounds have been intensively studied. Here, we report the realization of the quantum Hall effect on the surface Dirac states in (Bi 1 À x Sb x ) 2 Te 3 films. With electrostatic gate-tuning of the Fermi level in the bulk band gap under magnetic fields, the quantum Hall states with filling factor ±1 are resolved. Furthermore, the appearance of a quantum Hall plateau at filling factor zero reflects a pseudo-spin Hall insulator state when the Fermi level is tuned in between the energy levels of the non-degenerate top and bottom surface Dirac points. The observation of the quantum Hall effect in three-dimensional topological insulator films may pave a way toward topological insulator-based electronics.

The fractional quantum Hall (FQH) e ect emerges in high-quality two-dimensional electron systems exposed to a magnetic field when the Landau-level filling factor, ν e , takes on a rational value. Although the overwhelming majority of FQH states have odd-denominator fillings, the physical properties of the rare and fragile even-denominator states are most tantalizing in view of their potential relevance for topological quantum computation. For decades, GaAs has been the preferred host for studying these even-denominator states, where they occur at ν e = 5/2 and 7/2. Here we report an anomalous series of quantized evendenominator FQH states outside the realm of III-V semiconductors in the MgZnO/ZnO 2DES electron at ν e = 3/2 and 7/2, with precursor features at 9/2; all while the 5/2 state is absent. The e ect in this material occurs concomitantly with tunability of the orbital character of electrons at the chemical potential, thereby realizing a new experimental means for investigating these exotic ground states.T he framework for the wide range of ground states observed in two-dimensional electron systems (2DES) resides in the discretized energy spectrum with a high degeneracy of the allowed states which emerges with the addition of a perpendicular magnetic field, B p . A ladder of spin-split Landau-levels (LLs) results with B p , inducing quantization of the orbital motion and lifting of the spin degeneracy. Each level is characterized by its orbital index N e = 0, 1, . . . and spin orientation (↑ or ↓). These levels can host as many charge carriers as magnetic flux quanta thread the sample and the filling factor, ν e , indicates how many levels are occupied. With increasing B p these LLs are successively depopulated and, on emptying a level completely, ν e takes on an integer value and the bulk of the 2DES becomes incompressible (see ref. 1 for an overview). The system exhibits the integer quantum Hall effect: vanishing longitudinal resistance (R xx ) and a Hall resistance (R xy ) quantized in units of h/e 2 . Further incompressible ground states may form at fractional fillings p/q when the electron number and number of flux quanta are commensurable. In contrast to FQH states at odd-denominator fillings, where the anti-symmetry constraint on the many-particle wavefunction imposed by the Pauli exclusion principle for fermions is automatically fulfilled, the development of even-denominator states 2-11 requires some mechanism which either restores the anti-symmetry of the manyparticle wavefunction or simply lifts the need to fulfil the Pauli exclusion principle. For systems where the charge carriers possess another degree of freedom, such as a layer or subband index, the anti-symmetry issue at even-denominator fillings may be solved by a two-component wavefunction. Indeed, in wide GaAs quantum wells with two subbands or in double-layer systems evendenominator states have been observed 2-7 and consensus has been reached that they are described by many-particle wavefunctions like the two-component ψ 331 -Laughlin sta...

The magnesium content in MgxZn1-xO/ZnO heterostructures grown by molecular beam epitaxy enables the careful control of the carrier density of the two-dimensional electron system down to 5.6×1010 cm-2 while retaining a mobility of 200,000 cm2 V-1 s-1 when pursuing magnesium concentrations as low as x = 0.0038. By selecting an optimum magnesium content (x∼0.01), the mobility is enhanced to over 700,000 cm2 V-1 s-1 due to reduced impurity levels associated with the use of pure distilled ozone and avoiding interface roughness scattering. This control technique allows access to the coherent transport region with strong electron–electron interaction.

Spin-orbit coupling has proven indispensable in the realization of topological materials and, more recently, Ising pairing in two-dimensional superconductors. This pairing mechanism relies on inversion symmetry–breaking and sustains anomalously large in-plane polarizing magnetic fields whose upper limit is predicted to diverge at low temperatures. Here, we show that the recently discovered superconductor few-layer stanene, epitaxially strained gray tin (α-Sn), exhibits a distinct type of Ising pairing between carriers residing in bands with different orbital indices near the Γ-point. The bands are split as a result of spin-orbit locking without the participation of inversion symmetry–breaking. The in-plane upper critical field is strongly enhanced at ultralow temperature and reveals the predicted upturn.