Formal derivation of the Laughlin function and its generalization for other topological phases of FQHE

Using the braid symmetry we demonstrate the derivation of the Laughlin function for the main hierarchy 1/q of FQHE in the lowest Landau level of two-dimensional electron system with a mathematical rigour. This proves that the derivation of Laughlin function unavoidably requires some topological elements and cannot be completed within a local quantum mechanics, i.e., without global topological constraints imposed. The method shows the way for the generalization of this function onto other fractions from the general quantum Hall hierarchy. A generalization of the Laughlin function is here formulated.

Quantum hall effects in two-dimensional electron systems: a global approach

Up to almost the last two decades all the experimental results concerning the quantum Hall effect (QHE), i.e. the observation of plateaux at integer or fractional (FQHE) values of the constant h/e2, were related to quantum-wells in semiconductor heterostructures. However, more recently, a renewed interest in revisiting these phenomena has arisen thanks to the observation of entirely similar effects in graphene and topological insulators. In this paper we show an approach encompassing all these QHEs using the same theoretical frame, entailing both Hall effect plateaux and Shubnikov-de Haas oscillations. Moreover, the model also enables the analysis of both phenomena as a function not only of the magnetic field but the gate voltage as well. More specifically, in the light of the approach, the FQHE in any two-dimensional electron system appears to be an effect of the breaking of the degeneration of every Landau level, n, as a result of the electrostatic interaction involved, and being characterized by the set of three integer numbers (n, p, q), where p and q have clear physical meanings too.

Nanopatterning of oxide 2-dimensional electron systems using low-temperature ion milling

We present a "top-down" patterning technique based on ion milling performed at low- temperature, for the realization of oxide two-dimensional electron system (2DES) devices with dimensions down to 160 nm. Using electrical transport and scanning SQUID measurements we demonstrate that the low-temperature ion milling process does not damage the 2DES properties nor creates oxygen vacancies-related conducting paths in the STO substrate. As opposed to other procedures used to realize oxide 2DES devices, the one we propose gives lateral access to the 2DES along the in-plane directions, finally opening the way to coupling with other materials, including superconductors.

Marginal metallic state at a fractional filling of ’8/5’ and ’4/3’ of Landau levels in the GaAs/AlGaAs 2D electron system

A metallic state with a vanishing activation gap, at a filling factor $$\nu = 8/5$$ ν = 8 / 5 in the untilted specimen with $$n= 2 \times 10^{11} cm^{-2}$$ n = 2 × 10 11 c m - 2 , and at $$\nu = 4/3$$ ν = 4 / 3 at $$n=1.2 \times 10^{11} cm^{-2}$$ n = 1.2 × 10 11 c m - 2 under a $$\theta = 66^{0}$$ θ = 66 0 tilted magnetic field, is examined through a microwave photo-excited transport study of the GaAs/AlGaAs 2 dimensional electron system (2DES). The results presented here suggest, remarkably, that at the possible degeneracy point of states with different spin polarization, where the 8/5 or 4/3 FQHE vanish, there occurs a peculiar marginal metallic state that differs qualitatively from a quantum Hall insulating state and the usual quantum Hall metallic state. Such a marginal metallic state occurs most prominently at $$\nu =8/5$$ ν = 8 / 5 , and at $$\nu =4/3$$ ν = 4 / 3 under tilt as mentioned above, over the interval $$1 \le \nu \le 2$$ 1 ≤ ν ≤ 2 , that also includes the $$\nu = 3/2$$ ν = 3 / 2 state, which appears perceptibly gapped in the first instance.

Interplay of spin–orbit coupling and Coulomb interaction in ZnO-based electron system

Spin–orbit coupling (SOC) is pivotal for various fundamental spin-dependent phenomena in solids and their technological applications. In semiconductors, these phenomena have been so far studied in relatively weak electron–electron interaction regimes, where the single electron picture holds. However, SOC can profoundly compete against Coulomb interaction, which could lead to the emergence of unconventional electronic phases. Since SOC depends on the electric field in the crystal including contributions of itinerant electrons, electron–electron interactions can modify this coupling. Here we demonstrate the emergence of the SOC effect in a high-mobility two-dimensional electron system in a simple band structure MgZnO/ZnO semiconductor. This electron system also features strong electron–electron interaction effects. By changing the carrier density with Mg-content, we tune the SOC strength and achieve its interplay with electron–electron interaction. These systems pave a way to emergent spintronic phenomena in strong electron correlation regimes and to the formation of quasiparticles with the electron spin strongly coupled to the density.

Unequal on-site interaction effects in the one-dimensional electron system at quarter filling

The one-dimensional antiferromagnetic correlated electron system described by the unusual t–U–J model with alternating on-site interactions at odd ($$U_o$$ U o ) and even ($$U_e$$ U e ) sites is studied analytically. At weak coupling, the use of bosonization and renormalization-group techniques helps to obtain ground-state phase diagram. At quarter filling, the unequal on-site repulsion ($$U_e\ne U_o$$ U e ≠ U o ) causes the occurrence of umklapp processes and the generation of a charge excitation gap. Contrary to the usual case ($$U_e=U_o$$ U e = U o ), the system is not metallic but insulating. For $$U_e+U_o<2J$$ U e + U o < 2 J , the system is in a spin-gapped phase with charge-density-wave (CDW) instability; for $$U_e+U_o\ge 2J$$ U e + U o ≥ 2 J , the system is in a spin-gapless phase characterized by the coexistence of both CDW and spin-density-wave (SDW) instabilities, where the SDW correlation dominates over the CDW one.