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Register a new userFractional Quantum Hall Effect in a Diluted Magnetic Semiconductor
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Alexei Iankilevitch
Publication date
2014
fields
Physics
and research's language is
English
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We report the observation of the fractional quantum Hall effect in the lowest Landau level of a two-dimensional electron system (2DES), residing in the diluted magnetic semiconductor Cd(1-x)Mn(x)Te. The presence of magnetic impurities results in a giant Zeeman splitting leading to an unusual ordering of composite fermion Landau levels. In experiment, this results in an unconventional opening and closing of fractional gaps around filling factor v = 3/2 as a function of an in-plane magnetic field, i.e. of the Zeeman energy. By including the s-d exchange energy into the composite Landau level spectrum the opening and closing of the gap at filling factor 5/3 can be modeled quantitatively. The widely tunable spin-splitting in a diluted magnetic 2DES provides a novel means to manipulate fractional states.
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Magnetic semiconductors are attracting high interest because of their potential use for spintronics, a new technology which merges electronics and manipulation of conduction electron spins. (GaMn)As and (GaMn)N have recently emerged as the most popular materials for this new technology. While Curie temperatures are rising towards room temperature, these materials can only be fabricated in thin film form, are heavily defective, and are not obviously compatible with Si. We show here that it is productive to consider transition metal monosilicides as potential alternatives. In particular, we report the discovery that the bulk metallic magnets derived from doping the narrow gap insulator FeSi with Co share the very high anomalous Hall conductance of (GaMn)As, while displaying Curie temperatures as high as 53 K. Our work opens up a new arena for spintronics, involving a bulk material based only on transition metals and Si, and which we have proven to display a variety of large magnetic field effects on easily measured electrical properties.
We study transport properties of a charge qubit coupling two chiral Luttinger liquids, realized by two antidots placed between the edges of an integer $ u=1$ or fractional $ u=1/3$ quantum Hall bar. We show that in the limit of a large capacitive coupling between the antidots, their quasiparticle occupancy behaves as a pseudo-spin corresponding to an orbital Kondo impurity coupled to a chiral Luttinger liquid, while the inter antidot tunnelling acts as an impurity magnetic field. The latter tends to destabilize the Kondo fixed point for the $ u=1/3$ fractional Hall state, producing an effective inter-edge tunnelling. We relate the inter-edge conductance to the susceptibility of the Kondo impurity and calculate it analytically in various limits for both $ u=1$ and $ u=1/3$.
A simple one-dimensional model is proposed, in which N spinless repulsively interacting fermions occupy M>N degenerate states. It is argued that the energy spectrum and the wavefunctions of this system strongly resemble the spectrum and wavefunctions of 2D electrons in the lowest Landau level (the problem of the Fractional Quantum Hall Effect). In particular, Laughlin-type wavefunctions describe ground states at filling factors v = N/M = 1(2m+1). Within this model the complimentary wavefunction for v = 1-1/(2m + 1) is found explicitly and extremely simple ground state wavefunctions for arbitrary odd-denominator filling factors are proposed.
A conceptual difficulty in formulating the density functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.
We measure the chemical potential jump across the fractional gap in the low-temperature limit in the two-dimensional electron system of GaAs/AlGaAs single heterojunctions. In the fully spin-polarized regime, the gap for filling factor nu=1/3 increases LINEARLY with magnetic field and is coincident with that for nu=2/3, reflecting the electron-hole symmetry in the spin-split Landau level. In low magnetic fields, at the ground-state spin transition for nu=2/3, a correlated behavior of the nu=1/3 and nu=2/3 gaps is observed.
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