Session A1: Spectroscopy of Two-Dimensional Electronic Systems

Fractionally Charged Excitations in Optical Emission Spectroscopy

We discuss recent experiments and theory of the signatures of fractionally charged excitations in optical emission spectroscopy of two dimensional electrons subjected to a high magnetic field [1]. We show that the two flux quanta in a composite fermion interacting with an exciton lead to filling factor dependent features in optical emission spectrum symmetric around filling factor 1/2 while fractionally charged excitations lead to fractionally charged exciton. In the vicinity of the incompressible filling factor 1/3 state we observe a doublet structure in the emission line, corresponding to excitations of the incompressible fluid. At filling factors lower then 1/3 , corresponding to the transition to a compressible, metallic state, a new emission line appears which is attributed to the fractionally charged quasi-exciton. These observations are supported by extensive numerical calculations of the emission spectrum of finite number of electrons and holes on a Haldane sphere. \newline [1] M. Byszewski, B. Chwalisz, D.K. Maude, M.L. Sadowski, M. Potemski, T. Saku, and Y. Hirayama, S. Studenikin, D. G. Austing, A.S. Sachrajda, and P. Hawrylak, Nature Physics 2, 239 (2006).   

Soft spin waves and magnetic instability in Skyrmion systems

In this work the highly correlated ground states of spin in 2D electron layers (2DES) near filling factor $\nu $=1 are probed by inelastic light scattering [1]. In this filling factor range the ground state of the 2DES is affected by the proliferation of spin-charge textures known as Skyrmions. Recent experiments [2] have suggested the possibility of observing a long range Skyrme crystal phase with non-collinear magnetic order at low temperatures. The magnetic properties of the 2DES close to $\nu $=1 are studied by the direct measurement of the low-lying spin wave excitations by inelastic light scattering between 2.5K and 40mK. We discovered a very low energy spin wave that emerges on both sides of $\nu $=1. The spin wave is well below the Zeeman energy and exhibit surprising soft behavior with temperature changes: its energy increases with temperature and reaches the Zeeman energy for temperatures above 2K. These results suggest an instability of the 2DES towards magnetic order at low temperatures and filling factors close to $\nu $=1. The spin excitation spectra are consistent with the ordering of the in-plane components of spin in a square Skyrme crystal phase proposed in theoretical evaluations [3], but never fully confirmed by experiments. Our experiments create venues for the determination of Skyrme crystal phases from measurements of low-lying spin excitations by inelastic light scattering. \newline [1] Y. Gallais et al, arXiv:0709.3240 \newline [2] G. Gervais et al., Phys.Rev.Lett. 94, 196803 (2005) \newline [3] L. Brey et al., Phys.Rev.Lett. 75, 2562 (1995)   

High Resolution Spectroscopy of the Quantum Hall Liquid

We present precise and unprecedentedly high resolution spectra of the tunneling density of states (TDOS) of a cold two dimensional electron system (2DES) in GaAs over an energy range from 15 meV above to 15 meV below the Fermi surface. The results provide the first direct measurements of the width of the single-particle exchange gap and lifetimes in the quantum Hall system. At higher energies, we show the first observations of exchange-induced spin-splittings in fully filled or unfilled Landau levels not at the Fermi energy. The results demonstrate a counter-intuitive fact: the high energy spectrum reflects correlations that only appear at very low temperatures. For instance, upon raising the temperature from 100 mK (0.01 meV) to 1 K (0.1 meV) changes are seen in the spectrum at 10 meV away from the Fermi energy. Along with measurements of exchange splittings and lifetimes, we observe an unpredicted new structure appearing only at high magnetic fields and low temperatures that appears to be a long lived quasi-particle. The results are made possible by a novel technique, time domain capacitance spectroscopy. It allows us to measure the TDOS of a 2DES with resolution only limited by temperature, even at large tunneling energies. In TDCS, sharp voltage pulses disequilibrate a 2DES from a nearby metallic contact inducing a tunnel current perpendicular to the plane of the 2DES. We detect this current by monitoring the image charge of the tunneling electrons on a distant electrode. No ohmic contact to the 2DES is required. The technique works even when the 2DES is empty or has vanishing in-plane conductivity, as frequently occurs in the quantum Hall effect. Importantly, we can eliminate the effects of ohmic heating in the experiment by using short duty cycle pulses, with currents flowing only 0.01\% of the time. The obtained spectra reveal the beautiful and difficult to reach structure present far from the Fermi surface in the quantum Hall system.   

Magnetotunneling spectroscopy: Imaging electron wavefunctions and measuring electron dispersion curves in GaMnAs- and GaAsN-based heterostructures

Magnetotunnelling spectroscopy is a powerful tool for imaging the wavefunctions of electrons in quantum wires [1] and dots [2] and for measuring the energy-wavevector dispersion curves of holes [3] and electrons [4] in novel quantum well structures. It uses the effect of the Lorentz force to tune the in-plane momentum of a tunneling electron when it enters a quantum-confined structure [4]. This talk will describe recent work to spatially image the ground and excited state wavefunction of electrons confined in quantum dots in ferromagnetic GaMnAs tunnel diodes. These dots are formed by the electrostatic potential arising from clusters of charged Mn interstitial donors. It will also be shown how the fragmented conduction electron dispersion curves of GaAsN give rise to highly non-linear electron dynamics and a new type of negative differential conductivity effect. \newline [1] Beton et al, Phys Rev Lett \textbf{75}, 1996 (1995); [2] Vdovin et al, Science 290, 122 (2000) and Patane et al, Phys Rev B \textbf{65}, 165308 (2002); [3] Hayden et al, Phys Rev Lett \textbf{66}, 1749 (1991); [4] Endicott et al, Phys Rev Lett \textbf{91} 126802 (2003)