I am a theoretical solid state physicist mainly focussing on many-body problems in nanostructures. I have primarily used numerical techniques to treat effective models trying to accurately match recent experiments, with emphasis on metal-insulator transitions in disordered, interacting systems at high magnetic field.
Integer quantum Hall effect
Coulomb blockade and compressibility in the integer quantum
Hall effect
Recently, the local inverse compressibility of an integer quantum Hall system has been measured (Ilani et. al., Nature 427,328(2004) as a function of electron density $n$ and magnetic field $B$, a quantity which mimics the change of the chemical potential in the system with respect to the particle density. These compressibility patterns reveal signatures of charging in the quantum Hall system, which in general are attributed to Coulomb interaction in correlated systems and are incompatible with single-particle physics.
We have developed a mean-field description for these charging patterns within a spin-unrestricted Hartree-Fock approximation, but allowing for charge rearrangement in the ground state with respect to changes in $n$ and $B$. Our results match the experimental observations at least in the localized regions and are compatible with the single-particle picture of the localization-delocalization transition. In agreement with experimental data we show that electron-electron interaction cannot be neglegted in a comprehensive theory of the integer quantum Hall effect ( A. Struck, B. Kramer,
Phys. Rev. Lett. 97, 106801 (2006)).
Critical exponents in presence of disorder and
interaction
The integer quantum Hall effect is observed, if the kinetic energy of the electrons is quantized into equidistant Landau levels, which are broadened into bands due to the presence of a disorder potential. If the Fermi energy is in the tail of Landau band $i$, the Hall conductance exhibits a plateau of magnitude $e^2/h\cdot i$, whereas the magnetoconductance vanishes. This phenomenon is well understood within a single-particle picture as a second order phase transition between localized electronic states at the band edges and extended states in the center, governed by a power law dependence of the localization length with respect to the energy distance to the band center with an universal static critical exponent.
We have scrutinized this power law behaviour in the presence of mutual electron interactions, which are treated in spin-unrestricted self-consistent Hartree-Fock approximation. We show for the lowest Landau level that the static critical exponent is unchanged in the presence of electron-electron interaction and for various types of disorder. Moreover, we estimate the effects of interaction and disorder type on the dynamical critical exponent, which governs the impact of quantum fluctuations induced by an external time-dependent electric field. We demonstrate by calculating the frequency-dependent conductivity in linear response theory that the dynamical critical exponent can be altered by interaction and disorder (A. Struck, submitted to Ann. Phys. (2006)).
Quantum wires in a strong magnetic field
Interaction- driven $g$-factor enhancement in clean
parabolic quantum wires
The spin splitting of the electronic subbands in a parabolically confined quantum wire in a strong magnetic field is calculated using the self-consistent Hartree-Fock approximation and a phenomenological short-ranged interaction potential. The interaction potential has been adjusted with respect to experimental data (Palecchi et. al, Phys. Rev. B 65,125303 (2002)). The effective g-factor and the critical density at which the subbands become almost spin-degenerate are determined. We have demonstrated that the Hartree term, which is sometimes neglected, is important and supports the exchange term in driving the system to the polarized state. The results are in good agreement with a rigorous time-dependent Hartree-Fock calculation reported by Balev et. al. ( Phys. Rev. B 72, 085345 (2005)). Our results provide a consistent interpretation of the experimental data (A. Struck, S. Mohammadi, S. Kettemann, B. Kramer, Phys. Rev. B 72, 245317 (2005) ).
The chiral metal insulator transition in disordered quantum
wires in strong magnetic fields
We have studied the quantum phase diagram of disordered wires in a strong magnetic field as a function of wire width and energy. The two-terminal conductance shows zero-temperature discontinuous transitions between exactly integer plateau values and zero. In the vicinity of this transition, the chiral metal-insulator transition (CMIT), states are identified that are superpositions of edge states with opposite chirality. The bulk contribution of such states is found to decrease with increasing wire width. Based on exact diagonalization results for the eigenstates and their participation ratios, we conclude that these states are characteristic for the CMIT, have the appearance of nonchiral edges states, and are thereby distinguishable from other states in the quantum Hall wire, namely extended edge states, two-dimensionally (2D) localized, quasi-1D localized, and 2D critical states (A. Struck, B. Kramer, T. Ohtsuki, S. Kettemann, Phys. Rev. B 72, 035339 (2005)).
Electron tunneling through an interacting quantum dot
We study electron transport through a parabolic quantum dot in a magnetic field. In the dot, 15-25 interacting electrons are confined, which are treated in self-consistent Hartree-Fock approximation. The resulting quasiparticle orbitals are not restricted with respect to angular momentum or spin. This leads to anticrossings in the single-particle spectrum and modifies the electrochemical potential. We try to estimate the change of the electron tunneling rate due to interactions and compare the results to recent experiments (M. Rogge et. al., cond-mat/0507036).