Persistent currents in quantum rings

In this thesis, three different types of quantum rings arestudied. These are quantum rings with diamagnetic,paramagnetic or spontaneous persistent currents. It turns out that the main observable to characterizequantum rings is the Drude weight. Playing a key role inthis thesis, it will be used to distinguish betweendiamagnetic (positive Drude weight) and paramagnetic(negative Drude weight) ring currents. In most models, theDrude weight is positive. Especially in the thermodynamiclimit, it is positive semi-definite. In certain modelshowever, intuitivelysurprising, a negative Drude weight is found. This rareeffect occurs, e.g., in one-dimensional models with adegenerate ground state in conjunction with the possibilityof Umklapp scattering. One aim of this thesis is to examineone-dimensional quantum rings for the occurrence of anegative Drude weight. It is found, that the sign of theDrude weight can also be negative, if the band structurelacks particle-hole symmetry. The second aim of this thesis is the modeling of quantumrings intrinsically showing a spontaneous persistentcurrent. The construction of the model starts from theextended Hubbard model on a ring threaded by anAharonov-Bohm flux. A feedback term through which thecurrent in the ring can generate magnetic flux is added.Another extension of the Hamiltonian describes the energystored in the internally generated field. This model isevaluated using exact diagonalization and an iterativescheme to find the minima of the free energy. The quantumrings must satisfy two conditions to exhibit a spontaneousorbital magnetic moment: a negative Drude weight and aninductivity above the critical level. The magneticproperties of cyclic conjugated hydrocarbons likebenzene due to electron delocalization [magnetic anisotropy,magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)]---that have become important criteriafor aromaticity---can be examined using this model. Corrections to the presented calculations are discussed. Themost substantial simplification made in this thesis is theneglect of the Zeeman interaction of the electron spins withthe magnetic field. If a single flux tube threads a quantumring, the Zeeman interaction is zero, but in mostexperiments, this situation is difficult to realize. In themore realistic situation of a homogeneous field, the Zeemaninteraction has to be included, if the electrons have atotal spin component in the direction of the magnetic field,or if the magnetic field is strong.

Resonance properties of different neuronal populations in the immature mouse neocortex

Subthreshold resonance is a characteristic membrane property of different neuronal classes, is critically involved in the generation of network oscillations, and tunes the integration of synaptic inputs to particular frequency ranges. In order to investigate whether resonance properties of distinct neuronal populations in the immature neocortex contribute to these network oscillations, I performed whole-cell patch-clamp recordings from visually identified neurons in tangential and coronal neocortical slices from postnatal day (P) P0-P7 C57Bl/6 and P6-P13 GAD67-GFP knock-in mice. Subthreshold resonance was analyzed by sinusoidal current injection of varying frequency. All Cajal-Retzius cells showed subthreshold resonance with an average frequency of 2.6 ± 0.1 Hz (n=60), which was massively reduced by ZD7288, a blocker of hyperpolarization-activated cation currents. About 65.6% (n=61) of the supragranular pyramidal neurons showed subthreshold resonance with an average frequency of 1.4 ± 0.1 Hz (n=40). Application of 1 mM Ni2+ suppressed subthreshold resonance, suggesting that low-threshold Ca2+ currents contribute to resonance in these neurons. About 63.6% (n=77) of the layer V pyramidal neurons showed subthreshold resonance with an average frequency of 1.4 ± 0.2 Hz (n=49), which was abolished by ZD7288. Only 44.1% (n=59) of the subplate neurons showed subthreshold resonance with an average frequency of 1.3 ± 0.2 Hz (n=26) and a small resonance strength. Finally, 50% of the investigated GABAergic interneurons showed subthreshold resonance with an average frequency of 2.0 ± 0.2 Hz (n=42). Membrane hyperpolarization to –86 mV attenuated the frequency and strength of subthreshold resonance. Subthreshold resonance was virtually abolished in the presence of 1 mM Ni2+, suggesting that t-type Ca2+ currents are critically involved in the generation of resonance, while ZD7288 had no effect. Application of 0.4 µM TTX suppressed subthreshold resonance at depolarized, but not hyperpolarized membrane potential, suggesting that persistent Na+ current contribute to the amplification of membrane resonance. rnIn summary, these results demonstrate that all investigated neuronal subpopulations reveal resonance behavior, with either hyperpolarization-activated cation or low-threshold Ca2+ currents contributing to the subthreshold resonance. GABAergic interneurons also express subthreshold resonance at low frequencies, with t-type Ca2+ and persistent Na+ currents underlying the generation of membrane resonance. The membrane resonance of immature neurons may contribute to the generation of slow oscillatory activity pattern in the immature neocortex and enhance the temporal precision of synaptic integration in developing cortical neurons.rn