Two-dimensional Bloch electrons in perpendicular magnetic fields: an exact calculation of the Hofstadter butterfly spectrum

The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's Butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the strong field limiting cases. Here we report calculations of the full spectrum of the single-particle Schr\"{o}dinger equation without further approximations. Our method is exact, up to numerical precision, for any combination of potential and uniform field strength. We first study a situation that corresponds to the strong potential limit, and compare the exact results to the predictions of a Hofstadter-like model. We then go on to analyze the evolution of the fractal spectrum from a Landau-like nearly-free electron system to the Hofstadter tight-binding limit by tuning the amplitude of the modulation potential

Evaluation of the Signature Molecular Descriptor with BLOSUM62 and an All-Atom Description for Use in Sequence Alignment of Proteins

This Honors Project focused on a few aspects of this topic. The second is comparing the molecular signature kernels to three of the BLOSUM matrices (30, 62, and 90) to test the accuracy of the mathematical model. The kernel matrix was manipulated in order to improve the relationship by focusing on side groups and also by changing how the structure was represented in the matrix by increasing the initial height distance from the central atom (Height 1 and Height 2 included). There were multiple design constraints for this project. The first was the comparison with the BLOSUM matrices (30, 62, and 90) which characterized the substitution ability of each pair of amino acids as found in nature. The last constraint was the usage of the signature kernel equation which was used in order to repeat a previous study by Jean-Loup Faulon. The manipulated kernel matrix including side groups improved the linear correlation from 0.83 to 0.87. While using Height 2, the linear correlation R2 improved from 0.83 to 0.93. From the results, polarity is a factor for structure as in nature and using height 1 or a two-dimensional method will limit the results

Stability of the shell structure in 2D quantum dots

We study the effects of external impurities on the shell structure in semiconductor quantum dots by using a fast response-function method for solving the Kohn-Sham equations. We perform statistics of the addition energies up to 20 interacting electrons. The results show that the shell structure is generally preserved even if effects of high disorder are clear. The Coulomb interaction and the variation in ground-state spins have a strong effect on the addition-energy distributions, which in the noninteracting single-electron picture correspond to level statistics showing mixtures of Poisson and Wigner forms.Comment: 7 pages, 8 figures, submitted to Phys. Rev.

Electrically detected magnetic resonance of carbon dangling bonds at the Si-face 4H-SiC/SiO2_2 interface

SiC based metal-oxide-semiconductor field-effect transistors (MOSFETs) have gained a significant importance in power electronics applications. However, electrically active defects at the SiC/SiO$_2$ interface degrade the ideal behavior of the devices. The relevant microscopic defects can be identified by electron paramagnetic resonance (EPR) or electrically detected magnetic resonance (EDMR). This helps to decide which changes to the fabrication process will likely lead to further increases of device performance and reliability. EDMR measurements have shown very similar dominant hyperfine (HF) spectra in differently processed MOSFETs although some discrepancies were observed in the measured $g$-factors. Here, the HF spectra measured of different SiC MOSFETs are compared and it is argued that the same dominant defect is present in all devices. A comparison of the data with simulated spectra of the C dangling bond (P$_\textrm{bC}$) center and the silicon vacancy (V$_\textrm{Si}$) demonstrates that the P$_\textrm{bC}$ center is a more suitable candidate to explain the observed HF spectra.Comment: Accepted for publication in the Journal of Applied Physic

Geometric and impurity effects on quantum rings in magnetic fields

We investigate the effects of impurities and changing ring geometry on the energetics of quantum rings under different magnetic field strengths. We show that as the magnetic field and/or the electron number are/is increased, both the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become insensitive to whether the ring is circular or square in shape. This is in qualitative agreement with experiments. However, we also find that the Aharonov-Bohm oscillation can be greatly phase-shifted by only a few impurities and can be completely obliterated by a high level of impurity density. In the many-electron calculations we use a recently developed fourth-order imaginary time projection algorithm that can exactly compute the density matrix of a free-electron in a uniform magnetic field.Comment: 8 pages, 7 figures, to appear in PR

Effects of nitridation on SiC/SiO2 structures studied by hard X-ray photoelectron spectroscopy

SiC is set to enable a new era in power electronics impacting a wide range of energy technologies, from electric vehicles to renewable energy. Its physical characteristics outperform silicon in many aspects, including band gap, breakdown field, and thermal conductivity. The main challenge for further development of SiC-based power semiconductor devices is the quality of the interface between SiC and its native dielectric SiO$_2$. High temperature nitridation processes can improve the interface quality and ultimately the device performance immensely, but the underlying chemical processes are still poorly understood. Here, we present an energy-dependent hard X-ray photoelectron spectroscopy (HAXPES) study probing non-destructively SiC and SiO$_2$ and their interface in device stacks treated in varying atmospheres. We successfully combine laboratory- and synchrotron-based HAXPES to provide unique insights into the chemistry of interface defects and their passivation through nitridation processes