Browsing by Subject "Disorder"
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Item Disorder in quasi-1D topological phases and gapless superconductivity in 2D(2023-02) Kasturirangan, SaumitranWe consider how disorder affects the electronic transport and localization in the vicinity of a topological phase transition in quasi-1D. This is studied for one of the most elementary examples of a topological insulator, the SSH chain. At the topological phase transition, the addition of disorder that respects the chiral symmetry of the system keeps it at a critical point. The electronic wavefunctions at zero energy are not exponentially localized, as one would expect in 1D. The conventional Fokker-Planck approach governing the evolution of transport statistics and the associated single parameter scaling, breaks down in describing the crossover of statistics from class BDI to class AI. We show that a second parameter, the product of energy and relaxation time, is required to capture this crossover. This is demonstrated using data collapse of numerically obtained transport. The regimes of transport behavior are characterized and appear to be universal. These results are used to study zigzag graphene nanoribbons, which is a topological semi-metal. The edge states have a power-law dispersion depending on the width and it is shown that the system is at a topological multicritical point. Upon adding hopping disorder, the transport, density of states, and localization length all obey the same behavior as the SSH chain at criticality, when re-scaled. The edge states are found to be energetically stable and remain close to the boundary. However, they are localized at any non-zero energy. We consider the implications of an out-of-plane field on superconductivity in monolayer NbSe$_2$. We find that the strong Ising spin-orbit coupling arising from the broken inversion symmetry, results in mixing the singlet and triplet components of the superconducting gap. On increasing the magnetic field strength, is it possible to find a gapless superconductor with Bogoliubov Fermi surfaces if the triplet pairing is sufficiently large.Item Electrostatic modification of novel materials(2013-10) Lee, YeonbaeElectric double layer transistor configurations have been employed to electrostatically modify the physical properties of two novel materials; single crystals of insulating strontium titanate (SrTiO3) and thin films of amorphous indium oxide (a-InO). First the results of doping SrTiO3 over broad ranges of temperature and carrier concentration employing an ionic liquid as the gate dielectric are reported. The surprising results are, with increasing carrier concentration, an apparent carrier-density dependent conductor-insulator transition, a regime of the anomalous Hall effect, suggesting magnetic ordering, and finally the appearance of superconductivity. The possible appearance of magnetic order near the boundary between the insulating and superconducting regimes is reminiscent of effects associated with quantum critical behavior in some complex compounds. Secondly, the evolution with carrier concentration of the electrical properties of a-InO thin films has been studied. Carrier variations of up to 7 x 1014 carriers-cm-2 were achieved again using an ionic liquid as a gate dielectric. The superconductor-insulator transition was traversed, and both the magnitude and the position of large magnetoresistance peak found in the insulating regime were modified. The systematic variation of the magnetoresistance peak with charge concentration was found to be qualitatively consistent with a simulation based on a model involving granularity.Item Excitonic eigenstates of disordered semiconductor quantum wires: adaptive wavelet computation of eigenvalues for the electron-hole Schrödinger equation(University of Minnesota. Institute for Mathematics and Its Applications, 2011-09) Mollet, Christian; Kunoth, Angela; Meier, TorstenItem Simulation data for: "Two parameter scaling in the crossover from symmetry class BDI to AI"(2022-08-01) Kasturirangan, Saumitran; Kamenev, Alex; Burnell, Fiona J; kastu007@umn.edu; Kasturirangan, SaumitranThe transport statistics at finite energies near a quantum critical point in the presence of disorder were not well understood analytically. This was approached by performing extensive simulations of transport using the package KWANT for python for disordered 1D quantum chains and metallic arm-chair graphene nanoribbons. This dataset contains the resulting data for several system sizes, strengths, and energies. This was used to establish two-parameter scaling and characterize the transport statistics.