arXiv subjects

Junmo Jeon

Publications and source records attributed to Junmo Jeon.

22 records · Page 2Linked to original sources

arXiv2021

Pattern-dependent proximity effect and Majorana edge mode in one-dimensional quasicrystals

The Majorana edge states of the Kitaev chain model have attracted extensive attention on their stability and experimental realization. One of the interesting aspects is finding the exotic proximity effect, which guarantees the presence of the Majorana modes, further enables efficient braidings between them. In this paper, we explore the superconducting proximity effect for quasi-periodic quantum wires and discuss how quasi-periodic patterns affect the stability of the Majorana modes. Considering the Kitaev chain model of the one-dimensional quasi-periodic system, we discuss the pattern-dependent proximity effects. First, we argue that the presence of quasi-periodic hoppings energetically induces the $p$-wave pairing also to be quasi-periodic rather than uniform pairing. More interestingly, when the normal metallic wire is adjacent to the quasiperiodic superconducting wire, we have found that the Majorana edge modes are being transferred to the edge of the normal metallic side with enhanced stability. Finally, we discover the proximity effect on the strengths of the quasi-periodicities with a general power-law relationship, whose power depends on the tiling pattern. Our results show how quasi-periodic patterns play an important role in the Kitaev chain and the stabilization of the Majorana mode.

cond-mat.supr-con↗

arXiv2021

Length scale formation in the Landau levels of quasicrystals

Exotic tiling patterns of quasicrystals have motivated extensive studies of quantum phenomena such as critical states and phasons. Nevertheless, the systematic understanding of the Landau levels of quasicrystals in the presence of the magnetic field has not been established yet. One of the main obstacles is the complication of the quasiperiodic tilings without periodic length scales, thus it has been thought that the system cannot possess any universal features of the Landau levels. In this paper, contrary to these assertions, we develop a generic theory of the Landau levels for quasicrystals. Focusing on the two dimensional quasicrystals with rotational symmetries, we highlight that quasiperiodic tilings induce anomalous Landau levels where electrons are localized near the rotational symmetry centers. Interestingly, the localization length of these Landau levels has a universal dependence on n for quasicrystals with n-fold rotational symmetry. Furthermore, macroscopically degenerate zero energy Landau levels are present due to the chiral symmetry of the rhombic tilings. In this case, each Landau level forms an independent island where electrons are trapped at given fields, but with field control, the interference between the islands gives rise to an abrupt change in the local density of states. Our work provide a general scheme to understand the electron localization behavior of the Landau levels in quasicrystals.

cond-mat.mes-hall↗

arXiv2020

Phonon transmittance of one dimensional quasicrystals

In quasicrystals, special tiling patterns could give rise to unique physical phenomena such as critical states distinct from periodic systems. In this paper, we study how quasi-periodicity in aperiodic systems results in anomalous phonon modes, especially focusing on thermal transmittance in one-dimensional quasicrystals. Unlike periodic or compeletly random systems, we classify certain quasicrystals could host critical phonon modes whose transport properties are topologically protected based on their pattern equivariant cohomology group of supertilings. Starting from discussing general rule to find such critical phonon modes, we discuss classification of topologically distinct thermal transmittance in quasiperiodic systems. To be more specific, we exemplify (decorated) metallic-mean tilings and Cantor tiling, and derive universal features for resonant and decaying phonon modes as a function of quasi-periodic strength. Our study paves a new way to understand thermal transmittance of quasi-periodic systems based on the topological classification and offers quasicrystals as strong candidates to control drastic phonon modes.

cond-mat.mes-hall↗

arXiv2020

Topological critical states and anomalous electronic transmittance in one dimensional quasicrystals

Due to the absence of periodic length scale, electronic states and their topological properties in quasicrystals have been barely understood. Here, we focus on one dimensional quasicrystal and reveal that their electronic critical states are topologically robust. Based on tiling space cohomology, we exemplify the case of one dimensional aperiodic tilings especially Fibonacci quasicrystal and prove the existence of topological critical states at zero energy. Furthermore, we also show exotic electronic transmittance behavior near such topological critical states. Within the perturbative regime, we discuss lack of translational symmetries and presence of topological critical states lead to unconventional scaling behavior in transmittance. Considering both analytic analysis and numerics, electronic transmittance is computed in cases where the system is placed in air or is connected by semi-infinite periodic leads. Finally, we also discuss generalization of our analysis to other quasicrystals. Our findings open a new class of topological quantum states which solely exist in quasicrystals due to exotic tiling patterns in the absence of periodic length scale, and their anomalous electronic transport properties applicable to many experiments.

cond-mat.mes-hall↗