scholarly journals Revealing the interference effect of Majorana fermions in a topological Josephson junction

2018 ◽  
Vol 9 ◽  
pp. 520-529 ◽  
Author(s):  
Jie Liu ◽  
Tiantian Yu ◽  
Juntao Song
Keyword(s):  
Josephson Junction ◽  
Interference Effect ◽  
Josephson Effect ◽  
Andreev Reflection ◽  
Local Density ◽  
Localized States ◽  
Majorana Fermions ◽  
Local Density Of States ◽  
Single Side ◽  
Period Oscillation

We study theoretically the local density of states (DOS) in a topological Josephson junction. We show that the well-known 4π Josephson effect originates from the interference effect between two Majorana fermions (MFs) that are localized at the Josephson junction. In addition, the DOS for electrons (holes) shows the 4π interference information along each parity conserved energy spectrum. The DOS displays a 2π period oscillation when two trivial states interfere with each other. This means that the DOS information may be used to distinguish the MFs from trivial localized states. We suggest that the interference effect and the DOS can be detected by using two STM leads or two normal leads. A single side lead can only detect the Andreev reflection tunneling process in the junction, which cannot reveal information about the interference effect in general. However, using two side leads, we can reveal information about the interference effect of the MFs as well as the DOS by combining Andreev reflection with the electron transmission process.

Calculation of bulk and surface electronic properties of diamond-like semiconductors

1984 ◽  
Vol 49 (3) ◽  
pp. 666-672 ◽  
Author(s):  
G. V. Gadiyak ◽  
A.A. Karpushin ◽  
Yu. N. Morokov ◽  
Mojmír Tomášek
Keyword(s):  
Experimental Data ◽  
Chemical Nature ◽  
Crystal Surface ◽  
Local Density ◽  
Surface States ◽  
Localized States ◽  
Total Density ◽  
Local Density Of States ◽  
Recursion Method ◽  
The Ideal

Local density of states (LDS) calculations have been performed by the recursion method for a model diamond-like semiconductor. LDS have been obtained for the following situations: the bulk, the vacancy and bivacancy in the bulk, the ideal (100) and (111) surfaces and the steps on these surfaces. Numerical results have been compared with experimental data for silicon. The calculated LDS show a one to one correspondence between the number of broken bonds on the investigated atom and the type of localized states near that atom. This supports the idea about the chemical nature of surface states, since the presence of steps on a strictly oriented surface leads to the appearance in the total density of surface states of additional peaks corresponding to another crystal surface.

ANDREEV REFLECTION AND SUBGAP TRANSPORT DUE TO ELECTRON-MAGNON INTERACTIONS IN FERROMAGNET-SUPERCONDUCTOR JUNCTIONS

2003 ◽  
Vol 17 (28) ◽  
pp. 5001-5005 ◽  
Author(s):  
G. TKACHOV ◽  
E. MCCANN ◽  
V. I. FAL'KO
Keyword(s):  
Low Temperature ◽  
Density Of States ◽  
Andreev Reflection ◽  
Cooper Pair ◽  
Local Density ◽  
Green Functions ◽  
Local Density Of States ◽  
Hamiltonian Method ◽  
New Process ◽  
Additional Channel

We show that electron-magnon interactions at a ferromagnetic metal-superconductor interface lead to a new process of magnon-assisted Andreev reflection, which consists of the simultaneous injection of a Cooper pair from the superconductor and the emission of a magnon inside the ferromagnet. At low temperature this process represents an additional channel for subgap transport across an FS interface, which lifts restrictions on the current I resulting from the necessity to match spin-polarised current in the ferromagnet with spin-less current in the superconductor. We calculate I using the tunnelling Hamiltonian method and the nonequilibrium (Keldysh) Green functions technique. It is shown that the inelastic magnon-assisted Andreev process would manifest itself as a nonlinear addition to the I(V) characteristics which is asymmetric with respect to the sign of the bias voltage and is related to the local density of states of magnons at the interface.

scholarly journals ELECTRONIC STATES AND LOCAL DENSITY OF STATES NEAR GRAPHENE CORNER EDGE

2012 ◽  
Vol 11 ◽  
pp. 151-156 ◽  
Author(s):  
YUJI SHIMOMURA ◽  
YOSITAKE TAKANE ◽  
KATSUNORI WAKABAYASHI
Keyword(s):  
Density Of States ◽  
Nearest Neighbor ◽  
Local Density ◽  
Tight Binding ◽  
Localized States ◽  
Destructive Interference ◽  
Edge States ◽  
Local Density Of States ◽  
Binding Model ◽  
Recursion Method

We study that stability of edge localized states in semi-infinite graphene with a corner edge of the angles 60°, 90°, 120° and 150°. We adopt a nearest-neighbor tight-binding model to calculate the local density of states (LDOS) near each corner edge using Haydock's recursion method. The results of the LDOS indicate that the edge localized states stably exist near the 60°, 90°, and 150° corner, but locally disappear near the 120° corner. By constructing wave functions for a graphene ribbon with three 120° corners, we show that the local disappearance of the LDOS is caused by destructive interference of edge states and evanescent waves.

scholarly journals Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Luca Fresta
Keyword(s):  
Density Of States ◽  
Local Density ◽  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Local Density Of States ◽  
Weak Disorder ◽  
Cluster Expansions ◽  
Strong Disorder ◽  
Lifshitz Tail

AbstractWe study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

scholarly journals Near-Field Excitation of Bound States in the Continuum in All-Dielectric Metasurfaces through a Coupled Electric/Magnetic Dipole Model

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 998
Author(s):  
Diego R. Abujetas ◽  
José A. Sánchez-Gil
Keyword(s):  
Magnetic Dipole ◽  
Density Of States ◽  
Bound States ◽  
Local Density ◽  
Near Field ◽  
Field Pattern ◽  
Local Density Of States ◽  
Optical Modes ◽  
Source Excitation ◽  
The Continuum

Resonant optical modes arising in all-dielectric metasurfaces have attracted much attention in recent years, especially when so-called bound states in the continuum (BICs) with diverging lifetimes are supported. With the aim of studying theoretically the emergence of BICs, we extend a coupled electric and magnetic dipole analytical formulation to deal with the proper metasurface Green function for the infinite lattice. Thereby, we show how to excite metasurface BICs, being able to address their near-field pattern through point-source excitation and their local density of states. We apply this formulation to fully characterize symmetry-protected BICs arising in all-dielectric metasurfaces made of Si nanospheres, revealing their near-field pattern and local density of states, and, thus, the mechanisms precluding their radiation into the continuum. This formulation provides, in turn, an insightful and fast tool to characterize BICs (and any other leaky/guided mode) near fields in all-dielectric (and also plasmonic) metasurfaces, which might be especially useful for the design of planar nanophotonic devices based on such resonant modes.

scholarly journals Wavefront dislocations reveal the topology of quasi-1D photonic insulators

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Clément Dutreix ◽  
Matthieu Bellec ◽  
Pierre Delplace ◽  
Fabrice Mortessagne
Keyword(s):  
Local Density ◽  
Topological Defects ◽  
Wave Functions ◽  
Topological Classification ◽  
Local Density Of States ◽  
Topological Phase Transition ◽  
Interference Fringes ◽  
Classical Wave ◽  
Phase Singularities

AbstractPhase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of wave functions are also at the heart of the topological classification of the gapped phases of matter. Despite identical singular features, topological insulators and topological defects in waves remain two distinct fields. Realising 1D microwave insulators, we experimentally observe a wavefront dislocation – a 2D phase singularity – in the local density of states when the systems undergo a topological phase transition. We show theoretically that the change in the number of interference fringes at the transition reveals the topological index that characterises the band topology in the insulator.

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 798-803 ◽  
Author(s):  
C. VILLARREAL ◽  
R. ESQUIVEL-SIRVENT ◽  
G. H. COCOLETZI
Keyword(s):  
Density Of States ◽  
Casimir Force ◽  
Periodic Structures ◽  
Local Density ◽  
Band Gaps ◽  
Basic Unit ◽  
Local Density Of States ◽  
Casimir Forces ◽  
Unit Cells ◽  
The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

scholarly journals Checkerboard local density of states in striped domains pinned by vortices

2003 ◽  
Vol 67 (13) ◽  
Author(s):  
Brian Møller Andersen ◽  
Per Hedegård ◽  
Henrik Bruus
Keyword(s):  
Density Of States ◽  
Local Density ◽  
Local Density Of States
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