Introduction to fractional quantum Hall effect - PowerPoint PPT Presentation

Loading...

PPT – Introduction to fractional quantum Hall effect PowerPoint presentation | free to download - id: 441f09-Y2QxM



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Introduction to fractional quantum Hall effect

Description:

Introduction to fractional quantum Hall effect (Talk at Physics Faculty, Belgrade, 2010) Milica V. Milovanovi Institute of Physics Belgrade Scientific Computing ... – PowerPoint PPT presentation

Number of Views:176
Avg rating:3.0/5.0
Slides: 22
Provided by: win1163
Learn more at: http://www1.scl.rs
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Introduction to fractional quantum Hall effect


1
Introduction to fractional quantum Hall effect
(Talk at Physics Faculty, Belgrade, 2010)
  • Milica V. Milovanovic
  • Institute of Physics Belgrade
  • Scientific Computing Laboratory

2
Hall experiment
3
Classical picture in 2D
4
J.P.Eisenstein and H.L.Stormer, Science
248,1461(1990)
T 85mK
Plateaus ! Rigidity !
filling factor
5
Quantum Mechanics a particle in 2D in
perpendicular B
Velocity
Landau levels
6
act in a fixed Landau level
7
Summary
cyclotron velocity
guiding center coordinate
8
Degeneracy of Landau level
unit of flux flux quantum
9
quantum Hall effect
onedimensional problem
localized states in bulk
no backscattering!
10
integer quantum Hall effect
(Laughlin argument)
Insertion of one flux quantum does not change
spectrum! and expect transfer of integer (i)
number of electrons
localized states
11
In rotationally symmetric gauge in two dimensions
Single particle wave functions
Orbits at radius
Imagine that we are at the middle of the plateau
at 1/3 - How the ground state of the system
would look like?
12
Laughlin answer
R.B. Laughlin, PRL 50, 1995 (1983)
antisymmetry
and in the cases of other hierarchical
constructions odd denominator expected!
13
FQHE at 5/2 !
R. Willet et al., PRL 59, 1776, 1987
W. Pan et al.,PRL 83, 3530 ,1999.
14
Moore-Read answer
G. Moore and N. Read, Nucl. Phys. B 360, 362
(1991)
Pfaffian part describes a pairing among particles
as in a superconductor BCS pairing of
spinless fermions
Pfaffian
15
Pfaffian for 4 particles
16
Pfaffian (p-wave superconductor)
otherwise we would have Fermi-liquid-like state
17
  • 5/2 numerics favorable for Pfaffian in 2nd
    LL
  • Pfaffian is the most simple
    ansatz if not only
  • explanation of plateau
  • R.H. Morf, PRL 80, 1505
    (1998), E.H. Rezayi and F.D.M. Haldane, PRL 84,
  • 4685 (2000)
  • (b) 1/2 exps. and numerics find
    Fermi-liquid-like phase
  • (no plateau) E. Rezayi and N.
    Read, PRL 72, 900 (1994)

18
at 1/2 (1/4) in WQWs (wide quantum wells)
signatures of FQHE minima in !
J. Shabani et al., Phys. Rev. Lett. 103, 256802
(2009)
likely nature of these states is multi-component

(two-component)
19
theory (mathematical identity)
two-component
20
Pf state can lead to a first topological quantum
computer!
We want to know how to make Pfaffian!
21
The quest for Pfaffian begins!
About PowerShow.com