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Brief introduction to textures in Quantum Hall Systems : At
certain filling factors the lowest lying excitations of Quantum Hall fluid
are many body topological objects formed by electron spins in two dimensional
semiconductor quantum wells. These objects called Skyrmion (Fig. 2, 3) carry
charge and cause a major depolarization in the system. This depolarization
has been detected in a number of experiments ( Fig 1)
(Fig.1)
Optically Pumped NMR Knight Shift Data
(Fig.
4) Excess of the charge density associated
with a presence of a Skyrmion. |
(Fig.2)
3D Plot of a Skyrmion. Arrows
are the spin of electrons.
(Fig.
3) The same Skyrmion projected on 2D plane.
(Fig5.) :
I.B. Spielman, et. Al.,84(25),5808 (2000)
(Fig.
6): A Bimeron consists of a pair of
merons each with a charge e/2. |
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Double
quantum well is another semiconductor heterostructure that consists of two
quantum wells separated by a thin barrier layer. Electrons in the two wells
can form a quantum mechanical coherent fluid even in the absence of
tunneling. Observation of zero bias tunneling conductance peak is a signature
of this coherent state (Fig 5.) The
lowest energy electron’s wavefunction in this double well structure is
symmetric between the two wells and the antisymmetric state is higher in
energy with 2t= The
layer index of an electron in this system can be interpreted as a pseudospin
index. Electron is in pseudospin up (down) when it is in the left (right)
layer. The pseudospin vector is lying in the x-y plane in the symmetric state
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This
formulation helps us understand the excitations of the bilayer systems. The ground
state is obviously a pseudospin polarized state. The lowest lying excitation
would be a Skyrmion in pseudospin (Symmetric-Antisymmetric) space most often
called a Bimeron because in the rotated basis of Left and Right it consists
of a pair of vortex-antivortex each with a charge e/2 called meron (Fig.6). |
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