448
15 External Fields
Fig. 15.20 Normalized
Hall potential profile for
different magnetic fields
around filling factor ν = 2.
The overall voltage drop
corresponds to 20 mV. The
insets show the sample
geometry and transport
data. The 2DEG is from a
GaAs/Al 0.33 Ga 0.67 As
modulation-doped
heterostructure,
n s = 4.3 × 10 11 cm −2 ,
μ = 5 × 10 5 cm 2 /Vs,
T = 1.4 K. Adapted
from [1473]
A decisive role is played by the magnetic flux quanta. The presence of the magnetic field requires the
many-electron wavefunction to assume as many zeros per unit area as there are flux quanta penetrating
it. The decay of the wavefunction has a length scale of the magnetic length l 0 =
√
/(eB). Since the
magnetic field implies a 2π phase shift around the zero, such an object is also termed a vortex, being
the embodiment of the magnetic flux quanta in the electron system. Such a vortex represents a charge
deficit (compared to a homogeneous charge distribution) and thus electrons and vortices attract each
other. If a vortex and an electron are placed onto each other, considerable Coulomb energy is gained.
At ν = 1/3, there are three times more vortices than there are electrons, each vortex representing
a charge deficit of 1/3 e. Such a system is described with many-particle wavefunctions, such as the
Laughlin theory for ν = 1/q [1468] and novel quasi-particles called composite fermions [1481, 1482]
for other fractional fillings. For further reading we refer readers to [1483] and references therein.
15 External Fields
Fig. 15.20 Normalized
Hall potential profile for
different magnetic fields
around filling factor ν = 2.
The overall voltage drop
corresponds to 20 mV. The
insets show the sample
geometry and transport
data. The 2DEG is from a
GaAs/Al 0.33 Ga 0.67 As
modulation-doped
heterostructure,
n s = 4.3 × 10 11 cm −2 ,
μ = 5 × 10 5 cm 2 /Vs,
T = 1.4 K. Adapted
from [1473]
A decisive role is played by the magnetic flux quanta. The presence of the magnetic field requires the
many-electron wavefunction to assume as many zeros per unit area as there are flux quanta penetrating
it. The decay of the wavefunction has a length scale of the magnetic length l 0 =
√
/(eB). Since the
magnetic field implies a 2π phase shift around the zero, such an object is also termed a vortex, being
the embodiment of the magnetic flux quanta in the electron system. Such a vortex represents a charge
deficit (compared to a homogeneous charge distribution) and thus electrons and vortices attract each
other. If a vortex and an electron are placed onto each other, considerable Coulomb energy is gained.
At ν = 1/3, there are three times more vortices than there are electrons, each vortex representing
a charge deficit of 1/3 e. Such a system is described with many-particle wavefunctions, such as the
Laughlin theory for ν = 1/q [1468] and novel quasi-particles called composite fermions [1481, 1482]
for other fractional fillings. For further reading we refer readers to [1483] and references therein.