We discuss the Luttinger Liquid behaviour of a semiconducting Quantum Wire.
We show that the measured value of the bulk critical exponent, αbulk,
for the tunneling density of states can be easily calculated.
Then, the problem of the transport through a Quantum Dot formed by two
Quantum Point Contacts along the Quantum Wire, weakly coupled to spinless
Tomonaga-Luttinger liquids is studied, including the action of a strong
transverse magnetic field B.
The known magnetic dependent peaks of the conductance, G(B), in the
ballistic regime at a very low temperature, T, have to be reflected also in
the transport at higher T and in different regimes. The temperature
dependence of the maximum Gmax of the conductance peak, according to the
Correlated Sequential Tunneling theory, yields the power law Gmax∝T2αend−1, with the critical exponent, αend, strongly
reduced by B.
This behaviour suggests the use of a similar device as a magnetic field
modulated transistor.Comment: 6 pages, 4 figure