Nanowires:
One of the group's major focuses has been on electronic properties of very small structures, in which electrons are confined in several directions to distances of the order or smaller than their quantum wavelength. The simplest of these are quantum dots and quantum wires, in which the confinement is in all or all but one dimension, respectively. Quantum dots have been the subject of much experimental and theoretical study, and at this stage, apart from the very challenging problem of creating and manipulating them in large arrays, are rather well understood. Quantum wires, by contrast, are still an experimental frontier, and in recent years we have begun for the first time to see real confrontations of theory and experiment. Ultimately, a detailed knowledge of such systems is an essential part of any prospective nanoelectronics, since these constitute the simplest element, the "interconnect".
Quantum wires are interesting theoretically because in one dimension, the Coulomb interaction between electrons has qualitatively significant effects, that require a description completely different from the "Fermi liquid theory" used for three-dimensional (and two-dimensional) metals. This is called Luttinger liquid theory, and leads to often dramatic effects (see e.g. earlier publications Kane et al , Bockrath et al , Yao et al and others). More recent explorations of the ramifications of strong Coulomb effects in quantum wires are described below:
- Spin incoherent Luttinger liquids
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A very recent topic of interest in nanowires has been to explore the
very low density limit of the electron gas, in which the Luttinger
liquid description itself breaks down. Instead, at very low density,
one has a strange situation in which charge disturbances propagate
essentially quantum mechanically, which the spin of the electron is
"non-degenerate", i.e. classical and strongly fluctuating. This
regime is believed to occur inside the constriction of quantum point
contacts - where the so-called "0.7 anomaly" (a fraction conductance
quasi-plateau where none was expected) has puzzled the community for
many years. It is also now being probed in gated cleaved edge quantum
wires by the Weizmann group. Recently, Cheianov and Zvonarev
were able to calculate the behavior of the tunneling density of states
(and some other properties) of such a low-density quantum wire. Their
result - obtained in a tour-de-force 40 page work of applied
mathematics and sophisticated Bethe Ansatz methods - were in sharp
contrast to Luttinger liquid behavior and quite intriguing. For
instance, one finds that the usual low-bias tunneling density of
states suppression is converted to a strong enhancement! These
results were interesting enough to be featured in the Bell Labs
condensed matter journal club ( here ). In
this letter , with Greg Fiete , we showed how these and more general
results for this regime could be obtained in a physically transparent
manner with no more than a few lines of fairly elementary math (our
entire paper, including all calculations and an extensive introduction
and discussion is 4 pages long)!
36 pages of Cheianov+Zvonarev's paper. One page containing calculations was left off for symmetry of the image. Our paper. There are 13 equations, several of which are definitions or final results. Our results are more general It is interesting that, though the Green's function decays exponentially in space in this regime, there is actually an enhanced power-law local (tunneling) density of states. We are currently pursuing other properties of the electron gas in the spin incoherent limit. In the same regime, an interesting result for an idealized 2-terminal transport measurement was obtained by Matveev, see cond-mat/0405542 . More recently (5/2/05), we discussed various aspects of electrical transport in the spin incoherent regime. Our ( Greg Fiete , Karyn Le Hur, and LB) paper studies electrical transport in such quantum wires in a variety of situations. Read the cond-mat .
- Generating quantum entanglement
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One remarkable result we found was that these effects could be
harnessed to further the goals of quantum information science. In
that field, quantum entanglement-i.e. the superposition of two
non-local observables in a very uncertain state-is used as a resource
for applications impossible in the classical realm. For instance, a
source of pairs of electrons or photons in an entangled spin state
(this means that the two spins are known to be antiparallel but the
spin of either is completely uncertain quantum mechanically) can be
used to create a communication channel that is perfectly secure to
unwanted listeners, protected by the laws of quantum mechanics rather
than human ingenuity.
For solid state applications, one desires electron spins rather than photons. The trick is not only to create an entangled electron pair, but to spatially separate the two electrons of the pair (e.g. then exchanged between communicators). In this letter , we demonstrated that Luttinger liquid effects actually enable one to construct (in principle at least!) a device out of two quantum wires-e.g. carbon nanotubes- to extract and separate entangled electron pairs from a superconductor, and that the Luttinger liquid physics makes such a device more and more efficient as it is cooled. This work was featured in Physics Focus online . Less publicized work, here , calculated some detailed properties of the conductance of superconducting-nanotube junctions. 
Schematic of nanotube-superconductor entanglement generator.
