Synopsis: Half In, Half Out

New calculations confront the notion that adding impurities to one-dimensional solids called Luttinger liquids necessarily makes them insulators.
Synopsis figure
A. Altland et al., Phys. Rev. Lett. (2012)

In one-dimensional solids, strong Coulomb interactions can make the low-lying excitations look nothing like normal electrons. In this so-called Luttinger liquid, which has been observed in nanotubes, quantum wires, and the edges of quantum Hall systems, the spin and charge of electrons propagate independently and the concept of a Fermi surface, with well-defined electronic states, breaks down. Now, writing in Physical Review Letters, Alexander Altland from the University of Cologne, Germany, and his colleagues present calculations that challenge the usual way of thinking about the effects of impurities on the conductivity of Luttinger liquids.

In a 1992 seminal paper, Kane and Fisher predicted that even a weakly scattering impurity would block a current in a Luttinger liquid; that is, the Luttinger liquid would become an insulator. At finite temperatures, the conductance would follow a power law with an exponent that is a measure of the interaction strength of the Luttinger liquid.

Kane and Fisher’s analysis assumed currents were coherently scattered from the impurity; Altland et al. have extended the earlier model to the case of a Luttinger liquid with an impurity that permits both coherent and incoherent scattering. In this picture, Altland et al. find that carriers are transmitted or reflected with equal probability, a finding that is robust and insensitive to the details of the impurity or coupling to the leads. Their results could be tested by measuring the edge states in a fractional quantum Hall system. – Sarma Kancharla


Announcements

More Announcements »

Subject Areas

NanophysicsStrongly Correlated Materials

Previous Synopsis

Nonlinear Dynamics

Telling Left From Right

Read More »

Next Synopsis

Related Articles

Viewpoint: Rescuing the Quasiparticle
Condensed Matter Physics

Viewpoint: Rescuing the Quasiparticle

Experiments with heavy-fermion materials show that quasiparticles exist at the critical point of a quantum phase transition. Read More »

Synopsis: Insulator Sees the Light
Nanophysics

Synopsis: Insulator Sees the Light

The observation of conducting states in titanium dioxide, an insulator, opens a route to light-assisted nanoengineering of electronic properties. Read More »

Synopsis: Molecular Voltage Shift
Nanophysics

Synopsis: Molecular Voltage Shift

Small changes in the configuration of a molecule can significantly influence its resistive behavior in a circuit. Read More »

More Articles