Shumway Research Group

Department of PhysicsArizona State UniversityTempe • AZ
Research in Path Integral Simulations, Quantum States of Matter, and Nanoscale Electronics

Simulations of Nanoscale Devices

In addition to our studies of quantum dots, we are also looking at other systems that can be used for nanoelectronic devices. The goal is to develop path integral Monte Carlo (PIMC) as a reliable tool for simulating conductance of strongly correlated electron systems. We are starting with studies of Luttinger liquids, since these are well-known theoretically, then moving on to simulations of quantum point contacts and other systems, where PIMC should be a unique and valuable tool.

Charge density for a quantum point contact.

To motivate this work, first consider static properties of a quantum point contact. The image to the right shows the charge density (in cm-2) for a GaAs quantum point contact, formed by a split gate over a 2DEG. The simulation is PIMC at T=750 mK, with over 100 interacting eletrons in a 0.5 μm supercell.

Several features are apparent from the static charge density. First, you can see a 2DEG region on the left and right side of the image, separated by dark blue patches where the gates ahve completely depleted the electrons. The gates are at a voltage VG=-0.4 V, and we've shown contour lines of resulting electrostatic potential as thin gray lines. The contact itself is a narrow line of electrons connecting the left and right sides.

If you look closely at the 2DEG, you can see Friedel oscillations, appearing as standing waves with fronts parallel to the edge of the gates. The wavelegth of these oscillations is roughly the interelectron spacing. Next, look at the strucutre along the QPC. You can see some longer-wavelength oscillations, most notably a peak in charge density in center of the dot. This is ordering of electrons along the wire, as you would expect to see in a Luttinger liquid or a 1D Wigner crystal. In fact, pair correlation functions (not shown) reveal that the electron spins have some antiferromagnetic ordering. This is raw simulation data that has not been symmetrized, so the apparent symmetry is an indicator of how thoroughly the path integral has been sampled.

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