Anomalous Giant Piezoresistance in AlAs 2D Electron Systems with Antidot Lattices

An AlAs two-dimensional electron system patterned with an antidot lattice exhibits a giant piezoresistance effect at low temperatures, with a sign opposite to the piezoresistance observed in the unpatterned region. We suggest that the origin of this anomalous giant piezoresistance is the nonuniform strain in the antidot lattice and the exclusion of electrons occupying the two conduction-band valleys from different regions of the sample. This is analogous to the well-known giant magnetoresistance effect, with valley playing the role of spin and strain the role of magnetic field.

Figure 1

The piezoresistance of an AlAs 2DES in the unpatterned (blank) region (lower trace) and in three antidot (AD) regions (upper three traces). The dotted line is the best fit to the piezoresistance in the blank region based on a conventional model. Upper insets: a micrograph of an AD lattice ($a=0.8\mu \mathrm{m}$) and sections of the Hall bar. Lower insets: the orientation and occupation of the valleys are schematically shown for the blank region at $ϵ=0$ where the two valleys are equally occupied and for $ϵ>1.5\times {10}^{-4}$ where all the electrons are transferred to the $Y$ valley.

Figure 2

Finite element simulation of the strain distribution in a 2D medium perforated with an AD lattice. Boxes A and B highlight areas of enhanced strain while box C marks a region of reduced strain. Strain in box D is close to its average value (${ϵ}_0$).

Figure 3

(a) Magnetoresistance (MR) traces of the $1\mu \mathrm{m}$-AD region at different values of applied strain, showing the commensurability peaks labeled with indices $i=1,2,\dots$, and the peak amplitudes ($\Delta R_{P,i}$). Inset: $X1$ orbit associated with the fundamental ($i=1$) peak. (b) Plots of $\Delta R_{P,i}$ as a function of strain. (c) Schematic diagram of the elongated AD lattice with channel width $w$ and period $a$, and the bouncing orbits that could give rise to subharmonic peaks. The black areas are the original AD (holes); the dotted lines mark the boundaries of the hypothesized, local strain-induced, “extended AD”. (d) MR traces of the three AD regions. The MR peak positions in these traces are analyzed in: (e) the $i=1$ peak position $B_{P,1}$ versus reciprocal AD lattice spacing $1/a$, and (f) peak positions $B_{P,i}$ versus index $i$. Each set of data points fits well to a straight line that goes through the origin.