Valley Susceptibility of an Interacting Two-Dimensional Electron System

Abstract

We report direct measurements of the valley susceptibility, the change of valley population in response to applied symmetry-breaking strain, in an AlAs two-dimensional electron system. As the two-dimensional density is reduced, the valley susceptibility dramatically increases relative to its band value, reflecting the system's strong electron-electron interaction. The increase has a remarkable resemblance to the enhancement of the spin susceptibility and establishes the analogy between the spin and valley degrees of freedom.PACS numbers: 71.70.Fk , 73.43.Qt Currently, there is considerable interest in controlled manipulation of electron spin in semiconductors. This interest partly stems from the technological potential of spintronics, namely, the use of carrier spin to realize novel electronic devices. More important, successful manipulation of spins could also impact the more exotic field of quantum computing since many of the current proposals envision spin as the quantum bit (qubit) of information [1,2,3]. Here we describe measurements of another property of electrons, namely their valley degree of freedom, in a semiconductor where they occupy multiple conduction band minima (valleys) [ Fig. 1(a)]. Specifically, for a two-valley, two-dimensional electron system (2DES) in an AlAs quantum well, we have determined the "valley susceptibility", χ v , i.e., how the valley populations respond to the application of symmetry-breaking strain. This is directly analogous to the spin susceptibility, χ s , which specifies how the spin populations respond to an applied magnetic field [Figs. 1(d)]. Our data show that χ v and χ s have strikingly similar behaviors, including an interaction-induced enhancement at low electron densities. The results establish the general analogy between the spin and valley degrees of freedom, implying the potential use of valleys in applications such as quantum computing. We also discuss the implications of our results for the controversial metal-insulator transition problem in 2D carrier systems.It is instructive to describe at the outset the expressions for the band values of spin and valley susceptibilities χ s,b and χ v,b [4]. The spin susceptibility is defined as χ s,b = d∆n/dB = g b µ B ρ/2, where ∆n is the net spin imbalance, B is the applied magnetic field, g b is the band Landé g-factor, and ρ is the density of states at the Fermi level. Inserting the expression ρ = m b /πh 2 for 2D electrons, we have χ s,b = (µ B /2πh 2 )g b m b , where m b is the band effective mass. In analogy to spin, we can define valley susceptibility as χ v,b = d∆n/dǫ = ρE 2,b = (1/πh 2 )m b E 2,b , where ∆n is the difference between the populations of the majority and minority valleys, ǫ is strain, and E 2,b is the conduction band deformation potential [5]. In a Fermi liquid picture, the interparticle interaction results in replacement of the parameters m b , g b , and E 2,b [6] by their normalized values m * , g * , and E * 2 . Note that χ s ∝ m * g * and χ v ∝ m * E * 2 . Our experiments were performed on...

Universal Increase in the Superconducting Critical Temperature of Two-Dimensional Semiconductors at Low Doping by the Electron-Electron Interaction

“…This equality was experimentally verified in AlAs quantum wells [24] where the pseudo magnetic field was generated by a strain deformation. Similarly to the strain case in AlAs, an intervalley phonon can also act as a pseudo magnetic field by inducing a valley splitting and a valley polarization via the electron-phonon interaction.…”

Valley degeneracy in biaxially strained aluminum arsenide quantum wells

“…Evidence for a QW width crossover from double-to single-valley occupation has been shown for (001)AlAs wells 8,9 , as has evidence for single valley occupancy in wide (110)AlAs wells 5 . Dynamic control of the valley degeneracy has been realized with uniaxially strained (001)AlAs QWs to induce valley degeneracy splitting 1,10,11 . Such studies can quantify interaction effects, calibrating valley strain susceptibility and valley effective mass 10,[12][13][14] .…”

“…Dynamic control of the valley degeneracy has been realized with uniaxially strained (001)AlAs QWs to induce valley degeneracy splitting 1,10,11 . Such studies can quantify interaction effects, calibrating valley strain susceptibility and valley effective mass 10,[12][13][14] . Quantum confinement to a one-dimensional multi-valley system has been achieved in cleaved-edge overgrown quantum wires 15,16 and quantum point contacts 17 .…”

Intervalley Scattering and Localization Behaviors of Spin-Valley Coupled Dirac Fermions

“…Like the spin index in spintronics, the valley index is a well defined degree of freedom for lowenergy carriers, thus can be used to encode information as well. This has led to the concept of valleytronics, a new type of electronics based on manipulating the valley index of carriers [1][2][3][4][5]. The timescale of intervalley scattering determines how long the information represented by valley polarization can be retained.…”