Low-temperature, <i>in situ</i> tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator

Shayegan, M.; Karraï, K.; Shkolnikov, Y. P.; Vakili, K.; Poortere, E. P. De; Manus, S.

doi:10.1063/1.1635963

Cited by 92 publications

(132 citation statements)

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“…3a), have measured its magnitude in both [100] and [010] directions. 15 Such strain results in a splitting between the X and Y valley energies that is equal to, in the absence of interaction, εE 2 , where ε = (∆L/L) [100] -(∆L/L) [010] , and E 2 = 5.8eV is the AlAs deformation potential for the splitting between the X and Y valley energies (∆L/L is the fractional change in sample size). 16 Figure 3b provides exemplary data of the sample resistance as a function of V P .…”

Section: Tuning the Valley Population Via Application Of In-plane Strmentioning

confidence: 99%

“…We developed a simple technique to induce symmetry-breaking strain in the sample plane at low temperatures and change the populations of the X and Y valleys. 15 We simply glue a thinned sample, made in the shape of a Hall bar, on the side of a commercial, stacked, piezoelectric actuator (Fig. 3a).…”

Section: Tuning the Valley Population Via Application Of In-plane Strmentioning

confidence: 99%

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Two‐dimensional electrons occupying multiple valleys in AlAs

Shayegan

Poortere

Gunawan

et al. 2006

Physica Status Solidi (b)

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Two-dimensional electrons in AlAs quantum wells occupy multiple conduction-band minima at the Xpoints of the Brillouin zone. These valleys have large effective mass and g-factor compared to the standard GaAs electrons, and are also highly anisotropic. With proper choice of well width and by applying symmetry-breaking strain in the plane, one can control the occupation of different valleys thus rendering a system with tuneable effective mass, g-factor, Fermi contour anisotropy, and valley degeneracy. Here we review some of the rich physics that this system has allowed us to explore.

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Section: Tuning the Valley Population Via Application Of In-plane Strmentioning

confidence: 99%

Section: Tuning the Valley Population Via Application Of In-plane Strmentioning

confidence: 99%

Two‐dimensional electrons occupying multiple valleys in AlAs

Shayegan

Poortere

Gunawan

et al. 2006

Physica Status Solidi (b)

Self Cite

127

202

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“…1(b)]. To apply tunable strain we glued the sample to one side of a piezoelectric (piezo) stack actuator [8]. The piezo polling direction is aligned along [100] as shown in Fig.…”

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Valley Susceptibility of an Interacting Two-Dimensional Electron System

et al. 2006

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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...

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“…Each valley is characterized by a longitudinal m l = 1.1m 0 and a transverse m t = 0.2m 0 electron effective mass (m 0 is electron mass in vacuum). In our experiments we apply external strain in the plane of the sample to tune the populations of the X and Y valleys [23,24,25], and study the evolution of the 2DES as it becomes valley polarized. This is done by gluing the sample to one side of a stacked piezoelectric actuator with the sample's [100] crystal orientation aligned with the piezo's poling direction [ Fig.…”

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Spin–valley phase diagram of the two-dimensional metal–insulator transition

et al. 2007

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Using symmetry breaking strain to tune the valley occupation of a two-dimensional (2D) electron system in an AlAs quantum well, together with an applied in-plane magnetic field to tune the spin polarization, we independently control the system's valley and spin degrees of freedom and map out a spin-valley phase diagram for the 2D metal-insulator transition. The insulating phase occurs in the quadrant where the system is both spin-and valley-polarized. This observation establishes the equivalent roles of spin and valley degrees of freedom in the 2D metal-insulator transition.PACS numbers: 71.30.+h, 73.43.Qt, 73.50.Dn, The scaling theory of localization in two dimensions [1], which predicts an insulating phase for two-dimensional electron systems (2DESs) with arbitrarily weak disorder, was challenged by the observation of a metallic temperature dependence (dρ/dT > 0) of the resistivity, ρ, in low-disorder Si metal-oxide-semiconductor field-effect transistors (Si-MOSFETs) [2]. The associated metal-toinsulator transition (MIT) has subsequently become the subject of intense interest and controversy [3]. While behavior similar to that of Ref.[2] has now been reported for a wide variety of 2D carrier systems such as n-AlAs, 10], and p-Si/SiGe [11,12], the origin of the metallic state and its transition into the insulating phase remain major puzzles in solid state physics.Several experiments have demonstrated the important role of the spin degree of freedom in the MIT problem, either in systems with a strong spin-orbit interaction [10,13,14], or via the application of an external magnetic field to spin polarize the carriers [15,16,17,18,19]. The latter experiments have shown that a magnetic field applied parallel to the 2DES plane suppresses the metallic temperature dependence, ultimately driving the 2DES into the insulating regime as the 2DES is spin polarized. The relevance of multiple conduction-band valleys, on the other hand, is less known. Although it has been discussed theoretically that the occupation of multiple valleys may also be important [20,21], there has been no direct experimental demonstration. Here we show that the electrons' valley degree of freedom indeed plays a crucial role, analogous to that of spin. We study a 2DES, confined to an AlAs quantum well, in which we can independently tune both the spin and valley degrees of freedom. By studying the temperature dependence of ρ at various degrees of spin and valley polarization, we map out the metal-insulator phase diagram in this system at a constant density. The 2DES exhibits a metallic behavior when either the valley or spin are left fully unpolarized, and a minimum amount of both spin and valley polarization is required to enter the insulating phase.We performed experiments on 2DESs confined to modulation-doped, AlAs quantum wells of width 11 nm and 15 nm [22]. In these systems, the electrons occupy two conduction-band valleys of AlAs centered at the edges of the Brillouin zone along the [100] and [010] directions. We denote these valleys as X and Y...

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Low-temperature, in situ tunable, uniaxial stress measurements in semiconductors using a piezoelectric actuator

Cited by 92 publications

References 12 publications

Two‐dimensional electrons occupying multiple valleys in AlAs

Two‐dimensional electrons occupying multiple valleys in AlAs

Valley Susceptibility of an Interacting Two-Dimensional Electron System

Spin–valley phase diagram of the two-dimensional metal–insulator transition

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