arXiv subjects

K. Vakili

Publications and source records attributed to K. Vakili.

17 recordsLinked to original sources

arXiv2015

Robust PCA with FastHCS

Principal component analysis (PCA) is widely used to analyze high-dimensional data, but it is very sensitive to outliers. Robust PCA methods seek fits that are unaffected by the outliers and can therefore be trusted to reveal them. FastHCS (High-dimensional Congruent Subsets) is a robust PCA algorithm suitable for high-dimensional applications, including cases where the number of variables exceeds the number of observations. After detailing the FastHCS algorithm, we carry out an extensive simulation study and three real data applications, the results of which show that FastHCS is systematically more robust to outliers than state-of-the-art methods.

stat.ME↗

arXiv2009

Effective mass suppression upon complete spin-polarization in an isotropic two-dimensional electron system

We measure the effective mass (m*) of interacting two-dimensional electrons confined to a 4.5 nm-wide AlAs quantum well. The electrons in this well occupy a single out-of-plane conduction band valley with an isotropic in-plane Fermi contour. When the electrons are partially spin polarized, m* is larger than its band value and increases as the density is reduced. However, as the system is driven to full spin-polarization via the application of a strong parallel magnetic field, m* is suppressed down to values near or even below the band mass. Our results are consistent with the previously reported measurements on wide AlAs quantum wells where the electrons occupy an in-plane valley with an anisotropic Fermi contour and effective mass, and suggest that the effective mass suppression upon complete spin polarization is a genuine property of interacting two-dimensional electrons.

cond-mat.mes-hall↗

arXiv2008

Parallel Magnetic Field Tuning of Valley Splitting in AlAs Two-Dimensional Electrons

We demonstrate that, in a quasi-two-dimensional electron system confined to an AlAs quantum well and occupying two conduction-band minima (valleys), a parallel magnetic field can couple to the electrons' orbital motion and tune the energies of the two valleys by different amounts. The measured density imbalance between the two valleys, which is a measure of the valley susceptibility with respect to parallel magnetic field, is enhanced compared to the predictions of non-interacting calculations, reflecting the role of electron-electron interaction.

cond-mat.mes-hall↗

arXiv2007

Valley polarization and susceptibility of composite fermions around nu=3/2

We report magnetotransport measurements of fractional quantum Hall states in an AlAs quantum well around Landau level filling factor nu = 3/2, demonstrating that the quasiparticles are composite Fermions (CFs) with a valley degree of freedom. By monitoring the valley level crossings for these states as a function of applied symmetry-breaking strain, we determine the CF valley susceptibility and polarization. The data can be explained well by a simple Landau level fan diagram for CFs, and are in nearly quantitative agreement with the results reported for CF spin polarization.

cond-mat.mes-hall↗

arXiv2006

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

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.

cond-mat.str-el↗

arXiv2006

Two-dimensional electrons occupying multiple valleys in AlAs

Two-dimensional electrons in AlAs quantum wells occupy multiple conduction-band minima at the X- points of the Brillouin zone. These valleys have large effective mass and g-factor compared to the stan-dard 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.

cond-mat.mes-hall↗

arXiv2006

Zeeman splitting of interacting two-dimensional electrons with two effective masses

We have realized an AlAs two-dimensional electron system in which electrons occupy conduction-band valleys with different Fermi contours and effective masses. In the quantum Hall regime, we observe both resistivity spikes and persistent gaps at crossings between the Landau levels originating from these two valleys. From the positions of the spikes in tilted magnetic field and measurements of the energy gaps away from the crossings, we find that, after occupation of the minority valley, the spin susceptibility drops rapidly, and the electrons possess a {\it single} interaction-enhanced g-factor, despite the dissimilarity of the two occupied valleys.

cond-mat.mes-hall↗

arXiv2006

High-mobility AlAs quantum wells with out-of-plane valley occupation

Employing state-of-the-art molecular beam epitaxy techniques to grow thin, modulation-doped AlAs quantum wells, we have achieved a low temperature mobility of 5.5 m$^2$/Vs with out-of-plane occupation, an order of magnitude improvement over previous studies. However, due to the narrow well width, mobilities are still limited by scattering due to interface roughness disorder. We demonstrate the successful implementation of a novel technique utilizing thermally-induced, biaxial, tensile strain that forces electrons to occupy the out-of-plane valley in thicker quantum wells, reducing interface roughness scattering and allowing us to achieve mobilities as high as 8.8 m$^2$/Vs.

cond-mat.mes-hall↗

arXiv2006

Dependence of persistent gaps at Landau level crossings on relative spin

We report measurements of the quantum Hall state energy gap at avoided crossings between Landau levels originating from different conduction band valleys in AlAs quantum wells. These gaps exhibit an approximately linear dependence on magnetic field over a wide range of fields and filling factors. More remarkably, we observe an unexpected dependence of the gap size on the relative spin orientation of the crossing levels, with parallel-spin crossings exhibiting larger gaps than antiparallel-spin crossings.

cond-mat.mes-hall↗

arXiv2006

Valley susceptibility of an interacting two-dimensional electron system

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.

cond-mat.mes-hall↗

arXiv2005

Spin-dependent resistivity at transitions between integer quantum Hall states

The longitudinal resistivity at transitions between integer quantum Hall states in two-dimensional electrons confined to AlAs quantum wells is found to depend on the spin orientation of the partially-filled Landau level in which the Fermi energy resides. The resistivity can be enhanced by an order of magnitude as the spin orientation of this energy level is aligned with the majority spin. We discuss possible causes and suggest a new explanation for spike-like features observed at the edges of quantum Hall minima near Landau level crossings.

cond-mat.mes-hall↗

arXiv2004

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

We demonstrate the use of a piezoelectric actuator to apply, at low temperatures, uniaxial stress in the plane of a two-dimensional electron system confined to a modulation-doped AlAs quantum well. Via the application of stress, which can be tuned in situ and continuously, we control the energies and occupations of the conduction-band minima and the electronic properties of the electron system. We also report measurements of the longitudinal and transverse strain versus bias for the actuator at 300, 77, and 4.2 K. A pronounced hysteresis is observed at 300 and 77 K, while at 4.2 K, strain is nearly linear and shows very little hysteresis with the applied bias.

cond-mat.mes-hall↗

arXiv2004

Giant low-temperature piezoresistance effect in AlAs two-dimensional electrons

We present piezoresistance measurements in modulation doped AlAs quantum wells where the two-dimensional electron system occupies two conduction band valleys with elliptical Fermi contours. Our data demonstrate that, at low temperatures, the strain gauge factor (the fractional change in resistance divided by the sample's fractional length change) in this system exceeds 10,000. Moreover, in the presence of a moderate magnetic field perpendicular to the plane of the two-dimensional system, gauge factors up to 56,000 can be achieved. The piezoresistance data can be explained qualitatively by a simple model that takes into account intervalley charge transfer.

cond-mat.mes-hall↗

arXiv2004

Spin susceptibility of two-dimensional electrons in narrow AlAs quantum wells

We report measurements of the spin susceptibility in dilute two-dimensional electrons confined to a 45$Å$ wide AlAs quantum well. The electrons in this well occupy an out-of-plane conduction-band valley, rendering a system similar to two-dimensional electrons in Si-MOSFETs but with only one valley occupied. We observe an enhancement of the spin susceptibility over the band value that increases as the density is decreased, following closely the prediction of quantum Monte Carlo calculations and continuing at finite values through the metal-insulator transition.

cond-mat.mes-hall↗

arXiv2004

Dependence of spin susceptibility of a two-dimensional electron system on the valley degree of freedom

We report measurements of the spin susceptibility, $χ\propto g_v g^*m^*$, in an AlAs two-dimensional electron system where, via the application of in-plane stress, we transfer electrons from one conduction-band valley to another ($g_v$ is the valley degeneracy, and $m^*$ and $g^*$ are the electron effective mass and g-factor). At a given density, when the two valleys are equally populated ($g_v=2$), the measured $g^*m^*$ is smaller than when only one valley is occupied ($g_v=1$). This observation counters the common assumption that a two-valley two-dimensional system is effectively more dilute than a single-valley system because of its smaller Fermi energy.

cond-mat.str-el↗

arXiv2003

Realization of an Interacting Two-Valley AlAs Bilayer System

By using different widths for two AlAs quantum wells comprising a bilayer system, we force the X-point conduction-band electrons in the two layers to occupy valleys with different Fermi contours, electron effective masses, and g-factors. Since the occupied valleys are at different X-points of the Brillouin zone, the interlayer tunneling is negligibly small despite the close electron layer spacing. We demonstrate the realization of this system via magneto-transport measurements and the observation of a phase-coherent, bilayer $ν$=1 quantum Hall state flanked by a reentrant insulating phase.

cond-mat.mes-hall↗

arXiv2002

Magnetic Field Induced Spin Polarization of AlAs Two-dimensional Electrons

Two-dimensional (2D) electrons in an in-plane magnetic field become fully spin polarized above a field B_P, which we can determine from the in-plane magnetoresistance. We perform such measurements in modulation-doped AlAs electron systems, and find that the field B_P increases approximately linearly with 2D electron density. These results imply that the product |g*|m*, where g* is the effective g-factor and m* the effective mass, is a constant essentially independent of density. While the deduced |g*|m* is enhanced relative to its band value by a factor of ~ 4, we see no indication of its divergence as 2D density approaches zero. These observations are at odds with results obtained in Si-MOSFETs, but qualitatively confirm spin polarization studies of 2D GaAs carriers.

cond-mat.mes-hall↗