Quantum Monte Carlo calculation of the Fermi-liquid parameters in the two-dimensional electron gas

Spin independence of the strongly enhanced effective mass in ultra-clean SiGe/Si/SiGe two-dimensional electron system

The effective mass at the Fermi level is measured in the strongly interacting two-dimensional (2D) electron system in ultra-clean SiGe/Si/SiGe quantum wells in the low-temperature limit in tilted magnetic fields. At low electron densities, the effective mass is found to be strongly enhanced and independent of the degree of spin polarization, which indicates that the mass enhancement is not related to the electrons' spins. The observed effect turns out to be universal for silicon-based 2D electron systems, regardless of random potential, and cannot be explained by existing theories.

Observing separate spin and charge Fermi seas in a strongly correlated one-dimensional conductor

An electron is usually considered to have only one form of kinetic energy, but could it have more, for its spin and charge, by exciting other electrons? In one dimension (1D), the physics of interacting electrons is captured well at low energies by the Tomonaga-Luttinger model, yet little has been observed experimentally beyond this linear regime. Here, we report on measurements of many-body modes in 1D gated wires using tunneling spectroscopy. We observe two parabolic dispersions, indicative of separate Fermi seas at high energies, associated with spin and charge excitations, together with the emergence of two additional 1D "replica" modes that strengthen with decreasing wire length. The interaction strength is varied by changing the amount of 1D intersubband screening by more than 45%. Our findings not only demonstrate the existence of spin-charge separation in the whole energy band outside the low-energy limit of the Tomonaga-Luttinger model but also set a constraint on the validity of the newer nonlinear Tomonaga-Luttinger theory.

Quasiparticle Effective Mass of the Three-Dimensional Fermi Liquid by Quantum Monte Carlo

According to Landau's Fermi liquid theory, the main properties of the quasiparticle excitations of an electron gas are embodied in the effective mass m^{*}, which determines the energy of a single quasiparticle, and the Landau interaction function, which indicates how the energy of a quasiparticle is modified by the presence of other quasiparticles. This simple paradigm underlies most of our current understanding of the physical and chemical behavior of metallic systems. The quasiparticle effective mass of the three-dimensional homogeneous electron gas has been the subject of theoretical controversy, and there is a lack of experimental data. In this Letter, we deploy diffusion Monte Carlo (DMC) methods to calculate m^{*} as a function of density for paramagnetic and ferromagnetic three-dimensional homogeneous electron gases. The DMC results indicate that m^{*} decreases when the density is reduced, especially in the ferromagnetic case. The DMC quasiparticle energy bands exclude the possibility of a reduction in the occupied bandwidth relative to that of the free-electron model at density parameter r_{s}=4, which corresponds to Na metal.

Pomeranchuk Instability of Composite Fermi Liquids

Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter F_{ℓ}≤-1 in the angular momentum ℓ=2 channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational Monte Carlo technique, Fermi liquid parameters F_{ℓ} of the composite fermion Fermi liquid with a finite layer width. We consider F_{ℓ} in different Landau levels n=0, 1, 2 as a function of layer width parameter η. We find that unlike the lowest Landau level, which shows no sign of Pomeranchuk instability, higher Landau levels show nematic instability below critical values of η. Furthermore, the critical value η_{c} is higher for the n=2 Landau level, which is consistent with observation of nematic order in ambient conditions only in the n=2 Landau levels. The picture emerging from our work is that approaching the true 2D limit brings half-filled higher Landau-level systems to the brink of nematic Pomeranchuk instability.

Nonlinear spectra of spinons and holons in short GaAs quantum wires

One-dimensional electronic fluids are peculiar conducting systems, where the fundamental role of interactions leads to exotic, emergent phenomena, such as spin-charge (spinon-holon) separation. The distinct low-energy properties of these 1D metals are successfully described within the theory of linear Luttinger liquids, but the challenging task of describing their high-energy nonlinear properties has long remained elusive. Recently, novel theoretical approaches accounting for nonlinearity have been developed, yet the rich phenomenology that they predict remains barely explored experimentally. Here, we probe the nonlinear spectral characteristics of short GaAs quantum wires by tunnelling spectroscopy, using an advanced device consisting of 6000 wires. We find evidence for the existence of an inverted (spinon) shadow band in the main region of the particle sector, one of the central predictions of the new nonlinear theories. A (holon) band with reduced effective mass is clearly visible in the particle sector at high energies.

Recently, theories have emerged that describe the nonlinear high-energy excitations of one-dimensional electronic fluids. Here, the authors report experimental evidence of their existence and behaviour in tunnelling spectra of short GaAs quantum wires.

Dependence of effective mass on spin and valley degrees of freedom

We measure the effective mass (m) of interacting two-dimensional electrons confined to an AlAs quantum well while we change the conduction-band valley occupation and the spin polarization via the application of strain and magnetic field, respectively. Compared to its band value, m is enhanced unless the electrons are fully valley- and spin-polarized. Incidentally, in the fully spin- and valley-polarized regime, the electron system exhibits an insulating behavior.

Effective mass suppression in dilute, spin-polarized two-dimensional electron systems

We report effective mass (m*) measurements, via analyzing the temperature dependence of the Shubnikov-de Haas oscillations, for dilute, interacting, two-dimensional electron systems (2DESs) occupying a single conduction-band valley in AlAs quantum wells. When the 2DES is partially spin-polarized, m* is larger than its band value, consistent with previous results on various 2DESs. However, as we fully spin-polarize the 2DES by subjecting it to strong parallel magnetic fields, m* is unexpectedly suppressed and falls even below the band mass.

Observation of spin Coulomb drag in a two-dimensional electron gas

An electron propagating through a solid carries spin angular momentum in addition to its mass and charge. Of late there has been considerable interest in developing electronic devices based on the transport of spin that offer potential advantages in dissipation, size and speed over charge-based devices. However, these advantages bring with them additional complexity. Because each electron carries a single, fixed value (- e) of charge, the electrical current carried by a gas of electrons is simply proportional to its total momentum. A fundamental consequence is that the charge current is not affected by interactions that conserve total momentum, notably collisions among the electrons themselves. In contrast, the electron's spin along a given spatial direction can take on two values, +/- [planck]/2 (conventionally upward arrow, downward arrow), so that the spin current and momentum need not be proportional. Although the transport of spin polarization is not protected by momentum conservation, it has been widely assumed that, like the charge current, spin current is unaffected by electron-electron (e-e) interactions. Here we demonstrate experimentally not only that this assumption is invalid, but also that over a broad range of temperature and electron density, the flow of spin polarization in a two-dimensional gas of electrons is controlled by the rate of e-e collisions.

Computational Methods in Coupled Electron-Ion Monte Carlo Simulations

In the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer approximation: the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT-based ab initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.

Measurements of the density-dependent many-body electron mass in two dimensional GaAs/AlGaAs heterostructures

We determine the density-dependent electron mass m(*) in two-dimensional electron systems of GaAs/AlGaAs heterostructures by performing detailed low-temperature Shubnikov-de Haas measurements. Using very high-quality transistors with tunable electron densities we measure m(*) in single, high mobility specimens over a wide range of r(s) (6 to 0.8). Toward low densities we observe a rapid increase of m(*) by as much as 40%. For 2>r(s)>0.8 the mass values fall approximately 10% below the band mass of GaAs. Numerical calculations are in qualitative agreement with our data but differ considerably in detail.

Spin mass of an electron liquid

We show that in order to calculate correctly the spin current carried by a quasiparticle in an electron liquid one must use an effective "spin mass" m(s) that is larger than both the band mass m(b), which determines the charge current, and the quasiparticle effective mass m(*), which determines the heat capacity. We present two independent estimates of the spin mass enhancement, m(s)/m(b), in two- and three-dimensional electron liquids, based on (i) previously calculated values of the Landau parameters and (ii) a recent theory of the dynamical local field factor in the spin channel. Both methods yield a significant spin mass enhancement, which is larger in two dimensions than in three.

Backflow correlations for the electron gas and metallic hydrogen

We justify and evaluate backflow three-body wave functions for a two-component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use and the analytical form of the backflow function from different points of view. The resulting wave functions are used in variational and diffusion Monte Carlo calculations of the electron gas and of solid and liquid metallic hydrogen. For the electron gas, the purely analytic backflow and three-body form gives lower energies than those of previous calculations. For bcc hydrogen, analytical and optimized backflow-three-body wave functions lead to energies nearly as low as those from using local density approximation orbitals in the trial wave function. However, compared to wave functions constructed from density functional solutions, backflow wave functions have the advantage of only few parameters to estimate, the ability to include easily and accurately electron-electron correlations, and that they can be directly generalized from the crystal to a disordered liquid of protons.

Spin-independent origin of the strongly enhanced effective mass in a dilute 2D electron system

We accurately measure the effective mass in a dilute two-dimensional electron system in silicon by analyzing the temperature dependence of the Shubnikov-de Haas oscillations in the low-temperature limit. A sharp increase of the effective mass with decreasing electron density is observed. We find that the enhanced effective mass is independent of the degree of spin polarization, which points to a spin-independent origin of the mass enhancement and is in contradiction with existing theories.

Low-density spin susceptibility and effective mass of mobile electrons in Si inversion layers

We studied the Shubnikov-de Haas (SdH) oscillations in high-mobility Si-MOS samples over a wide range of carrier densities n approximately (1-50)x10(11) cm(-2), which includes the vicinity of the apparent metal-insulator transition in two dimensions (2D MIT). Using a novel technique of measuring the SdH oscillations in superimposed and independently controlled parallel and perpendicular magnetic fields, we determined the spin susceptibility chi(*), the effective mass m(*), and the g(*) factor for mobile electrons. These quantities increase gradually with decreasing density; near the 2D MIT, we observed enhancement of chi(*) by a factor of approximately 4.7.

Spin polarization and g factor of a dilute GaAs two-dimensional electron system

The effective g factor (g(*)) of a dilute interacting two-dimensional electron system is expected to increase with respect to its bare value as the density is lowered, and to eventually diverge as the system makes a transition to a ferromagnetic state. We report here measurements of g(*) in dilute (density 0.8 to 6.5x10(10) cm(-2)), high-mobility GaAs two-dimensional electrons from their spin polarization in a parallel magnetic field. The data reveal a surprising trend. While g(*) is indeed significantly enhanced with respect to the band g factor of GaAs, the enhancement factor decreases from about 6 to 3 as the density is reduced.

Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms

We develop and test Quantum Monte Carlo algorithms that use a"twist" or a phase in the wave function for fermions in periodic boundary conditions. For metallic systems, averaging over the twist results in faster convergence to the thermodynamic limit than periodic boundary conditions for properties involving the kinetic energy and has the same computational complexity. We determine exponents for the rate of convergence to the thermodynamic limit for the components of the energy of coulomb systems. We show results with twist averaged variational Monte Carlo on free particles, the Stoner model and the electron gas using Hartree-Fock, Slater-Jastrow, and three-body and backflow wave function. We also discuss the use of twist averaging in the grand canonical ensemble, and numerical methods to accomplish the twist averaging.

Highly anisotropic g-factor of two-dimensional hole systems

Coupling the spin degree of freedom to the anisotropic orbital motion of two-dimensional (2D) hole systems gives rise to a highly anisotropic Zeeman splitting with respect to different orientations of an in-plane magnetic field B relative to the crystal axes. This mechanism has no analog in the bulk band structure. We obtain good, qualitative agreement between theory and experimental data, taken in GaAs 2D hole systems grown on (113) substrates, showing the anisotropic depopulation of the upper spin subband as a function of in-plane B.