arXiv subjects

E. Rasanen

Publications and source records attributed to E. Rasanen.

At least 19 recordsLinked to original sources

arXiv2021

Airy gas model: From three to reduced dimensions

By using the propagator of linear potential as a main tool, we extend the Airy gas model, originally developed for the three-dimensional ($d=3$) edge electron gas, to systems in reduced dimensions ($d=2,1$). First, we derive explicit expressions for the edge particle density and the corresponding kinetic energy density (KED) of the Airy gas model in all dimensions. The densities are shown to obey the local virial theorem. We obtain a functional relationship between the positive KED and the particle density and its gradients and analyze the results inside the bulk as a limit of the local-density approximation. We show that in this limit the KED functional reduces to that of the Thomas-Fermi model in $d$ dimensions.

cond-mat.stat-mech↗

arXiv2016

On the validity of power functionals for the homogeneous electron gas in reduced.density-matrix-functional theory

Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced density-matrix functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form $f(n,n')=(n n')^α$ for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power $α$ to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition $n({\mathbf k})<1$ for all wave vectors ${\mathbf k}$. The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for $α$ that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at $α\gtrsim 0.6$ and at $r_s\gtrsim 10$ for the density parameter, corresponding to relatively low densities.

cond-mat.str-el↗

arXiv2014

Construction of the B88 exchange-energy functional in two dimensions

We construct a generalized-gradient approximation for the exchange-energy density of finite two-dimensional systems. Guided by non-empirical principles, we include the proper small-gradient limit and the proper tail for the exchange-hole potential. The observed performance is superior to that of the two-dimensional local-density approximation, which underlines the usefulness of the approach in practical applications.

cond-mat.str-el↗

arXiv2013

Self-consistent energy approximation for orbital-free density-functional theory

Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation and yields the total energy and density as a function of the external potential, the number of electrons, and the chemical potential determined upon normalization. Our tests for Hooke's atoms, jellium, and model atoms up to $\sim 1000$ electrons show that reasonable total energies can be obtained with almost a negligible computational cost. The results are also consistent in the important large-$N$ limit.

physics.chem-ph↗

arXiv2013

Optimal control of strong-field ionization with time-dependent density-functional theory

We show that quantum optimal control theory (OCT) and time-dependent density-functional theory (TDDFT) can be combined to provide realistic femtosecond laser pulses for an enhanced ionization yield in many-electron systems. Using the H$_2$-molecule as a test case, the optimized laser pulse from the numerically exact scheme is compared to pulses obtained from OCT+TDDFT within the TD exact-exchange (TDEXX) and the TD local-density approximation (TDLDA). We find that the TDDFT-pulses produces an ionization yield of up to 50% when applied to the exact system. In comparison, pulses with a single frequency but the same fluence typically reach to yields around 5-15%, unless the frequency is carefully tuned into a Fano-type resonance that leads to $\sim 30%$ yield. On the other hand, optimization within the exact system alone leads to yields higher than 80%, demonstrating that correlation effects beyond the TDEXX and TDLDA can give rise to even more efficient ionization mechanisms.

physics.atom-ph↗

arXiv2013

Stability of spin droplets in realistic quantum Hall devices

We study the formation and characteristics of "spin droplets",i.e., compact spin-polarized configurations in the highest occupied Landau level, in an etched quantum Hall device at filling factors $2\leqν\leq3$. The confining potential for electrons is obtained with self-consistent electrostatic calculations on a GaAs/AlGaAs heterostructure with experimental system parameters. Real-space spin-density-functional calculations for electrons confined in the obtained potential show the appearance of stable spin droplets at $ν\sim 5/2$. The qualitative features of the spin droplet are similar to those in idealized (parabolic) quantum-dot systems. The universal stability of the state against geometric deformations underline the applicability of spin droplets in, e.g., spin-transport through quantum point contacts.

cond-mat.mes-hall↗

arXiv2013

Many-electron transport in Aharonov-Bohm interferometers: Time-dependent density-functional study

We apply time-dependent density-functional theory to study many-electron transport in Aharonov-Bohm interferometers in a non-equilibrium situation. The conductance properties in the system are complex and depend on the enclosed magnetic flux in the interferometer, the number of interacting particles, and the mutual distance of the transport channels at the points of encounter. Generally, the electron-electron interactions do not suppress the visibility of Aharonov-Bohm oscillations if the interchannel distance -- determined by the positioning of the incompressible strips through the external magnetic field -- is optimized. However, the interactions also impose an interesting Aharonov-Bohm phase shift with channel distances below or above the optimal one. This effect is combined with suppressed oscillation amplitudes. We analyze these effects within different approximations for the exchange-correlation potential in time-dependent density-functional theory.

cond-mat.str-el↗

arXiv2013

Chaotic properties of Coulomb-interacting circular billiards

We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more quantitative view on the dynamics as the interaction strength is varied, we compute and analyze the escape rates of the system. Apart from very weak or strong interactions, the escape rates show consistently exponential behavior, thus suggesting strongly chaotic dynamics and a phase space without significant sticky regions within the considered time scales.

nlin.CD↗

arXiv2013

Large two-dimensional electronic systems: Self-consistent energies and densities at low cost

We derive a self-consistent local variant of the Thomas-Fermi approximation for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The scheme results in an explicit orbital-free representation of the electron density and energy in terms of the external potential, the number of electrons, and the chemical potential determined upon normalization. We test the method over a variety 2D nanostructures by comparing to the Kohn-Sham 2D-LDA calculations up to 600 electrons. Accurate results are obtained in view of the negligible computational cost. We also assess a local upper bound for the Hartree energy.

cond-mat.str-el↗

arXiv2012

Optimal control of quantum revival

Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.

quant-ph↗

arXiv2012

Optical Control of Entangled States in Quantum Wells

We present theory and calculations for coherent high-fidelity quantum control of many-particle states in semiconductor quantum wells. We show that coupling a two-electron double quantum dot to a terahertz optical source enables targeted excitations that are one to two orders of magnitude faster and significantly more accurate than those obtained with electric gates. The optical fields subject to physical constraints are obtained through quantum optimal control theory that we apply in conjunction with the numerically exact solution of the time-dependent Schrodinger equation. Our ability to coherently control arbitrary two-electron states, and to maximize the entanglement, opens up further perspectives in solid-state quantum information.

cond-mat.mes-hall↗

arXiv2012

On the violation of a local form of the Lieb-Oxford bound

In the framework of density-functional theory, several popular density functionals for exchange and correlation have been constructed to satisfy a local form of the Lieb-Oxford bound. In its original global expression, the bound represents a rigorous lower limit for the indirect Coulomb interaction energy. Here we employ exact-exchange calculations for the G2 test set to show that the local form of the bound is violated in an extensive range of both the dimensionless gradient and the average electron density. Hence, the results demonstrate the severity in the usage of the local form of the bound in functional development. On the other hand, our results suggest alternative ways to construct accurate density functionals for the exchange energy.

cond-mat.other↗

arXiv2012

Time-dependent transport in Aharonov-Bohm interferometers

A numerical approach is employed to explain transport characteristics in realistic, quantum Hall based Aharonov-Bohm interferometers. First, the spatial distribution of incompressible strips, and thus the current channels, are obtained applying a self-consistent Thomas-Fermi method to a realistic heterostructure under quantized Hall conditions. Second, the time-dependent Schrödinger equation is solved for electrons injected in the current channels. Distinctive Aharonov-Bohm oscillations are found as a function of the magnetic flux. The oscillation amplitude strongly depends on the mutual distance between the transport channels and on their width. At an optimal distance the amplitude and thus the interchannel transport is maximized, which determines the maximum visibility condition. On the other hand, the transport is fully suppressed at magnetic fields corresponding to half-integer flux quanta. The results confirm the applicability of realistic Aharonov-Bohm interferometers as controllable current switches.

cond-mat.mes-hall↗

arXiv2012

Electron-Electron Interactions in Artificial Graphene

Recent advances in the creation and modulation of graphene-like systems are introducing a science of "designer Dirac materials". In its original definition, artificial graphene is a man-made nanostructure that consists of identical potential wells (quantum dots) arranged in a adjustable honeycomb lattice in the two-dimensional electron gas. As our ability to control the quality of artificial graphene samples improves, so grows the need for an accurate theory of its electronic properties, including the effects of electron-electron interactions. Here we determine those effects on the band structure and on the emergence of Dirac points.

cond-mat.str-el↗

arXiv2011

Quantitative modeling of spin relaxation in quantum dots

We use numerically exact diagonalization to calculate the spin-orbit and phonon-induced triplet-singlet relaxation rate in a two-electron quantum dot exposed to a tilted magnetic field. Our scheme includes a three-dimensional description of the quantum dot, the Rashba and the linear and cubic Dresselhaus spin-orbit coupling, the ellipticity of the quantum dot, and the full angular description of the magnetic field. We are able to find reasonable agreement with the experimental results of Meunier et al. [Phys. Rev. Lett. 98, 126601 (2007)] in terms of the singlet-triplet energy splitting and the spin relaxation rate, respectively. We analyze in detail the effects of the spin-orbit factors, magnetic-field angles, and the dimensionality, and discuss the origins of the remaining deviations from the experimental data.

cond-mat.str-el↗

arXiv2011

On the Kirzhnits gradient expansion in two dimensions

We derive the semiclassical Kirzhnits expansion of the D-dimensional one-particle density matrix up to the second order in $\hbar$. We focus on the two-dimensional (2D) case and show that all the gradient corrections both to the 2D one-particle density and to the kinetic energy density vanish. However, the 2D Kirzhnits expansion satisfies the consistency criterion of Gross and Proetto [J. Chem. Theory Comput. 5, 844 (2009)] for the functional derivatives of the density and the noninteracting kinetic energy with respect to the Kohn-Sham potential. Finally we show that the gradient correction to the exchange energy diverges in agreement with the previous linear-response study.

cond-mat.str-el↗

arXiv2011

Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas

Reduced density-matrix functional theory (RDMFT) has become an appealing alternative to density-functional theory to describe electronic properties of highly-correlated systems. Here we derive exact conditions for the suitability of RDMFT to describe the two-dimensional homogeneous electron gas, which is the base system for, e.g., semiconductor quantum dots and quantum Hall devices. Following the method of Cioslowski and Pernal [J. Chem. Phys. {\bf 111}, 3396 (1999)] we focus on the properties of power functionals of the form $f(n,n')=(n n')^α$ for the scaling function in the exchange-correlation energy. We show that in order to have stable and analytic solutions, and for $f$ to satisfy the homogeneous scaling constraint, the power is restricted to $1/4 \leq α\leq 3/4$. Applying a reasonable ansatz for the momentum distribution and the lower bound for the exchange-correlation energy tightens the physical regime further to $0.64 \lesssim α\leq 0.75$.

cond-mat.str-el↗

arXiv2011

Strictly correlated uniform electron droplets

We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching the tighter forms of the Lieb-Oxford bound recently proposed by Rasanen et al. [Phys. Rev. Lett. 102, 206406 (2009)]. The bound is satisfied in three-, two-, and one-dimensional droplets, and in the latter case it is reached exactly - regardless of the type of interaction considered. Our results provide useful reference data for delocalized strongly correlated systems, and they can be used in the development and testing of exchange-correlation density functionals in the framework of density-functional theory.

cond-mat.str-el↗