Related papers: Wigner molecules in quantum dots
The interaction between electronic and nuclear spins in the presence of external magnetic fields can be described by a spin Hamiltonian, with parameters obtained from first principles, electronic structure calculations. We describe an…
We present the first microscopic demonstration of a disorder-pinned hole Wigner crystal (WC), providing a natural explanation for the reentrant integer quantum Hall effect observed near $\nu=2/3$, as well as its analogs in fractional Chern…
An improved prescription for choosing a transformed harmonic oscillator (THO) basis for use in configuration-space Hartree-Fock-Bogoliubov (HFB) calculations is presented. The new HFB+THO framework that follows accurately reproduces the…
The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to $\approx 10^8-10^9$~T are calculated in this study. A pseudospectral method is employed for the computational procedure. The…
Mean-field methods such as Hartree-Fock (HF) or Hartree-Fock-Bogoliubov (HFB) constitute the building blocks upon which more elaborate many-body theories are based on. The HF and HFB wavefunctions are built out of independent…
The few-body problem (with $N \leq 6$ fermionic charge carriers) in isolated moir\'{e} quantum dots (MQDs) in transition metal dichalcogenide (TMD) bilayer materials with integer fillings, $\nu \geq 2$, is investigated by employing…
We consider the Wigner equation corresponding to a nonlinear Schroedinger evolution of the Hartree type in the semiclassical limit $\hbar\to 0$. Under appropriate assumptions on the initial data and the interaction potential, we show that…
We studied a vertical ``quantum dot molecule'', where one of the dots is occupied with electrons and the other with holes. We find that different phases occur in the ground state, depending on the carrier density and the interdot distance.…
Motivated by recent developments on the fabrication and control of semiconductor-based quantum dot qubits, we theoretically study a finite system of tunnel-coupled quantum dots with the electrons interacting through the long-range Coulomb…
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of…
Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of…
We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2…
We use Density Functional Theory to study interacting spinless electrons on a one-dimensional quantum ring in the density range where the system undergoes Wigner crystallization. The Wigner transition leads to a drastic ``collective''…
We report on numerical studies into the interplay of disorder and electron-electron interactions within the integer quantum Hall regime, where the presence of a strong magnetic field and two-dimensional confinement of the electronic system…
We revisit the Hartree-Fock (HF) calculation for the uniform electron gas, or jellium model, whose predictions -- divergent derivative of the energy dispersion relation and vanishing density of states (DOS) at the Fermi level -- are in…
Coherent interconnects between gate-defined silicon quantum processing units are essential for scalable quantum computation and long-range entanglement. We argue that one-dimensional electron channels formed in the silicon quantum well of a…
Converged approximate density functional calculations usually do not bind anions, due to large self-interaction error. But Hartree-Fock calculations have no such prob- lem, producing negative HOMO energies. A recently proposed scheme for…
External non-uniform magnetic fields acting on molecules induce non-collinear spin-densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a…
Eugene Wigner predicted long ago that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice. A variety of two-dimensional systems have shown…
Closed form analytical expressions are obtained for the Wigner transform of the Bloch density matrix and for the Wigner phase space density of a two dimensional harmonically trapped charged quantum gas in a uniform magnetic field of…