155 research outputs found
Monte Carlo study of Bose Laughlin wave function for filling factors 1/2, 1/4 and 1/6
Strongly correlated two-dimensional electronic systems subject to a
perpendicular magnetic field at lowest Landau level (LLL) filling factors: 1/2,
1/4 and 1/6 are believed to be composite fermion (CF) Fermi liquid phases. Even
though a Bose Laughlin wave function cannot describe these filling factors we
investigate whether such a wave function provides a lower energy bound to the
true CF Fermi liquid energies. By using Monte Carlo simulations in disk
geometry we compute the Bose Laughlin energies and compare them to
corresponding results for the spin-polarized LLL CF Fermi liquid state and
avalable data from literature.We find the unexpected result that, for filling
factors 1/4 and 1/6, the Bose Laughlin ground state energy is practically
identical to the true CF liquid energy while this is not the case at 1/2 where
the Bose Laughlin ground state energy is sizeably lower than the energy of the
CF Fermi liquid state.Comment: 7 pages, 2 figures, 2 table
Liquid crystalline states for two-dimensional electrons in strong magnetic fields
Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of
two-dimensional melting and the analogy between Laughlin states and the
two-dimensional one-component plasma (2DOCP), we investigate the possibility of
liquid crystalline states in a single Landau level (LL). We introduce many-body
trial wavefunctions that are translationally invariant but posess 2-fold (i.e.
{\em nematic}), 4-fold ({\em tetratic}) or 6-fold ({\em hexatic}) broken
rotational symmetry at respective filling factors , 1/5 and 1/7 of
the valence LL. We find that the above liquid crystalline states exhibit a soft
charge density wave (CDW) which underlies the translationally invariant state
but which is destroyed by quantum fluctuations. By means of Monte Carlo (MC)
simulations, we determine that, for a considerable variety of interaction
potentials, the anisotropic states are energetically unfavorable for the lowest
and first excited LL's (with index ), whereas the nematic is
favorable at the second excited LL ().Comment: 7 figures, submitted to PRB, high-quality figures available upon
reques
Fermi hypernetted-chain study of half-filled Landau levels with broken rotational symmetry
DOI: 10.1103/PhysRevB.65.205307
http://link.aps.org/doi/10.1103/PhysRevB.65.205307We investigate broken rotational symmetry (BRS) states at half-filling of the valence Landau level (LL). We generalize Rezayi and Read's (RR) trial wave function, a special case of Jain's composite fermion (CF) wave functions, to include anisotropic coupling of the flux quanta to electrons, thus generating a nematic order in the underlying CF liquid. Using the Fermi hypernetted-chain method, which readily gives results in the thermodynamic limit, we determine the properties of these states in detail. By using the anisotropic pair distribution and static structure functions we determine the correlation energy and find that, as expected, RR's state is stable in the lowest LL, whereas BRS states may occur at half- filling of higher LL's, with a possible connection to the recently discovered quantum Hall liquid crystals
Asymptotic Pomeranchuk instability of Fermi liquids in half-filled Landau levels
We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form ν = 2 n + 1/2). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the n → ∞ limit
Monte Carlo simulation method for Laughlin-like states in a disk geometry
We discuss an alternative accurate Monte Carlo method to calculate the
ground-state energy and related quantities for Laughlin states of the
fractional quantum Hall effect in a disk geometry. This alternative approach
allows us to obtain accurate bulk regime (thermodynamic limit) values for
various quantities from Monte Carlo simulations with a small number of
particles (much smaller than that needed with standard Monte Carlo approaches).Comment: 13 pages, 6 figures, 2 table
Shape-Dependent Energy of an Elliptical Jellium Background
The jellium model is commonly used in condensed matter physics to study the properties of a two-dimensional electron gas system. Within this approximation, one assumes that electrons move in the presence of a neutralizing background consisting of uniformly spread positive charge. When properties of bulk systems (of infinite size) are studied, shape of the jellium domain is irrelevant. However, the same cannot be said when one is dealing with finite systems of electrons confined in a finite two-dimensional region of space. In such a case, geometry and shape of the jellium background play a role on the overall properties of the system. In this work, we assume that the region where the electrons are confined is represented by a jellium background charge with an elliptical shape. It is shown that, in this case, the Coulomb self-energy of the elliptically shaped region can be exactly calculated in closed analytical form by using suitable mathematical transformations. The results obtained reveal the external influence of geometry/shape on the properties of two-dimensional systems of few electrons confined to a small finite region of space
Shape-Dependent Energy of an Elliptical Jellium Background
The jellium model is commonly used in condensed matter physics to study the properties of a two-dimensional electron gas system. Within this approximation, one assumes that electrons move in the presence of a neutralizing background consisting of uniformly spread positive charge. When properties of bulk systems (of infinite size) are studied, shape of the jellium domain is irrelevant. However, the same cannot be said when one is dealing with finite systems of electrons confined in a finite two-dimensional region of space. In such a case, geometry and shape of the jellium background play a role on the overall properties of the system. In this work, we assume that the region where the electrons are confined is represented by a jellium background charge with an elliptical shape. It is shown that, in this case, the Coulomb self-energy of the elliptically shaped region can be exactly calculated in closed analytical form by using suitable mathematical transformations. The results obtained reveal the external influence of geometry/shape on the properties of two-dimensional systems of few electrons confined to a small finite region of space. The two-dimensional electron gas (2DEG) model has received a great deal of attention in condensed matter physics due to the richness and complexity of the emerging phenomena associated with it. The variety of possible scenarios makes this model fascinating from a theoretical and experimental point of view. In particular, a 2DEG in a strong perpendicular magnetic field has come to the forefront of current research as a result of the discovery of the integer quantum Hall effect (IQHE) However, there have been recent developments in the field of nanotechnology that make possible the fabrication of finite systems of few electrons confined in a finite 2D domai
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