Hartree-Fock Theory of Hole Stripe States

We report on Hartree-Fock theory results for stripe states of two-dimensional hole systems in quantum wells grown on GaAs (311)A substrates. We find that the stripe orientation energy has a rich dependence on hole density, and on in-plane field magnitude and orientation. Unlike the electron case, the orientation energy is non-zero for zero in-plane field, and the ground state orientation can be either parallel or perpendicular to a finite in-plane field. We predict an orientation reversal transition in in-plane fields applied along the $\lbrack\bar{2}33\rbrack$ direction.Comment: 5 pages including 4 figure

Perturbation theories for the S=1/2 spin ladder with four-spin ring exchange

The isotropic S=1/2 antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicinity of the known exact transition point is obtained. The critical exponent for the gap is found to be $\eta\simeq1$, in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase emerging for high values of the ring exchange is argued to be gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.Comment: 8 pages, 4 figures, some minor changes in text and reference

An Investigation of Orientational Symmetry-Breaking Mechanisms in High Landau Levels

The principal axes of the recently discovered anisotropic phases of 2D electron systems at high Landau level occupancy are consistently oriented relative to the crystal axes of the host semiconductor. The nature of the native rotational symmetry breaking field responsible for this preferential orientation remains unknown. Here we report on experiments designed to investigate the origin and magnitude of this symmetry breaking field. Our results suggest that neither micron-scale surface roughness features nor the precise symmetry of the quantum well potential confining the 2D system are important factors. By combining tilted field transport measurements with detailed self-consistent calculations we estimate that the native anisotropy energy, whatever its origin, is typically ~ 1 mK per electron.Comment: Reference added, minor notational changes; final published versio

Magnetoroton instabilities and static susceptibilities in higher Landau levels

We present analytical results concerning the magneto-roton instability in higher Landau levels evaluated in the single mode approximation. The roton gap appears at a finite wave vector, which is approximately independent of the LL index n, in agreement with numerical calculations in the composite-fermion picture. However, a large maximum in the static susceptibility indicates a charge density modulation with wave vectors $q_0(n)\sim 1/\sqrt{2n+1}$, as expected from Hartree-Fock predictions. We thus obtain a unified description of the leading charge instabilities in all LLs.Comment: 4 pages, 5 figure

Role of disorder in half-filled high Landau levels

We study the effects of disorder on the quantum Hall stripe phases in half-filled high Landau levels using exact numerical diagonalization. We show that, in the presence of weak disorder, a compressible, striped charge density wave, becomes the true ground state. The projected electron density profile resembles that of a smectic liquid. With increasing disorder strength W, we find that there exists a critical value, W_c \sim 0.12 e^2/\epsilon l, where a transition/crossover to an isotropic phase with strong local electron density fluctuations takes place. The many-body density of states are qualitatively distinguishable in these two phases and help elucidate the nature of the transition.Comment: 4 pages, 4 figure

Anisotropic transport in unidirectional lateral superlattice around half-filling of the second Landau level

We have observed marked transport anisotropy in short period (a=92 nm) unidirectional lateral superlattices around filling factors nu=5/2 and 7/2: magnetoresistance shows a sharp peak for current along the modulation grating while a dip appears for current across the grating. By altering the ratio a/l (with l=sqrt{hbar/eB_perp} the magnetic length) via changing the electron density n_e, it is shown that the nu=5/2 anisotropic features appear in the range 6.6 alt a/l alt 7.2 varying their intensities, becoming most conspicuous at a/l simeq 6.7. The peak/dip broadens with temperature roughly preserving its height/depth up to 250 mK. Tilt experiments reveal that the structures are slightly enhanced by an in-plane magnetic field B_| perpendicular to the grating but are almost completely destroyed by B_| parallel to the grating. The observations suggest the stabilization of a unidirectional charge-density-wave or stripe phase by weak external periodic modulation at the second Landau level.Comment: REVTeX, 5 pages, 3 figures, Some minor revisions, Added notes and reference

Mean-field Phase Diagram of Two-Dimensional Electrons with Disorder in a Weak Magnetic Field

We study two-dimensional interacting electrons in a weak perpendicular magnetic field with the filling factor $\nu \gg 1$ and in the presence of a quenched disorder. In the framework of the Hartree-Fock approximation, we obtain the mean-field phase diagram for the partially filled highest Landau level. We find that the CDW state can exist if the Landau level broadening $1/2\tau$ does not exceed the critical value $1/2\tau_{c}=0.038\omega_{H}$. Our analysis of weak crystallization corrections to the mean-field results shows that these corrections are of the order of $(1/\nu)^{2/3}\ll 1$ and therefore can be neglected

Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston

Using a multidimensional cut-off technique, we obtain expressions for the cut-off dependent part of the vacuum energy for parallelepiped geometries in any spatial dimension d. The cut-off part yields nonrenormalizable hypersurface divergences and we show explicitly that they cancel in the Casimir piston scenario in all dimensions. We obtain two different expressions for the d-dimensional Casimir force on the piston where one expression is more convenient to use when the plate separation a is large and the other when a is small (a useful $a \to 1/a$ duality). The Casimir force on the piston is found to be attractive (negative) for any dimension d. We apply the d-dimensional formulas (both expressions) to the two and three-dimensional Casimir piston with Neumann boundary conditions. The 3D Neumann results are in numerical agreement with those recently derived in arXiv:0705.0139 using an optical path technique providing an independent confirmation of our multidimensional approach. We limit our study to massless scalar fields.Comment: 29 pages; 3 figures; references added; to appear in JHE

Theory of the Quantum Hall Smectic Phase II: Microscopic Theory

We present a microscopic derivation of the hydrodynamic theory of the Quantum Hall smectic or stripe phase of a two-dimensional electron gas in a large magnetic field. The effective action of the low energy is derived here from a microscopic picture by integrating out high energy excitations with a scale of the order the cyclotron energy.The remaining low-energy theory can be expressed in terms of two canonically conjugate sets of degrees of freedom: the displacement field, that describes the fluctuations of the shapes of the stripes, and the local charge fluctuations on each stripe.Comment: 20 pages, RevTex, 3 figures, second part of cond-mat/0105448 New and improved Introduction. Final version as it will appear in Physical Review

Stripes in Quantum Hall Double Layer Systems

We present results of a study of double layer quantum Hall systems in which each layer has a high-index Landau level that is half-filled. Hartree-Fock calculations indicate that, above a critical layer separation, the system becomes unstable to the formation of a unidirectional coherent charge density wave (UCCDW), which is related to stripe states in single layer systems. The UCCDW state supports a quantized Hall effect when there is tunneling between layers, and is {\it always} stable against formation of an isotropic Wigner crystal for Landau indices $N \ge 1$. The state does become unstable to the formation of modulations within the stripes at large enough layer separation. The UCCDW state supports low-energy modes associated with interlayer coherence. The coherence allows the formation of charged soliton excitations, which become gapless in the limit of vanishing tunneling. We argue that this may result in a novel {\it ``critical Hall state''}, characterized by a power law $I-V$ in tunneling experiments.Comment: 10 pages, 8 figures include