We investigate quantum Hall stripes under in-plane magnetic field $B_\parallel$ in a variable-density two-dimensional electron gas. At filling factor $ν= 9/2$, we observe one, two, and zero $B_\parallel$-induced reorientations at low, intermediate, and high densities, respectively. The appearance of these distinct regimes is due to a strong density dependence of the $B_\parallel$-induced orienting mechanism which triggers the second reorientation, rendering stripes \emph{parallel} to $B_\parallel$. In contrast, the mechanism which reorients stripes perpendicular to $B_\parallel$ showed no noticeable dependence on density. Measurements at $ν= 9/2$ and $11/2$ at the same, tilted magnetic field, allows us to rule out density dependence of the native symmetry-breaking field as a dominant factor. Our findings further suggest that screening might play an important role in determining stripe orientation, providing guidance in developing theories aimed at identifying and describing native and $B_\parallel$-induced symmetry-breaking fields.
A strong anisotropy in the longitudinal resistivity of a 2D electron system has been observed at half-filled high Landau levels. We report on detailed Hartree-Fock calculations of the unidirectional charge density wave (UCDW) orientation energy induced by a tilted magnetic field. We find that stripes can orient both parallel or perpendicular to the in-plane field depending on the sample parameters and field strength. The close agreement between complex experimental data on different sample geometries and our theoretical results strongly support the UCDW picture as the origin of the observed an…
The orientation of the tilted magnetic anisotropy has crucial importance in many spintronic devices. However, it is very challenging to determine it especially in very small structures produced by lithography. Here, we propose a new experimental method to directly and accurately measure both the polar and azimuthal angles of a tilted magnetic anisotropy. By using the proposed experimental method, we have successfully determined the out-of-plane and in-plane angles of the tilted magnetic anisotropy in a micro-structured multilayer thin film. The orientation of the tilted magnetic anisotropy in …
We study the effect of a tilted magnetic field on the orientation of Wigner crystals by taking account of the width of a quantum well in the $z$-direction. It is found that the cohesive energy of the electronic crystal is always lower for the $[110]$ direction parallel to the in-plane field. In a realistic sample, a domain structure forms in the electronic solid and each domain orients randomly when the magnetic field is normal to the quantum well. As the field is tilted an angle, the electronic crystal favors to align along a preferred direction which is determined by the in-plane magnetic fi…
Effect of periodic potential on the stripe phase realized in the higher Landau levels is investigated by the Hartree-Fock approximation. The period of the potential is chosen to be two to six times of the fundamental period of the stripe phase. It is found that the stripe aligns perpendicularly to the external potential in contrast to a naive expectation and hydrodynamic theory. Charge modulation towards the Wigner crystallization along the stripe is essential for the present unexpected new result.
We investigate the phonon mechanism for the orientational pinning of Wigner crystals and stripes in two-dimensional electron layers in GaAs matrices. We find the orientation of bilayer Wigner crystals on the (001), (111), (0-11) and (311) interfaces versus the interlayer distance and determine the regions of parameters, where polydomain structures can emerge. For the stripe states in electron layers situated close to the (001) surface we show that the interference between the piezoelectric and deformation potential interaction may be responsible for the preferable orientation of the stripes al…
A piezoelectric mechanism of orientation of stripes in two-dimensional quantum Hall systems in GaAs heterostructures is considered. The anisotropy of the elastic moduli and the boundary of the sample are taken into account. It is found that in the average the stripes line up with the [110] axis. In double layer systems the wave vector of the stripe structure rotates from the [110] to [100] axis if the period of density modulation becomes large than the interlayer distance. From the experimental point of view it means that in double layer systems anisotropic part of resistivity changes its sign…
The enchanting Dirac fermions in graphene stimulated us to seek for other two-dimensional (2D) Dirac materials, and boron monolayers may be a good candidate. So far, a number of monolayer boron sheets have been theoretically predicted, and three have been experimentally prepared. However, none of them possesses Dirac electrons. Herein, by means of density functional theory (DFT) computations, we identified a new boron monolayer, namely hr-sB, with two types of Dirac fermions coexisting in the sheet: one type is related to Dirac nodal lines traversing Brillouin zone (BZ) with velocities approac…
We consider stripe formation in quantum Hall systems at integer filling factors. We use Hartree-Fock calculations to obtain the phase diagram of bilayer quantum Hall systems at $ν=4n+1$ in a tilted magnetic field. We derive and analyze an effective low energy theory for the stripe phases which may be present in such systems. We discuss the possibility of stripe formation in wide well systems in a tilted magnetic field and suggest that the resistance anisotropy, observed recently by W. Pan et.al. [phys. Rev. B 64 (2001) 121305], may be due to the existence of a skyrmion stripe phase.
In ultra-clean 2D electron systems on (001) GaAs/AlGaAs upon filling high Landau levels, it was recently observed a new class of collective states, which can be related to the spontaneous formation of a charge density wave (``striped phase''). We address to the following unsolved problem: what is the reason for stripe pinning along the crystallographic direction [110]? It is shown that in a single heterojunction (001) III-V the effective mass of 2D electrons is anisotropic. This natural anisotropy is due to the reduced (C_{2v}) symmetry of the heterojunction and, even being weak (0.1 percent),…
Recently reported giant anisotropy in the longitudinal resistivity of a 2D electron system with valence Landau level index $N \ge 2$ has been interpreted as a signal of unidirectional charge density wave (UCDW) ground states. We report on detailed Hartree-Fock calculations of the UCDW orientation energy induced by a tilted magnetic field. We find that for current experimental samples stripes are oriented perpendicular to the in-plane field, consistent with experiment. For wider 2D electron systems we predict tilt-induced stripe states with variable anisotropy energy sign.
Our magnetotransport measurements of quantum Hall stripes in a high-quality GaAs quantum well in a slightly tilted magnetic field reveal that the orientation of stripes can be changed by temperature. Field-cooling and field-warming measurements, as well as observation of hysteresis at intermediate temperatures allow us to conclude that the observed temperature-induced reorientation of stripes is owing to the existence of two distinct minima in the symmetry-breaking potential. We also find that the native symmetry-breaking mechanism does not depend on temperature and that low-temperature magnet…
A transport study of two-dimensional (2D) holes confined to wide GaAs quantum wells provides a glimpse of a subtle competition between different many-body phases at Landau level filling $ν=3/2$ in tilted magnetic fields. At large tilt angles ($θ$), an anisotropic, stripe (or nematic) phase replaces the isotropic compressible Fermi sea at $ν=3/2$ if the quantum well has a symmetric charge distribution. When the charge distribution is made asymmetric, instead of the stripe phase, an even-denominator fractional quantum state appears at $ν=3/2$ in a range of large $θ$, and reverts back to a compre…
We study striped states in the quantum Hall system around half-filled high Landau levels and obtain the optimal orientation of the striped state in the presence of an external unidirectional periodic potential. It is shown that the optimal orientation is orthogonal to the external modulation in the Coulomb dominant regime (the orthogonal phase) and is parallel in the external modulation dominant regime (the parallel phase). The phase boundary of these two phases is determined numerically in the parameter space of the strength and wave number of the external modulation at the half-filled third …
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.
The effect of a unidirectional periodic potential on the orientation of the stripe state is studied for the two-dimensional electron system at half-filled high Landau levels. By considering a quantum well with two electric subbands, it is found that the stripe is parallel to the external potential for weak modulation and is orthogonal for strong modulation. In the intermediate range, the orientation of the stripe changes from orthogonal to parallel as the electron density is increased. This result explains the recent experiment performed by J. Zhu {\it et al} that the anisotropy axis at half-f…
We calculate current and density distributions in stripe (2D planar) junctions between normal and Majorana nanowires having a finite ($y$) transverse length. In presence of a magnetic field with vertical and in-plane components, the $y$-symmetry of the charge current distribution in the normal lead changes strongly across the Majorana phase transition: from center-symmetric if a Majorana mode is present to laterally-shifted (as expected by the Hall effect) if the field is tilted such as to destroy the Majorana mode due to the projection rule. We compare quasi-particle and charge distributions …
The physical properties of striped Hall state in the presence of an external unidirectional periodic potential is investigated. The study of searching the optimal orientation of the state is reported for the state at filling factor $ν=2+1/2$ and for the state at higher Landau levels at $l+1/2$ where $l=3,4,5,6,7,8$. It is predicted that two phases of the orientation, parallel phase and perpendicular phase, exist and a phase transition from one to another phase occurs.
In a 2D electron system in (001) GaAs/AlGaAs upon filling high Landau levels, it was recently observed a new class of collective states, which are recognized now to relate to the spontaneous formation of a charge density wave (``stripe phase''). Here we analyze one of the possible mechanisms of the stripe pinning along the crystallographic direction [110]--the native effective mass anisotropy of 2D electrons. It is shown that for a symmetric quantum well this anisotropy is a linear function of applied perpendicular-to-plane electric field. So, if it is the anisotropy that defines the direction…
We develop a Chern-Simons theory to describe a two-dimensional electron gas in intermediate magnetic fields. Within this approach, inhomogeneous states emerge in analogy to the intermediate state of a superconductor. At half filling of the highest Landau level we find unidirectional charge-density-wave (CDW) solutions. With a semiclassical calculation we give an intuitive explanation of the change of CDW orientation in the presence of an in-plane magnetic field. An anisotropy in the electron band mass is suggested as a possible source of the reproducible orientation of the CDW.
We report on quantum Hall stripes (QHSs) formed in higher Landau levels of GaAs/AlGaAs quantum wells with high carrier density ($n_e > 4 \times 10^{11}$ cm$^{-2}$) which is expected to favor QHS orientation along unconventional $\left < 1\bar{1}0 \right >$ crystal axis and along the in-plane magnetic field $B_{||}$. Surprisingly, we find that at $B_{||} = 0$ QHSs in our samples are aligned along $\left < 110 \right >$ direction and can be reoriented only perpendicular to $B_{||}$. These findings suggest that high density alone is not a decisive factor for either abnormal native QHS orientation…
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to …
We investigate the effect of the filling factor on transport anisotropies, known as stripes, in high Landau levels of a two-dimensional electron gas. We find that at certain in-plane magnetic fields, the stripes orientation is sensitive to the filling factor within a given Landau level. This sensitivity gives rise to the emergence of stripes away from half-filling while an orthogonally-oriented, native stripes reside at half-filling. This switching of the anisotropy axes within a single Landau level can be attributed to a strong dependence of the native symmetry breaking potential on the filli…
Measurements in clean two-dimensional electron systems confined to wide GaAs quantum wells in which two electric subbands are occupied reveal an unexpected rotation of the orientation of the stripe phase observed at a half-filled Landau level. Remarkably, the reorientation is sensitive to the spin of the half-filled Landau level and the symmetry of the charge distribution in the quantum well.
We study the anisotropic pinning-mode resonances in the rf conductivity spectra of the stripe phase of 2D electron systems (2DES) around Landau level filling 9/2, in the presence of an in-plane magnetic field, B_ip. The polarization along which the resonance is observed switches as B_ip is applied, consistent with the reorientation of the stripes. The resonance frequency, a measure of the pinning interaction between the 2DES and disorder, increases with B_ip. The magnitude of this increase indicates that disorder interaction is playing an important role in determining the stripe orientation.
The far-infrared absorption in two-dimensional electron layers subject to magnetic field of general orientation was studied theoretically. The Kubo formula was employed to derive diagonal components of the magneto-conductivity tensor of two-dimensional electron single-layers and double-layers. A parabolic quantum well was used to model single-layer systems. Bilayer systems were represented by a pair of tunnel-coupled, strictly two-dimensional quantum wells. Obtained results were compared to experimental data.
Néel walls in soft magnetic NiFe/NiFeGa hybrid stripe structures surrounded by a NiFe film are investigated by high resolution Lorentz transmission electron microscopic imaging. An anti-parallel orientation of magnetization in 1000 nm wide neighboring unirradiated-irradiated stripes is observed by forming high angle domain walls during magnetization reversal. Upon downscaling the stripe structure size from 1000 nm to 200 nm a transition from a discrete domain pattern to an effective magnetic medium is observed for external magnetic field reversal. This transition is associated with vanishing a…
Interacting two-dimensional electrons confined in a GaAs quantum well exhibit isotropic transport when the Fermi level resides in the first excited ($N=1$) Landau level. Adding an in-plane magnetic field ($B_{||}$) typically leads to an anisotropic, stripe-like (nematic) phase of electrons with the stripes oriented perpendicular to the $B_{||}$ direction. Our experimental data reveal how a periodic density modulation, induced by a surface strain grating from strips of negative electron-beam resist, competes against the $B_{||}$-induced orientational order of the stripe phase. Even a minute ($<…
We propose that thermal noise in local stripe orientation should be readily detectable via STM on systems in which local stripe orientations are strongly affected by quenched disorder. Stripes, a unidirectional, nanoscale modulation of electronic charge, are strongly affected by quenched disorder in two-dimensional and quasi-two-dimensional systems. While stripe orientations tend to lock to major lattice directions, dopant disorder locally breaks rotational symmetry. In a host crystal with otherwise $C_4$ rotational symmetry, stripe orientations in the presence of quenched disorder map to the …
By varying the orientation of the applied magnetic field with respect to the normal of a two-dimensional electron gas, the chemical potential and the specific heat reveal persistent spin splitting in all field ranges. The corresponding shape of the thermodynamic quantities distinguishes whether the Rashba spin-orbit interaction RSOI, the Zeeman term or both dominate the splitting. The interplay of the tilting of the magnetic field and RSOI resulted to an amplified splitting in weak fields. The effects of changing the RSOI strength and the Landau level broadening are also investigated.
The far-infrared absorption in two-dimensional electron layers subject to magnetic field of general orientation was studied theoretically. The Kubo formula is employed to derive diagonal components of the magneto-conductivity tensor of two-dimensional electron single-layers and double-layers. The parabolic quantum well is used to model a simple single-layer system. Both single-layer and double-layer systems can be realized in a pair of tunnel-coupled, strictly two-dimensional quantum wells. Obtained results are compared to experimental data.
The collective modes of stripes in double layer quantum Hall systems are computed using the time-dependent Hartree-Fock approximation. It is found that, when the system possesses spontaneous interlayer coherence, there are two gapless modes, one a phonon associated with broken translational invariance, the other a pseudospin-wave associated with a broken U(1) symmetry. For large layer separations the modes disperse weakly for wavevectors perpendicular to the stripe orientation, indicating the system becomes akin to an array of weakly coupled one-dimensional XY systems. At higher wavevectors th…
We present observations of an anisotropic resistance state at Landau level filling factor $ν=5/2$ in a two-dimensional hole system (2DHS), which occurs for certain values of hole density $p$ and average out-of-plane electric field $E_\perp$. The 2DHS is induced by electric field effect in an undoped GaAs/AlGaAs quantum well, where front and back gates allow independent tuning of $p$ and $E_\perp$, and hence the symmetry of the confining potential. For $p\approx2\times10^{11}$~cm$^{-2}$ and $E_\perp \approx -2 \times10^{5}$~V/m, the magnetoresistance along $\langle01\bar1\rangle$ greatly exceed…
Spontaneously formed equilibrium nanopatterns with long-range order are widely observed in a variety of systems, but their pronounced temperature dependence remains an impediment to maintain such patterns away from the temperature of formation. Here, we report on a highly ordered stress-induced stripe pattern in a two-component, Pd-O, adsorbate monolayer on W(110), produced at high temperature and identically preserved at lower temperatures. The pattern shows a tunable period (down to 16 nm) and orientation, as predicted by a continuum model theory along with the surface stress and its anisotr…
We report on the effect of in-plane magnetic field $B_\parallel$ on stripe phases in higher ($N=2,3$) Landau levels of a high-mobility 2D electron gas. In accord with previous studies, we find that a modest $B_\parallel$ applied parallel to the native stripes aligns them perpendicular to it. However, upon further increase of $B_\parallel$, stripes are reoriented back to their native direction. Remarkably, applying $B_\parallel$ perpendicular to the native stripes also aligns stripes parallel to it. Thus, regardless of the initial orientation of stripes with respect to $B_\parallel$, stripes ar…
We introduce a new class of isolated magnetic skyrmions emerging within tilted ferromagnetic phases of polar magnets with easy-plane anisotropy. The asymmetric magnetic structure of these skyrmions is associated with an intricate pattern of the energy density, which exhibits positive and negative asymptotics with respect to the surrounding state with a ferromagnetic moment tilted away from the polar axis. Correspondingly, the skyrmion-skyrmion interaction has an anisotropic character and can be either attractive or repulsive depending on the relative orientation of the skyrmion pair. We invest…
Highly oriented pyrolytic graphite (HOPG) is an important substrate in many technological applications and is routinely used as a standard in Scanning Tunnelling Microscopy (STM) calibration, which makes the accurate interpretation of the HOPG STM contrast of great fundamental and applicative importance. We demonstrate by STM simulations based on electronic structure obtained from first principles that the relative local orientation of the STM-tip apex with respect to the HOPG substrate has a considerable effect on the HOPG STM contrast. Importantly for experimental STM analysis of HOPG, the s…
The orientation of a chiral magnetic domain wall in a racetrack determines its dynamical properties. In equilibrium, magnetic domain walls are expected to be oriented perpendicular to the stripe axis. We demonstrate the appearance of a unidirectional domain wall tilt in out-of-plane magnetized stripes with biaxial anisotropy and Dzyaloshinskii--Moriya interaction (DMI). The tilt is a result of the interplay between the in-plane easy-axis anisotropy and DMI. We show that the additional anisotropy and DMI prefer different domain wall structure: anisotropy links the magnetization azimuthal angle …
We study the role of different orientations of an applied magnetic field as well as the interplay of structural asymmetries on the characteristics of eigenstates in a quantum ring system. We use a nearly analytical model description of the quantum ring, which allows for a thorough study of elliptical deformations and their influence on the spin content and Berry phase of different quantum states. The diamagnetic shift and Zeeman interaction compete with the Rashba spin-orbit interaction, induced by confinement asymmetries and external electric fields, to change spin textures of the different s…
The evolution of multivariant patterns in thin plates of magnetic shape memory materials with an applied magnetic field was studied theoretically. A geometrical domain-model is considered composed of straight stripe-like martensite variants with constant internal magnetization (high anisotropy limit) and magnetic domain wall orientation fixed by the twin boundaries. Through integral transforms of the demagnetization energy, the micromagnetic energy is cast into a form convenient for direct numerical evaluation and analytical calculations. The equilibrium geometrical parameters of multivariant …
The evolution of magnetic domain structure in epitaxial La$_{0.625}$Ca$_{0.375}$MnO$_3$ films on (001) NdGaO$_3$ is monitored as a function of temperature and magnetic field using Magnetic Force Microscopy. We see two distinct regions of magnetic orientational order; one in-plane displaying contrast-less image and the other tilted away from the film plane forming a distinct stripe pattern. A strong domain splitting is observed at the boundary of two regions, which is resilient to reorientation with temperature and magnetic field. We propose a model magnetic free energy functional to explain th…
Magnetotransport and magneto-optics experiments offer a very powerful probe for studying the physical properties of materials. Here, we investigate the second-order nonlinear magnetoconductivity of tilted type-I Weyl and multi-Weyl semimetal. In contrast to the presence of chiral anomaly in the linear response regime, we show that Weyl semimetal do not host chiral charge pumping in the nonlinear transport regime. We predict that an inversion symmetry broken and tilted Weyl semimetal can support finite longitudinal nonlinear magnetoconductivity, which is otherwise absent in untilted Weyl semime…
Different types of angular magnetoresistance oscillations in quasi-one-dimensional layered materials, such as organic conductors (TMTSF)2X, are explained in terms of Aharonov-Bohm interference in interlayer electron tunneling. A two-parameter pattern of oscillations for generic orientations of a magnetic field is visualized and compared with the experimental data. Connections with angular magnetoresistance oscillations in other layered materials are discussed.
The effects of the tilt of the crystallographic orientation with respect to an incident electron probe on high-angle annular dark field (HAADF) imaging in aberration-corrected scanning transmission electron microscopy (STEM) have been investigated with experiments and simulations. A small specimen tilt can lead to unequal deviations of different atom species in the HAADF image and result in further relative displacement between anions and cations. Simulated HAADF images also confirm that the crystal tilt causes an artifact in atom polarization as well. The effect is derived from the scattering…
We have observed in a low density two-dimensional hole system (2DHS) of extremely high quality (with hole density p=1.6x10^{10} cm^{-2} and mobility μ=0.8x10^6 cm^2/Vs) that, as the 2DHS is continuously tilted with respect to the direction of the magnetic field, the ν=1/3 fractional quantum Hall effect (FQHE) state is weakened and its magnetoresistivity rises from ~ 0.4 kohm/square in the normal orientation to ~ 180 kohm/square at tilt angle θ\~ 80 degrees. We attribute this phenomenon to the transition of the 2DHS from the FQHE liquid state to the pinned Wigner solid state, and argue that its…
In several strongly correlated electron systems, defects, charge and local lattice distortions are found to show complex inhomogeneous spatial distributions. There is growing evidence that such inhomogeneity plays a fundamental role in unique functionality of quantum complex materials. La1.72Sr0.28NiO4 is a prototypical strongly correlated material showing spin striped order associated with lattice and charge modulations. In this work we present the spatial distribution of the spin organization by applying micro X-ray diffraction to La1.72Sr0.28NiO4, mapping the spin-density-wave order below t…
At each of the boundaries of the two-dimensional (2D) rectangular conductor parallel to the electric current there arises a stripe with an electric field transverse to the current and a 100% electron spin polarization. The two stripes have opposite spin orientations and opposite directions of electric fields. The magnitudes of the fields, directly related to the spin current if the spin relaxation is negligible, are the same. The periphery stripes are separated by a center-stripe, in which the magnitude and direction of the electric field depend on the ratio of the skew scattering and side jum…
We study the magnetoplasmon collective mode excitations of integer quantum Hall systems in a parabolically confined quantum well nanostructure in the presence of a tilted magnetic field by using the time-dependent Hartree-Fock approximation. For even integer filling, we find that the dispersion of a spin density mode has a magneto-roton minimum at finite wavevectors, at a few times 10^6 cm^{-1} for parallel fields of order 1-10 Tesla, only in the direction perpendicular to the in-plane magnetic field, while the mode energy increases monotonously with wavevector parallel to the in-plane magneti…
We present numerical calculations of lamellar phases of block copolymers at patterned surfaces. We model symmetric di-block copolymer films forming lamellar phases and the effect of geometrical and chemical surface patterning on the alignment and orientation of lamellar phases. The calculations are done within self-consistent field theory (SCFT), where the semi-implicit relaxation scheme is used to solve the diffusion equation. Two specific set-ups, motivated by recent experiments, are investigated. In the first, the film is placed on top of a surface imprinted with long chemical stripes. The …
