Fractional Plateaus Research Articles

Quantized fractional Thouless pumping of solitons

In many contexts, interaction between particles gives rise to emergent phenomena. An example is the fractional quantum Hall effect, where the interaction between electrons leads to fractionally quantized Hall conductance. In photonic systems, the nonlinear response of an ambient medium mediates the interaction between photons, and, in the mean-field limit, these dynamics are described by the nonlinear Schrödinger (also called Gross–Pitaevskii) equation. It was recently shown that at weak nonlinearity, soliton motion in nonlinear Thouless pumps—a dimensionally reduced implementation of a Chern insulator—could be quantized to the Chern number, because solitons track the single-band Wannier function throughout the pumping cycle. Here using arrays of coupled optical waveguides, we show that a sufficiently strong nonlinearity fractionally quantizes the motion of solitons. Specifically, we find that the soliton follows maximally localized multi-band Wannier functions and therefore returns to itself only after multiple cycles of the Thouless pump—but displaced by an integer number of unit cells—leading to a rich fractional plateau structure describing soliton motion. Our results represent an example of emergent behaviour in topologically non-trivial systems in the presence of interactions. Interactions between photons arise due to the presence of optical nonlinearities. In topological Thouless pumps, a sufficiently strong nonlinearity leads to soliton transport with a fractionally quantized plateau structure—reminiscent of transport in the fractional quantum Hall effect.

Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising-Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids.

The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin- Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate.

Majorana ensembles with fractional entropy and conductance in nanoscopic systems

Quantum thermodynamics is a promising route to unambiguous detections of Majorana bound states. Being fundamentally different from quantum transport, this approach reveals unique Majorana thermodynamic behavior and deepens our insight into Majorana quantum transport itself. Here, we demonstrate that a nanoscopic system with topological superconductors produces a remarkable accumulation of Majorana thermodynamic states in wide ranges of Majorana tunneling phases by means of increasing its temperature $T$. Revealing this physical behavior is twofold beneficial. First, it significantly reduces the dependence of the entropy on the tunneling phases which become almost irrelevant in experiments. Second, the fractional Majorana entropy ${S}_{M}^{(2)}={k}_{B}ln({2}^{\frac{3}{2}})$ may be observed at high temperatures, substantially facilitating experiments. Analyzing quantum transport, we predict that when the temperature increases, the above thermodynamic behavior will induce an anomalous increase of the linear conductance from vanishing values up to the unitary fractional Majorana plateau ${G}_{M}={e}^{2}/2h$ extending to high temperatures.

Ground state and stability of the fractional plateau phase in metallic Shastry\u2013Sutherland system TmB4

We present a study of the ground state and stability of the fractional plateau phase (FPP) with M/Msat = 1/8 in the metallic Shastry–Sutherland system TmB4. Magnetization (M) measurements show that the FPP states are thermodynamically stable when the sample is cooled in constant magnetic field from the paramagnetic phase to the ordered one at 2 K. On the other hand, after zero-field cooling and subsequent magnetization these states appear to be of dynamic origin. In this case the FPP states are closely associated with the half plateau phase (HPP, M/Msat = ½), mediate the HPP to the low-field antiferromagnetic (AF) phase and depend on the thermodynamic history. Thus, in the same place of the phase diagram both, the stable and the metastable (dynamic) fractional plateau (FP) states, can be observed, depending on the way they are reached. In case of metastable FP states thermodynamic paths are identified that lead to very flat fractional plateaus in the FPP. Moreover, with a further decrease of magnetic field also the low-field AF phase becomes influenced and exhibits a plateau of the order of 1/1000 Msat.

Fractional Charge of Quarks and Fractal Properties of Hadrons

The origin of fractional charge of a quark is investigated considering the fractal structure of a hadron. Hadron is suggested to be a fractal object with fractal dimension 9/2. Describing quark as a quasiparticle in an analogy with quasi particle in Fractional Quantum Hall Effect, the filling factors are extracted which show large fractional plateau. It is suggested that quarks behave like quasi particles and the fractional charges of quarks can be attributed to the fractal behavior of a hadron.

Finite element algorithms for nonlocal minimal graphs

<abstract><p>We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems.</p></abstract>

Engineered spin-orbit interactions in LaAlO3/SrTiO3-based 1D serpentine electron waveguides.

The quest to understand, design, and synthesize new forms of quantum matter guides much of contemporary research in condensed matter physics. One-dimensional (1D) electronic systems form the basis for some of the most interesting and exotic phases of quantum matter. Here, we describe a family of quasi-1D nanostructures, based on LaAlO3/SrTiO3 electron waveguides, in which a sinusoidal transverse spatial modulation is imposed. These devices display unique dispersive features in the subband spectra, namely, a sizeable shift (∼7 T) in the spin-dependent subband minima, and fractional conductance plateaus. The first property can be understood as an engineered spin-orbit interaction associated with the periodic acceleration of electrons as they undulate through the nanowire (ballistically), while the second property signifies the presence of enhanced electron-electron scattering in this system. The ability to engineer these interactions in quantum wires contributes to the tool set of a 1D solid-state quantum simulation platform.

Degeneracy of the 1/8 Plateau and Antiferromagnetic Phases in the Shastry-Sutherland Magnet TmB_{4}.

The 1/8 fractional plateau phase (1/8 FPP) in Shastry-Sutherland lattice (SSL) spin systems has been viewed an exemplar of emergence on an Archimedean lattice. Here we explore this phase in the Ising magnet TmB_{4} using high-resolution specific heat (C) and magnetization (M) in the field-temperature plane. We show that the 1/8 FPP is smoothly connected to the antiferromagnetic phase on ramping the field from H=0. Thus, the 1/8 FPP is not a distinct thermodynamic ground state of TmB_{4}. The implication of these results for Heisenberg spins on the SSL is discussed.

Magnetization plateaus and supersolid phases in an extended Shastry–Sutherland model

New magnetization plateaus and supersolid phases are identified in an extended Shastry–Sutherland model – with additional longer range interactions and exchange anisotropy – over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Using a plaquette representation and exact mapping of ground state configurations in the Ising limit, supplemented by large scale quantum Monte Carlo simulations to include the effects of exchange interactions, we have identified several magnetization plateaus and associated spin supersolid phases. Our methods enable us to elucidate the underlying structure and mechanism of formation of the supersolid phases, thus gaining deeper understanding into their emergence from competing interactions. Additionally, in this regime we find evidence of a fractional plateau at 1∕9 saturation magnetization, which may hold the clue to understanding the fractional plateau in TmB4 that exhibits magnetic hysteresis.

Magnetisation process in the rare earth tetraborides, NdB4 and HoB4

A field-induced magnetisation process in the frustrated antiferromagnets is often much richer compared to the materials without competing interactions. The applied field tends to stabilise unusual spin configurations which frequently results in the appearance of magnetisation plateaux. Here we report a study into the field-induced magnetisation of the two frustrated rare earth tetraborides, HoB4 and NdB4. NdB4 shows a fractional magnetisation plateau occurring at M/Msat ≈ tfrac{{bf{1}}}{{bf{5}}} before saturating in a field of 33 kOe. On cooling down to 0.5 K the temperature dependent susceptibility of NdB4 shows an unconventional transition where the system returns to the zero field antiferromagnetic state from a higher-temperature ferrimagnetic state. We are able to reconstruct the magnetic phase diagram of NdB4 from the magnetisation, susceptibility and resistivity measurements for both H parallel c and H ⊥ c. For HoB4, the most interesting behaviour is found at the lowest temperature of 0.5 K, where the field dependent magnetisation demonstrates a new fractional tfrac{{bf{1}}}{{bf{2}}}-magnetisation plateau. Further insight into the relations between the exchange interactions and single ion effects is gained through high-field magnetisation measurements in both HoB4 and NdB4.

The fractional acoustoelectric current plateau induced by the energy-dependent tunnelling from dynamic quantum dots into an impurity dot

The fractional acoustoelectric (AE) current plateau in surface-acoustic-waves (SAW) single-electron transport devices is studied by measuring the current plateau as a function of the SAW power and gate bias as well as a function of perpendicular magnetic filed. Our investigation indicates that the fractional plateau is induced by the tunnelling effect from the dynamic quantum dots (QDs) into a static impurity dot. Rate equations are used to extract the tunnelling rates, which change a lot with the number of electrons in the dynamic QDs, the SAW power and gate bias. In addition, the current plateau evolves into a fractional structure, when a strong perpendicular magnetic field is applied to the system.

Fractional flux plateau in magnetization curve of multicomponent superconductor loop

Time-reversal symmetry (TRS) may be broken in superconductors with three or more condensates interacting repulsively, yielding two degenerate states specified by chirality of gap functions. We consider a loop of such superconductor with two halves occupied by the two states with opposite chiralities. Fractional flux plateaus are found in magnetization curve associated with free-energy minima, where the two domain walls between the two halves accommodate different inter-component phase kinks leading to finite winding numbers in a part of the whole condensates around the loop. Fractional flux plateaus form pairs with their heights related to the flux quantum {\Phi}0 = hc/2e. This phenomenon is a clear evidence of time-reversal symmetry broken (TRSB) superconductivity, which in a general point of view provides a novel chance to explore relative phase difference, phase kink and soliton in ubiquitous multi-component superconductivity such as that in iron pnicitides.

Origin of modulated phases and magnetic hysteresis inTmB4

We investigate the low temperature magnetic phases in TmB_4, a metallic quantum magnet on the geometrically frustrated Shastry-Sutherland lattice, using co-ordinated experimental and theoretical studies. Our results provide an explanation for the appearance of the intriguing fractional plateau in TmB_4 and accompanying magnetic hysteresis. Together with observation of the bump in the half-plateau, our results support the picture that the magnetization plateau structure in TmB_4 is strongly influenced by the zero-field modulated phases. We present a phenomenological model to explain the appearance of the modulated phases and a microscopic Hamiltonian that captures the complete magnetic behavior of TmB_4.

Metal–insulator transition in the quasi-one-dimensional transport of fractional quantum hall states

We investigate edge state transmission in quantum point contacts (QPCs) in the fractional quantum-Hall regime, finding behavior reminiscent of a metal–insulator transition. The transition is suggested by an unusual behavior of the differential conductance in the fractional-quantum-Hall regime, and by the presence of a fixed point and universal scaling in the temperature dependence of the linear conductance. Noting that the 0.7 feature evolves continuously into a last fractional plateau at high magnetic fields, we suggest that this still unresolved feature may itself be viewed as a manifestation of a local, microscopic, metal–insulator transition.

Nonequilibrated counterpropagating edge modes in the fractional quantum Hall regime.

It is well established that density reconstruction at the edge of a two-dimensional electron gas takes place for hole-conjugate states in the fractional quantum Hall effect (such as v=2/3, 3/5, etc.). Such reconstruction leads, after equilibration between counterpropagating edge channels, to a downstream chiral current edge mode accompanied by upstream chiral neutral modes (carrying energy without net charge). Short equilibration length prevented thus far observation of the counterpropagating current channels-the hallmark of density reconstruction. Here, we provide evidence for such nonequilibrated counterpropagating current channels, in short regions (l=4 μm and l=0.4 μm) of fractional filling v=2/3 and, unexpectedly, v=1/3, sandwiched between two regions of integer filling v=1. Rather than a two-terminal fractional conductance, the conductance exhibited a significant ascension towards unity quantum conductance (GQ=e(2)/h) at or near the fractional plateaus. We attribute this conductance rise to the presence of a nonequilibrated channel in the fractional short regions.

Excluded Volume Causes Integer and Fractional Plateaus in Colloidal Ratchet Currents

We study the collective transport of paramagnetic colloids driven above a magnetic bubble lattice by an external rotating magnetic field. We measure a direct ratchet current which rises in integer and fractional steps with the field amplitude. The stepwise increase is caused by excluded volume interactions between the particles, which form composite clusters above the bubbles with mobile and immobile occupation sites. Transient energy minima located at the interstitials between the bubbles cause the colloids to hop from one composite cluster to the next with synchronous and period doubled modes of transport. The colloidal current may be polarized to make selective use of type up or type down interstitials.

Diffusional Kurtosis Imaging of the Developing Brain

Diffusional kurtosis imaging is an extension of DTI but includes non-Gaussian diffusion effects, allowing more comprehensive characterization of microstructural changes during brain development. Our purpose was to use diffusional kurtosis imaging to measure age-related microstructural changes in both the WM and GM of the developing human brain. Diffusional kurtosis imaging was performed in 59 subjects ranging from birth to 4 years 7 months of age. Diffusion metrics, fractional anisotropy, and mean kurtosis were collected from VOIs within multiple WM and GM structures and subsequently analyzed with respect to age. Diffusional kurtosis tractography images at various stages of development were also generated. Fractional anisotropy and mean kurtosis both showed age-related increases in all WM regions, reflecting progression of diffusional anisotropy throughout development, predominantly in the first 2 years of life (eg, 70% and 157% increase in fractional anisotropy and mean kurtosis, respectively, from birth to 2 years for the splenium). However, mean kurtosis detected continued microstructural changes in WM past the fractional anisotropy plateau, accounting for more delayed isotropic changes (eg, 90% of maximum fractional anisotropy was reached at 5 months, whereas 90% of maximum mean kurtosis occurred at 18 months for the external capsule). Mean kurtosis may also provide greater characterization of GM maturation (eg, the putamen showed no change in fractional anisotropy but an 81% change in mean kurtosis from birth to 4 years 7 months). Mean kurtosis detects significant microstructural changes consistent with known patterns of brain maturation. In comparison with fractional anisotropy, mean kurtosis may offer a more comprehensive evaluation of age-related microstructural changes in both WM and GM and is potentially a valuable technique for studying brain development.

Ground states of an Ising model on an extended Shastry-Sutherland lattice and the1/2-magnetization plateau in some rare-earth-metal tetraborides

A complete solution of the ground-state problem for an Ising model on the Shastry-Sutherland lattice with an additional interaction along the diagonals of "empty" squares in an applied magnetic field is presented. A rigorous proof is given that this interaction gives rise to a plateau at one-half of the saturation magnetization. Such a fractional plateau has been observed in some rare-earth-metal tetraborides, in particular in strong Ising magnets ErB(4) (where it is the only one) and TmB(4) (where it is the broadest one), but its origin has remained unclear. Our study sheds new light on the solution of this problem.

Phase diagram of the two-component fractional quantum Hall effect.

We calculate the phase diagram of the two component fractional quantum Hall effect as a function of the spin or valley Zeeman energy and the filling factor, which reveals new phase transitions and phase boundaries spanning many fractional plateaus. This phase diagram is relevant to the fractional quantum Hall effect in graphene and in GaAs and AlAs quantum wells, when either the spin or valley degree of freedom is active.

Quantum Hall Effect inn−p−nandn-2D Topological Insulator-nJunctions

We have studied quantized transport in HgTe wells with inverted band structure corresponding to the two-dimensional topological insulator phase (2D TI) with locally controlled density allowing n-p-n and n-2D TI-n junctions. The resistance reveals the fractional plateau 2h/e(2) in the n-p-n regime in the presence of the strong perpendicular magnetic field. We found that in the n-2D TI-n regime the plateaux in resistance in not universal and results from the edge state equilibration at the interface between chiral and helical edge modes. We provided the simple model describing the resistance quantization in n-2D TI-n regime.