Fractional Plateaus Research Articles

Ground States of the Ising Model on the Shastry-Sutherland Lattice and the Origin of the Fractional Magnetization Plateaus in Rare-Earth-Metal Tetraborides

A complete and exact solution of the ground-state problem for the Ising model on the Shastry-Sutherland lattice in an applied magnetic field is found. The magnetization plateau at one third of the saturation value is shown to be the only possible fractional plateau in this model. However, stripe magnetic structures with 1/2 and 1/n (n>3) magnetization, observed in the rare-earth-metal tetraborides RB(4), occur at the boundaries of the three-dimensional regions of the ground-state phase diagram. These structures give rise to new magnetization plateaus if interactions of longer range are taken into account. For instance, an additional third-neighbor interaction is shown to produce a 1/2 plateau. The results obtained significantly refine the understanding of the magnetization process in RB(4) compounds, especially in TmB(4) and ErB(4), which are strong Ising magnets.

Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

The ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed into the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg–Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the ‘classical’ Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal–transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of a two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin–spin correlations.

Quantum Spin State and Magnetization Plateaus in anS=1KagoméHeisenberg Antiferromagnet

The organic Heisenberg antiferromagnet m -MPYNN·BF 4 has a two-dimensional Kagomé lattice of S = 1 dimers with a small trigonal distortion. This antiferromagnet indicates a nonmagnetic ground state with a gap of 0.2 K in zero field. To investigate the ground state of this quantum magnet, we measured the AC susceptibility and the magnetization as a function of the magnetic field. Magnetization plateaus in applied fields were sensitively observed from steep decrements in the AC susceptibility at low temperatures. They indicate characteristic behaviors to be expanded at finite temperatures. The magnetization curve indicates that the fractional plateaus are at 1/2 and 3/4 of the saturation magnetization. The observed plateaus are not commensurate with the unit cell of the Kagomé lattice, suggesting a contribution of long-distance interactions.

Dynamic Nuclear Polarization in the Fractional Quantum Hall Regime

We investigate dynamic nuclear polarization in quantum point contacts (QPCs) in the integer and fractional quantum Hall regimes. Following the application of a dc bias, fractional plateaus in the QPC shift symmetrically about half filling of the lowest Landau level, ν=1/2, suggesting an interpretation in terms of composite fermions. Polarizing and detecting at different filling factors indicates that Zeeman energy is reduced by the induced nuclear polarization. Mapping effects from integer to fractional regimes extends the composite fermion picture to include hyperfine coupling.

Two-electron correlations and the acoustoelectric current through a quantum dot

We examine the two-electron correlations in a surface acoustic wave (SAW)-induced quantum dot moving in a pinched-off channel. For a small SAW amplitude and a narrow channel, singlet and triplet states are quasidegenerate and both contribute to the second plateau of the quantized acoustoelectric current. If SAW dots containing two electrons are driven through a small static dot whose confining potential is tuned by a gate pulse, then due to the Pauli principle, the current displays a fractional plateau.

Magnetic properties of magnetoactive spin clusters

A simple model is proposed for describing magnetic properties of magnetoactive nanoclusters, which permits exact analytic solution. Exact expressions are obtained for thermodynamic characteristics of the model, which hold in the entire range of temperatures, magnetic fields, and interaction parameters. It is found that in the case of easy-axis anisotropy, the field dependence of magnetization of a nanocluster consisting of N particles with a spin of 1/2 has [N/2] fractional plateaus ([…] is the integer part) corresponding to polarized phases with ruptures singlet pairs. A nonmonotonic behavior observed for the magnetic susceptibility of an easy-plane cluster is typical of gap magnets. The spin gap between the ground state and excited states is proportional to the anisotropy parameter.

Electronic Transport and Quantum Hall Effect in Bipolar Graphenep−n−pJunctions

We have developed a device fabrication process to pattern graphene into nanostructures of arbitrary shape and control their electronic properties using local electrostatic gates. Electronic transport measurements have been used to characterize locally gated bipolar graphene p-n-p junctions. We observe a series of fractional quantum Hall conductance plateaus at high magnetic fields as the local charge density is varied in the p and n regions. These fractional plateaus, originating from chiral edge states equilibration at the p-n interfaces, exhibit sensitivity to interedge backscattering which is found to be strong for some of the plateaus and much weaker for other plateaus. We use this effect to explore the role of backscattering and estimate disorder strength in our graphene devices.

Length Dependence of the Fractional Conductance Anomaly in Constricted Conducting Channels

In addition to the integer conductance quantization in units of G0 (=2e 2 /h), a quantum point contact (QPC) often reveals a fractional conductance plateau, especially at 0.7G0, which is called the 0.7 anomaly. The one-dimensionality of the constriction (or QPC) has been debated as to whether or not it is a key element in the appearance of the anomaly. In this study, we specifically focused on the length dependence of the conductance anomaly in QPC’s for a nominally identical width of nano-constrictions. The anomaly was shown to be more likely caused by the Kondo eect in a carrier-confining region formed inside a short QPC with its length comparable to its width while spontaneous spin polarization along with the opening of a spin gap better explains the anomalous conductance behavior in a longer QPC.

Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

(abbreviated) This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of real compounds. The ground state properties of the integrable two-leg spin-1/2 and the mixed spin-(1/2,1) ladder models at zero temperature are analyzed by means of the Thermodynamic Bethe Ansatz. Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are investigated in terms of the recently introduced High Temperature Expansion method, which is discussed in detail. It is shown that in the strong coupling limit the integrable spin-1/2 ladder model exhibits three quantum phases: (i) a gapped phase in the regime $H<H_{c1}$, (ii) a fully polarised phase for $H>H_{c2}$, and (iii) a Luttinger liquid magnetic phase in the regime $H_{c1}<H<H_{c2}$. The critical behaviour in the vicinity of the critical points is of the Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for a range of strong coupling ladder compounds. Similar analysis of the mixed spin-(1/2,1) ladder model reveals a rich phase diagram, with a 1/3 and a full saturation magnetisation plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetisation plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetisation curve obtained from the exact result derived from the HTE. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also investigated.

Anomalous Magnetization of Two-Dimensional S = 1/2 Frustrated Square-Lattice Antiferromagnet (CuCl)LaNb2O7

High-field magnetization measurements have been performed up to 56 T for a two-dimensional S = 1/2 frustrated square-lattice antiferromagnet (CuCl)LaNb 2 O 7 , a recently discovered spin gap system (Δ/ k B = 26.7 K). It is found that the spin gap closes at a surprisingly low field H c1 = 10.3 T compared with that expected from the zero-field spin gap (Δ/ g µ B = 18.4 T). For H > H c1 , the magnetization exhibits a linear increase without any trace of anomalies such as fractional plateaus until it saturates at H c2 = 30.1 T. This means that the gapless phase, where the field-induced magnetic ordering is expected to occur at low temperatures, is stable over a wide field region. These results suggest strong correlations of triplet excitations in the layer and the proximity of the spin-liquid phase to the magnetically ordered phase.

Magnetization Plateaux in Random FrustratedS=1/2 Heisenberg Chains

The $S=1/2$ frustrated Heisenberg chains with bond alternation is known to exhibit a magnetization plateau at half of the saturation magnetization $\Ms$ accompanied by the spontanuous translational symmetry breakdown. The effect of randomness on the magnetization process of this model is investigated. First we consider the mixture of the two kinds of chains both of which possess the $\Ms/2$-plateau in the common interval of the magnetization field. The plateau at $\Ms/2$ is found to vanish immediately if the randomness is switched on in agreement with Totsuka's prediction. The small plateau also appears near the saturation field due to the localization of inverted spins around the minority bond. On the other hand, if the stronger bond is replaced by the ferromagnetic bonds randomly, the randomness induced fractional plateau appears as in the nonfrustrated case. The plateau at $\Ms/2$ does not simply vanish but shifts and splits into two smaller plateaux. The magnetization on this plateau varies nonlinearly with $1-p$. The physical origin of this behavior is explained based on the strong coupling picture.

Fractional plateaus in the Coulomb blockade of coupled quantum dots

Ground-state properties of a double-large-dot sample connected to a reservoir via a single-mode point contact are investigated. When the interdot transmission is perfect and the dots controlled by the same dimensionless gate voltage, we find that for any finite backscattering from the barrier between the lead and the left dot, the average dot charge exhibits a Coulomb-staircase behavior with steps of size e/2 and the capacitance peak period is halved. The interdot electrostatic coupling here is weak. For strong tunneling between the left dot and the lead, we report a conspicuous intermediate phase in which the fractional plateaus get substantially altered by an increasing slope.

Fractional Magnetization Plateau in the Alternating Spin Heisenberg Chain

We study the S =1/2 and S =1 alternating spin Heisenberg chain with the next-nearest neighbor (NNN) interaction J 2 between neighboring S =1/2 spins, by using the numerical diagonalization method of a finite size system. It is found that a fractional plateau appears at magnetization m =1/2 in the magnetization curve for J 2 > J 2 c =0.106±0.001. The phase transition at J 2 c is characterized by the exponent σ=1, which controls the critical behavior of the spin gap Δ as Δ∼ exp(- a /( J 2 - J 2 c ) 1+σ ). For J 2 < J 2 c , the model at m =1/2 is described by the conformal field theory with central charge c =1 and exponent η for the spin correlation function of the transverse component to a magnetic field is calculated.

Activated conductivity in the quantum Hall effect

Activated dissipative conductivity σ xx = σ* xxexp(−Δ/ T) and the activated deviation of the Hall conductivity from the precise quantization δσ xy = σ xy − ie 2/ h= σ* xy exp(−Δ/ T) are studied in a plateau range of the quantum Hall effect. The prefactors σ* xx and σ* xy are calculated for the case of a long-range random potential in the framework of a classical theory. There is a range of temperatures T 1 ≪ T ≪ T 2 where σ* xy = e 2/ h. In this range σ* xy ≈ ( e 2/ h)( T/ T 2) 80/21 ≪ σ* xx. At large T ≫ T 2, on the other hand, σ* xy = e 2/ h and σ* xx = ( e 2h)( T 2 T) 10/13 ≪ σ* xy . Similar results are valid for a fractional plateau near the filling factor p/q if charge e is replaced by e/ q.

Quantum percolation and plateau transitions in the quantum Hall effect.

We introduce a simple model of quantum percolation and analyze it numerically using transfer matrix methods. A central point of this paper is that 3 both integer and fractional plateau transitions in the quantum Hall effect are due to quantum percolation. Within this model, we obtained the localization length exponent \ensuremath{\nu}=2.4\ifmmode\pm\else\textpm\fi{}0.2, the dynamical exponent z=1, and the scaling functions for the conductivity tensor for both the integer and the fractional transitions. We show that our results agree extremely well with the experimental results for the integer plateau transition obtained by McEuen et al.

Frequency-dependent magnetoconductance quantisation in 2D systems-a disorder effect

Strong frequency dependence is shown in the quantised magnetoconductance in high-mobility silicon MOSFETs, with the loss of integer quantised plateaux and enhancement of fractional quantisation. Fractional plateaux observed are quantised to within 5%, which is within experimental accuracy. The frequency at which the onset of these phenomena is observed is shown to be dependent upon sample length and Landau level filling factor. The results are similar to those previously obtained using low-mobility GaAs heterostructures, though in the highest mobility cases no effect is seen up to 50 MHz. The roles of sample length and disorder are discussed.