Probing spin physics in the quantum Hall regime by heat capacity and magnetotransport measurements

We review recent heat capacity and magnetotransport experiments on GaAs/AlGaAs heterostructures containing multilayer two-dimensional electron systems (2DESs) in the quantum Hall regime. Emphasis in this article is on the study of the heat capacity near Landau level filling factor ν=1. We also present a detailed survey of the development of the quantum Hall effect in tilted-magnetic fields for ν≲2. Among the novel phenomena we address is the strong coupling between the nuclear spins and the electrons associated with the spin phase transitions of the 2DES at ν=4/3 and near ν=1. To cite this article: S. Melinte et al., C. R. Physique 3 (2002) 667–676.     

Universal explicit expression for quantum Hall conductance at any temperatures and chemical potentials

This paper generalises the theorem already obtained [Solid State Commun. 127 (2003) 505] for the high mobility, dissipationless, integer quantum Hall systems at T=0 K to the T>0 K situations. The results obtained are again suitable at both microscopic and macroscopic scales. In comparison [Solid State Commun. 127 (2003) 505], this generalised form gives a universal explicit expression for the Hall conductance σ_xy(μ,T) between any two points selected in such a system as a function of chemical potential and temperature. Further, thermal deviation Δσ_xy(μ,T) from the exact quantised values of σ_xy(μ,T) and the minimum slopes of Hall plateaux in the T>0 cases, observed already in experiments, are also derived in theory. Similar to those in the T=0 K case [Solid State Commun. 127 (2003) 505], the overall quantum Hall behaviour of the system can again be obtained from this theory by simply selecting two points on the two Hall contacts.     

Temperature dependence of effective mobility edge and inelastic scattering time in silicon MOS inversion layers in strong magnetic fields

Temperature (T) dependence on Hall conductivity (σ_xy) in Si MOS inversion layers measured in 15 T at T=1.4?10 K is investigated by comparing dσ_xy/dN_s, N_s electron concentration, to the calculation based on an effective mobility edge (E_c) model. Temperature dependence of inelastic scattering time is discussed in connection to the T-dependence of E_c.     

Role of electron spin in integer quantum hall photoluminescence

We investigate numerically the photoluminescence (PL) spectrum in the integer quantum Hall regime and find that the electron spins play important roles. The spectra for the left circularly polarized light show peak splittings when the Fermi levels lies in the excited Landau level, which is caused by the inter Landau level scattering between electrons with anti-parallel spins. At around ν_e∼1 the PL energy is strongly affected by the interplay between the screening and multiple spin flipping (skyrmion) effects.     

Nonstationary phenomena in Si MOSFETs in the quantum hall effects regime

We report the observation of nonstationary hysteresis phenomena in charging of Si MOSFET at a quantizing magnetic field. In these experiments (Pudalovet al 1984; Pudalov and Semenchinsky 1985) the charging currentJ _g of the capacitance gate-2D-layer was measured while sweeping of the magnetic fieldH or a gate voltageV _g at a constant rate. The numerical integration of the measured valuesJ _g with respect to time gave the dependences of change inQ _s vsV _g or vsH. At low temperatureT<1 K there arise deviations from the linear dependenceQ _s(V _g) near those integer values of Landau level fillingν=n _s/n _H=2, 4, 6, 8, 12, which correspond to the most deep minima inρ _xx and flat plateaux inρ _xy. Heren _s is the 2D electron density,n _H being Landau level degeneracy number,ρ _xx andρ _xy —the resistivity tensor components. The inherent feature of the curveQ _s(V _g) is the hysteresis: at increasingV _g the chargeQ _s is less than the equilibrium value, while at decreasingV _g the charge exceeds the equilibrium one. The maximum difference of charges at an increase and decrease ofV _g grows-rapidly at loweringT and atT=0.42 K amounts to ～10% of the full charge confined by one Landau level (n _H.e.S). It is worth to note that such behaviour ofQ _s(V _g) does not influence the values ofρ _xy (with accuracy of ～ 10^?5) and the shape ofρ _xy plateaux andρ _xx-minima. Measurements at various sweep rates dV _g/dt demonstrated that if the sweep rate is lower, the hysteresis region is narrower and the deviation of chargesQ _s from its equilibrium value is smaller. By extrapolating the dependence of hysteresis loop width on dV _g/dt, the ultimate sweep rate may be estimated, for which a hysteresis will completely disappear. Thus, for instance, atT=0.42 K andν=4 it will occur when the time interval of one Landau level fillingτ _H will be equal to 100 years. A similar hysteresis in 2D-layer charge occurs in varying magnetic field also, when the gate voltage is disconnected with the battery and hence the charge in MOSFET is maintained constant. This hysteresis loop rapidly vanishes at temperatures >1 K. The long relaxation time of a nonequilibrium charge in 2D-layer can be connected phenomenologically with small drift velocities of electrons along the potential gradient due to a small value of conductivityσ _xx. This relaxation time may be estimated asτ～C/σ _xx whereC is the electrical capacitance of MOSFET area with a nonequilibrium charge. The value ofτ～10⁹ s givesσ _xx<10 _a ^?18 Ohm^?1/□, i.e.ρ _xx<10^?11 Ohm/□. Simultaneously with nonequilibrium charge relaxation in 2D-layer there arise circular Hall currents decaying with the same rate. In conclusion, we observed and investigated nonequilibrium charging of 2D-layer in quantum Hall effect regime. To explain the phenomenon we supposed that circular Hall currents is comparable to the eddy currents excited in a superconducting ring.     

Effect of in-plane vortex coupling on Hall conductivity in high-Tc superconducting thin films

The controversial pinning dependence of the Hall conductivity (σ_xy) is studied in the vortex-liquid phase of high-T_c superconducting thin films. A strong pinning dependence of σ_xy is found to be triggered by a crossover from a regular liquid to the glassy liquid (GL) where vortices remain coupled in ab-plane. This result suggests that a non-linear effect in the GL region needs to be considered to account for the behavior of σ_xy in the whole vortex-liquid phase.     

Disorder effect on the quantum Hall effect in thin films of three-dimensional topological insulators

We numerically study the quantum Hall effect (QHE) in three-dimensional topological insulator (3DTI) thin film in the presence of the finite Zeeman energy g and the hybridization gap Δ under a strong magnetic field and disorder. For Δ = 0 but g ≠ 0, the Hall conductivity remains to be odd-integer quanti-zed σ _xy = ν(e ²/h) , where ν = 2? + 1 with ? being an integer. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and the higher plateaus disappear first. The two central plateaus with ν = ± 1 around the band center are strongest against disorder scattering. With the increasing of the disorder strength, Hall plateaus are destroyed faster for the system with a weaker magnetic field. If g = 0 but Δ ≠ 0, there is a splitting of the central (n = 0) Landau level, yielding a new plateau with ν = 0, in addition to the original odd-integer plateaus. In the strong-disorder regime, the QHE plateaus can be destroyed due to the float-up of extended levels toward the band center. The ν = 0 plateau around the band center is strongest against disorder scattering, which eventually disappears. For both g ≠ 0 and Δ ≠ 0, the simultaneous presence of nonzero g and Δ causes the splitting of the degenerating Landau levels, so that all integer Hall plateaus ν = ? appear. The ν = 0,1 plateaus are the most stable ones. In the strong-disorder regime, all QHE states are destroyed by disorder, and the system transits into an insulating phase.     

Quantum transport studies of electron accumulation layers in InSe bulk crystals

Summary Experiments show that the Hall resistivityρ _xy of InSe bulk crystals is quantized into integer multiples ofh/e ². Quantum Hall effect in InSe is explained as a result of plane defects in InSe crystals. The electrons in bulk InSe are localized at these defects at low temperatures forming regions with two-dimensional conductivity. Concentration of electrons in these regions isN _2D=2·10¹¹ cm⁻² and their mobility μ=2·10⁴cm²/V·s. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Quantum magneto-transport in two-dimensional GaAs electron gases and SiGe hole gases

We have measured the low-temperature transport properties of two-dimensional (2D) GaAs electron gases and 2D SiGe hole gases. Our experimental results fall into three categories. (i) Collapse of spin-splitting and an enhanced Landé g-factor at Landau level filling factors both ν=3 and ν=1 in a 2D GaAs electron gas are observed. Our experimental results show direct evidence that the effective disorder is stronger at ν=1 than that at ν=3 over approximately the same perpendicular magnetic field range. (ii) We present evidence for spin-polarisation of a dilute 2D GaAs electron gas. The Lande g-factor of the system is estimated to be 1.66. This enhanced g value is ascribed to electron–electron interactions at ultra low carrier density limit. (iii) In a high-quality SiGe hole gas, there is a temperature-independent point in the magnetoresistivity ρ_xx and ρ_xy which is ascribed to experimental evidence for a quantum phase transition between ν=3 and ν=5. We also present a study on the temperature(T)-driven flow lines in our system.     

Helical-edge transport near ν = 0 of monolayer graphene

The complex nature of filling factor ν = 0 of monolayer graphene is studied in magnetotransport experiments. As a function of perpendicular magnetic field a metal-insulator transition is observed, which is attributed to disorder-induced Landau level broadening in the canted antiferromagnetic phase. In the metallic regime a separation of the zeroth Landau level appears and signs of the quantum spin Hall effect are seen near ν = 0. In addition to local transport, nonlocal transport experiments show results being consistent with helical edge transport.     

Magneto-oscillations of the Hall coefficient in n-type GaSb at the extreme quantum limit

Magnetoquantum oscillations of the Hall coefficient R_H were observed in Te-doped GaSb layers grown by molecular beam epitaxy. The free electron densities were in the low 10¹⁶ cm⁻³ range or even slightly lower, thus achieving, for the first time in GaSb, the extreme quantum limit, where all the electrons occupy the spin-split 0⁽⁺⁾ Landau level (LL). Similarly to other known cases, the amplitude of the last maximum of R_H could be explained as enhanced by the metal-to-insulator transition of the spin-down electron system in the n=0 LL. The occurrence of the last negative oscillation of R_H below its classical value, called Hall dip, could be frustrated, in samples with sufficiently low carrier densities, by an incipient carrier freeze-out at donor impurities induced by the magnetic field.     

Integer and fractional quantum Hall effect in a strip of stripes

We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe with a reciprocal wavevector 8k _F in a mean field approximation. This wavevector gives rise to Umklapp scattering and resonant scattering that results in gaps and chiral edge states at all known integer and fractional filling factors ν. The integer and odd denominator filling factors arise for a uniform distribution of stripes, whereas the even denominator filling factors arise for a non-uniform stripe distribution. We focus on the ground state of the system, and identify the quantum Hall regime via the quantized Hall conductance. For this we calculate the Hall conductance via the Streda formula and show that it is given by σ _H = νe ²/h for all filling factors. In addition, we show that the composite fermion picture follows directly from the condition of the resonant Umklapp scattering.     

第Ⅱ种强度不等的非对称两态叠加多模叠加态光场的偶数阶等阶N次方Y压缩

本文构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}>_q与多模虚共轭相干态的相反态|{-iZ_j^(b)*}>_q这两者的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)>_q,利用多模压缩态理论研究了态|Ψ_Ⅱ^(ab)>_q的任意偶数阶等阶N次方Y压缩特性.结果发现:1)在压缩阶数N取偶数,即N=2p的条件下,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要构成态|Ψ_Ⅱ^(ab)>_q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位都不相等,亦即R_j^(a)≠R_j^(b)和φ_j^(a)≠φ_j^(b)(j=1,2,3,…,q),并且 ,则当满足一定的量子化条件(或者在一些闭区间内连续取值)时,态|Ψ_Ⅱ^(ab)>_q总可呈现出周期性变化的、任意偶数阶的等阶N次方Y压缩效应.2)在N=2p且p=2m+1(m=0,1,2,3,…,…)的条件下,若R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),态|Ψ_Ⅱ^(ab)>_q则可呈现出等阶N次方Y压缩简并现象.     

Composite-Particles (Boson,Fermion) Theory of Fractional Quantum Hall Effect

A theory is developed for fractional quantum Hall effect in terms of composite (c)-bosons (fermions) without useing Laughlin’s results about the fractional charge. Here the c-particle (fermion, boson) is defined as a bound composite fermion (boson) containing a conduction electron and an even (odd) number of fluxons (elementary magnetic fluxes). The Bose-condensed c-bosons, each containing an electron and an odd number m of fluxons at the filling factor ν=1/m is shown to generate the Hall conductivity plateau value m e ²/h, where the density of c-particles, \(n_{\phi }^{(m)}\), either bosonic or fermionic, with m fluxons is given by \(n_{\phi }^{(m)}=n_{\mathrm {e}}/m\), n _e = electron density. The only assumption is that any c-fermion carries a charge magnitude equal to the electron charge e. The quantum Hall state is shown to be more stable at ν=1/3 than at ν=1.     

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ν=±4 being the most stable in the quantum Hall effect measurement, instead of ν=±8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ν=±4 is, down to very low fields, weakly dependent on the strength of the magnetic field.     

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range 2/5≥ν≥1/3. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor ν?1/3 and at ν?2/5 identify a structure of lowest spin-split Landau levels of composite fermions (CFs) that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At ν=1/3 energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results.     

Non-abelian spin-singlet quantum Hall states: wave functions and quasihole state counting

We investigate a class of non-abelian spin-singlet (NASS) quantum Hall phases, proposed previously. The trial ground and quasihole excited states are exact eigenstates of certain (k+1)-body interaction Hamiltonians. The k=1 cases are the familiar Halperin abelian spin-singlet states. We present closed-form expressions for the many-body wave functions of the ground states, which for k>1 were previously defined only in terms of correlators in specific conformal field theories. The states contain clusters of k electrons, each cluster having either all spins up, or all spins down. The ground states are non-degenerate, while the quasihole excitations over these states show characteristic degeneracies, which give rise to non-abelian braid statistics. Using conformal field theory methods, we derive counting rules that determine the degeneracies in a spherical geometry. The results are checked against explicit numerical diagonalization studies for small numbers of particles on the sphere.