Exchange-enhanced Spin Splitting Research Articles

Evolution of the quantum Hall bulk spectrum into chiral edge states

One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum. Here, we use a GaAs cleaved edge quantum wire to perform momentum-resolved spectroscopy of the quantum Hall edge states in a tunnel-coupled 2D electron gas. This reveals the momentum and position of the edge states with unprecedented precision and shows the evolution from very low magnetic fields all the way to high fields where depopulation occurs. We present consistent analytical and numerical models, inferring the edge states from the well-known bulk spectrum, finding excellent agreement with the experiment—thus providing direct evidence for the bulk to edge correspondence. In addition, we observe various features beyond the single-particle picture, such as Fermi level pinning, exchange-enhanced spin splitting and signatures of edge-state reconstruction.

Exchange-mediated dynamic screening in the integer quantum Hall effect regime

We study many-body interaction effects in the spatially resolved filling factor (ν) distribution for higher Landau levels (LLs) via self-consistent Hartree-Fock simulations in the integer quantum Hall (IQH) regime. Our results indicate a strong, interaction-induced tendency to avoid the simultaneous existence of partially filled spin-up and spin-down LLs. Rather, we find that such partially filled LLs consist of coexisting regions of full and empty LLs. At the boundaries between the regions of full and empty LLs, we observe edge stripes of nearly constant ν close to half-filling. This suggests that the exchange interaction induces a behavior similar to a Hund's rule for the occupation of the spin split LLs. The screening of the disorder and edge potential appears significantly reduced as compared to static Thomas-Fermi screening (Chklovskii D. B. et al., Phys. Rev. B, 46 (1992) 4026). Our results are consistent with a local, lateral ν-dependence of the exchange-enhanced spin splitting. Hence, on quantum-coherent length scales as probed here, the electron system of the IQH effect behaves similarly to a non-interacting single particle system —not because of the absence, but rather due to the dominance of many-body effects.

Magnetotransport in p-type Ge quantum well narrow wire arrays

We report magnetotransport measurements of a SiGe heterostructure containing a 20 nm p-Ge quantum well with a mobility of 800 000 cm2 V−1 s−1. By dry etching arrays of wires with widths between 1.0 μm and 3.0 μm, we were able to measure the lateral depletion thickness, built-in potential, and the phase coherence length of the quantum well. Fourier analysis does not show any Rashba related spin-splitting despite clearly defined Shubnikov-de Haas oscillations being observed up to a filling factor of ν = 22. Exchange-enhanced spin-splitting is observed for filling factors below ν = 9. An analysis of boundary scattering effects indicates lateral depletion of the hole gas by 0.5 ± 0.1 μm from the etched germanium surface. The built-in potential is found to be 0.25 ± 0.04 V, presenting an energy barrier for lateral transport greater than the hole confinement energy. A large phase coherence length of 3.5 ± 0.5 μm is obtained in these wires at 1.7 K.

Spin-dependent tunneling rates for electrostatically defined GaAs quantum dots

The tunneling rates for spin-up and -down electrons are investigated for a GaAs quantum dot in an in-plane magnetic field by using a real-time single-electron counting scheme with a nearby charge detector. An extremely small spin-polarized current on the order of attoamperes is analyzed with the spin and energy dependences of the tunneling rates. Fully spin-polarized current is obtained when only a spin-up Zeeman sublevel is located in the transport window. When both Zeeman sublevels are allowed to contribute to the transport, we find that the tunneling rate for spin-up electrons is considerably higher than that for spin-down electrons. This partially spin-polarized current can be explained by the exchange-enhanced spin splitting in low-density regions near the tunneling barriers.

Exchange-enhanced spin splitting in a two-dimensional electron gas in the presence of spin–orbit interaction and magnetic fields

Using a Green's function approach on the basis of the random-phase approximation, we examine how the many-body effect such as exchange interaction affects the spin-splitting in a two-dimensional electron gas system in the presence of the Rashba spin–orbit interaction and Zeeman splitting and of quantizing magnetic fields. We show that such a many-body interaction can lower the energy levels of the system and enlarge the spin-splitting around the Fermi level. We also find that the exchange-enhanced spin-splitting is mainly achieved via intra-Landau level scattering.

Exchange-enhanced spin-splitting in a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction

We present a theoretical study on how many-body effects can affect the spin-splitting of a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction. The standard Hartree–Fock approximation and Green's function approach are employed to calculate the energy spectrum and density of states of a spin-split two-dimensional electron gas (2DEG). We find that the presence of the exchange interaction can enhance significantly the spin-splitting of a 2DEG on top of the Rashba effect. The physical reasons behind this important phenomenon are discussed.

PROBING THE LOCAL DENSITY OF STATES OF DILUTE ELECTRON SYSTEMS IN DIFFERENT DIMENSIONS

Scanning tunneling spectroscopy at T = 6 K is used to investigate the local density of states (LDOS) of electron systems belonging to the bulk conduction band of InAs. In particular, the three-dimensional electron system (3DES) of the n-doped material, an adsorbate-induced two-dimensional electron system (2DES) and the tip-induced quantum dot (0DES) are investigated at B = 0 T and B = 6 T. It is found that the 3DES at B = 0 T can be described by Bloch states weakly interacting with the potential disorder provided by ionized dopants. The 2DES at B = 0 T exhibits much stronger LDOS corrugations, stressing the tendency for weak localization in the potential disorder. In a magnetic field, 3DES and 2DES show drift states, which are expected in 2D, but are surprising in 3D, where they point to a new electron phase consisting of droplets of quasi-2D systems. The 0DES at B = 0 T reveals quantized states in accordance with Hartree calculations. At B = 6 T it exhibits Landau states with exchange enhanced spin splitting. These states are used to investigate the influence of potential disorder on the exchange enhancement, which visualizes the nonlocality of the exchange interaction.

Magneto-transport of two-dimensional electron system in magnetic semiconductors heterostructure Cd(Mn)Te/(Cd,Mg)Te

We have grown n-type modulation-doped Cd(Mn)Te/(Cd,Mg)Te single quantum wells (SQWs) by molecular beam epitaxy (MBE). The properties of two-dimensional electron gas in obtained samples are the following; the sheet carrier density was about 3×1011cm−2 and the Hall mobility of CdTe SQW was 6×104cm2/Vs at 2K, but that of Cd1−xMnxTe SQWs with x=0.01–0.03 was decreased by about one order of magnitude. In the magnetotransport measurements up to 14T at 2K, typical features of the integer quantum Hall effect (IQHE), that is, zeros of magnetoresistance (MR) and quantized plateaux of the Hall resistance, were observed in a CdTe SQW sample. In Cd1−xMnxTe SQWs, on the other hand, the oscillation of MR associated with the transition between spin-split levels was observed at lower fields than the non-magnetic CdTe SQW, which reflected enhanced Zeeman splitting due to the exchange interaction with Mn2+ spins. Further, large positive and negative MR at low fields was observed in Cd1−xMnxTe SQWs, both of which are also attributed to the exchange-enhanced spin splitting.

Exciton spin polarization in magnetic semiconductor quantum wires

Electron-beam lithography and wet etching techniques are used to laterally pattern ZnSe/(Zn,Cd,Mn)Se single quantum wells into magnetically active quantum wires with widths ranging from 20 to 80 nm. Photoluminescence spectroscopy as a function of wire width reveals a competition between elastic strain relaxation and quantum confinement. Magnetophotoluminescence measurements at low temperatures indicate a strong exciton spin polarization due to the sp–d exchange-enhanced spin splitting, ranging from 20% to 60% at 4 T.

Critical collapse of the exchange-enhanced spin splitting in two-dimensional systems

The critical filling factor v_c where Shubnikov-de Haas oscillations become spin split is investigated for a set of GaAs-GaAlAs heterojunctions. Finite temperature magnetoresistance measurements are used to extract the value of v_c at zero temperature. The critically point is where the disorder potential has the same magnitude as the exchange energy, leading to the empirical relationship v_c = g* n t h / 2 m_0. This is valid for all the samples studied, where the density n and single particle lifetime t both vary by more than an order of magnitude and g* the exchange enhanced g-factor has a weak dependence on density. For each sample the spin gap energy shows a linear increase with magnetic field. Experiments in tilted magnetic field show the spin gap is the sum of the bare Zeeman energy and an exchange term. This explains why measurements of the enhanced g-factor from activation energy studies in perpendicular field and the coincidence method in tilted fields have previously disagreed.

Spin-dependent transport in a magnetic two-dimensional electron gas

Magneto-transport and magneto-optical probes are used to interrogate spin-dependent transport in magnetic heterostructures wherein a two dimensional electron gas (2DEG) is exchange-coupled to local moments. At low temperatures, the significant s–d exchange-enhanced spin splitting in these “magnetic” 2DEGs is responsible for the observation of unusual transport properties such as a complete spin polarization of the gas at large Landau level filling factors and a pronounced, non-monotonic background magneto-resistance. Magneto-transport measurements of gated samples performed in a parallel field geometry are used to systematically study the variation of the magneto-resistance with sheet concentration, yielding new insights into the dependence of spin transport on the Fermi energy of the majority spin carriers.

Two-dimensional electron liquid in a weak magnetic field

We present a theory describing the low-energy properties of an interacting two-dimensional electron gas in a magnetic field at large non-integer filling factors v ≫ 1. For a moderate interaction strength, r s < 1, we find two energy scales controlling the electron dynamics at energies less than ħω c. The first energy scale, (ħω c/ v)ln( vr s), appears in the one electron spectral density as the width of a pseudogap. The second and larger scale, r sħω c, characterizes the exchange-enhanced spin splitting and the thermodynamic density of states.

Two-dimensional electron liquid in a weak magnetic field.

We present an effective theory describing the low-energy properties of an interacting 2D electron gas at large non-integer filling factors $\nu\gg 1$. Assuming that the interaction is sufficiently weak, $r_s < 1$, we integrate out all the fast degrees of freedom, and derive the effective Hamiltonian acting in the Fock space of the partially filled Landau level only. This theory enables us to find two energy scales controlling the electron dynamics at energies less than $\hbar\omega_c$. The first energy scale, $(\hbar\omega_c/\nu)\ln\left(\nu r_s\right)$, appears in the one electron spectral density as the width of a pseudogap. The second scale, $r_s\hbar\omega_c$, is parametrically larger; it characterizes the exchange-enhanced spin splitting and the thermodynamic density of states.

Exchange-enhanced spin splitting in a two-dimensional electron system with lateral modulation.

The effective spin splitting of the Landau bands produced by an external unidirectional periodic-modulation potential is studied in the thermodynamic Hartree-Fock (HF) approximation. The HF energies, which depend on three quantum numbers, the center coordinates of the wave functions, and the discrete Landau and spin quantum numbers, and also the thermodynamic density of states (TDOS), which is experimentally accessible by magnetocapacitance measurements, are calculated numerically for representative values of wavelength and strength of the modulation potential. For GaAs at low temperatures, the exchange enhancement can yield an effective spin gap comparable with the cyclotron energy. The spin gaps occur in strips, in which the center coordinates correspond to HF energies near the Fermi energy. The width of these strips depends on the steepness of the modulation potential and, in an intricate manner, on temperature and screening effects. Screening effects may lead to broad peaks in the TDOS, while van Hove singularities due to the one-dimensional Landau bands lead to sharp peaks in the TDOS. The conditions, under which such structures should be resolved in experiments, are discussed.

Antiscreening and exchange-enhanced spin splitting in quantum wires.

Theoretical work is presented, suggesting that in regimes of experimental interest, the exchange enhancement of the spin splitting of Landau levels in quantum wires as evidenced in their two-terminal conductance is increased by the confinement. This is due to an effect in which electron-electron interactions are strengthened by interaction with polarizable edge-state charge. This antiscreening effect is confirmed by calculating exchange enhancement in a quasi-one-dimensional conductor in the ``screened'' Hartree-Fock approximation. Preliminary experimental evidence for the effect is also presented.