Zeeman Spin Splitting Research Articles

Interplay of spin and orbital magnetogyrotropic photogalvanic effects in InSb/(Al,In)Sb quantum well structures

We report on the observation of linear and circular magnetogyrotropic photogalvanic effects in InSb/AlInSb quantum well structures. We show that intraband (Drude-like) absorption of terahertz radiation in the heterostructures causes a dc electric current in the presence of an in-plane magnetic field. The photocurrent behavior upon variation of the magnetic field strength, temperature and wavelength is studied. We show that at moderate magnetic fields the photocurrent exhibits a typical linear field dependence. At high magnetic fields, however, it becomes nonlinear and inverses its sign. The experimental results are analyzed in terms of the microscopic models based on asymmetric relaxation of carriers in the momentum space. We demonstrate that the observed nonlinearity of the photocurrent is caused by the large Zeeman spin splitting in InSb/AlInSb structures and an interplay of the spin-related and spin-independent roots of the magnetogyrotropic photogalvanic effect.

Observation of the Kondo Effect in a Spin-32Hole Quantum Dot

We report the observation of Kondo physics in a spin-3/2 hole quantum dot. The dot is formed close to pinch-off in a hole quantum wire defined in an undoped AlGaAs/GaAs heterostructure. We clearly observe two distinctive hallmarks of quantum dot Kondo physics. First, the Zeeman spin splitting of the zero-bias peak in the differential conductance is independent of the gate voltage. Second, this splitting is twice as large as the splitting for the lowest one-dimensional subband. We show that the Zeeman splitting of the zero-bias peak is highly anisotropic and attribute this to the strong spin-orbit interaction for holes in GaAs.

Thin topological insulator film in a perpendicular magnetic field

We report on a study of an ultrathin topological insulator film with hybridization between the top and bottom surfaces, placed in a quantizing perpendicular magnetic field. We calculate the full Landau-level spectrum of the film as a function of the applied magnetic field and the magnitude of the hybridization matrix element, taking into account both the orbital and the Zeeman spin splitting effects of the field. For an undoped film, we find a quantum phase transition between a state with a zero Hall conductivity and a state with a quantized Hall conductivity equal to ${e}^{2}/h$, as a function of the magnitude of the applied field. The transition is driven by the competition between the Zeeman and the hybridization energies.

Exchange Enhancement of Spin-Splitting in AlxGa1−xN/GaN Heterostructures in Tilted Magnetic Fields

AlxGa1−xN/GaN heterostructures are investigated by magnetotransport experiments in tilted magnetic fields at low temperatures. The spin-split peaks of the Shubnikov-de Haas (SdH) oscillations are observed at high magnetic fields, which are attributed to the Zeeman spin-splitting of the two-dimensional electron gas at the heterointerface. The exchange enhanced g* of the spin-splitting is investigated by measuring the positions of the pairs of spin-split SdH maxima. Moreover, it is found that g* becomes smaller with the increasing tilt angle, which suggests the anisotropy of g* is due to the strong polarization-induced electric field at the AlxGa1−xN/GaN heterointerface.

Interface edge states and quantum Hall effect in graphene under a modulated magnetic field

Graphene properties can be manipulated by a periodic potential. Based on the tight-binding model, we study graphene under a one-dimensional (1D) modulated magnetic field which contains both a uniform and a staggered component. New chiral current-carrying edge states are generated at the interfaces where the staggered component changes direction. These edge states lead to an unusual integer quantum Hall effect (QHE) in graphene, which can be observed experimentally by a standard four-terminal Hall measurement. When Zeeman spin splitting is considered, a novel state is predicted where the electron edge currents with opposite polarization propagate in the opposite directions at one sample boundary, whereas propagate in the same directions at the other sample boundary.

Observation of orientation- and k-dependent Zeeman spin-splitting in hole quantum wires on (100)-oriented AlGaAs/GaAs heterostructures

In this paper, We study the Zeeman spin-splitting in hole quantum wires oriented along the [011] and crystallographic axes of a high mobility undoped (100)-oriented AlGaAs/GaAs heterostructure. Our data show that the spin-splitting can be switched ‘on’ (finite g*) or ‘off’ (zero g*) by rotating the field from a parallel to a perpendicular orientation with respect to the wire, and the properties of the wire are identical for the two orientations with respect to the crystallographic axes. We also find that the g-factor in the parallel orientation decreases as the wire is narrowed. This is in contrast to electron quantum wires, where the g-factor is enhanced by exchange effects as the wire is narrowed. This is evidence for a k-dependent Zeeman splitting that arises from the spin- nature of holes.

Field-orientation dependence of the Zeeman spin splitting in (In,Ga)As quantum point contacts

We study the Zeeman spin splitting in a quantum point contact (QPC) etched into an InGaAs/InP heterostructure for three orthogonal magnetic field orientations with respect to the QPC. For the two in-plane orientations we observe an isotropic Zeeman spin splitting, which becomes stronger as the system is made more one dimensional. The Lande $g$ factor is enhanced by up to a factor of two compared to two-dimensional electron systems in InGaAs/InP. A much larger Zeeman splitting is observed when the field is oriented perpendicular to the heterostructure, resulting in a $g$ factor of 15.7 in the one-dimensional limit.

Oscillatory spin-polarized tunnelling from silicon quantum wells controlled by electric field

Spin-dependent electronic transport is widely used to probe and manipulate magnetic materials and develop spin-based devices. Spin-polarized tunnelling, successful in ferromagnetic metal junctions, was recently used to inject and detect electron spins in organics and bulk GaAs or Si. Electric field control of spin precession was studied in III-V semiconductors relying on spin-orbit interaction, which makes this approach inefficient for Si, the mainstream semiconductor. Methods to control spin other than through precession are thus desired. Here we demonstrate electrostatic modification of the magnitude of spin polarization in a silicon quantum well, and detection thereof by means of tunnelling to a ferromagnet, producing prominent oscillations of tunnel magnetoresistance of up to 8%. The electric modification of the spin polarization relies on discrete states in the Si with a Zeeman spin splitting, an approach that is also applicable to organic, carbon-based and other materials with weak spin-orbit interaction.

De Haas-van Alphen effect and energy gaps of a correlated two-dimensional electron system in an AlAs two-valley pseudospin system

We report highly sensitive de Haas-van Alphen (dHvA) effect measurements on a high-mobility two-dimensional electron system in an AlAs quantum well. Here two valleys are occupied forming a pseudospin system. At 400 mK, the dHvA effect shows pronounced oscillations at filling factors nu=1 to four. In the quantum limit at nu=1 the data are consistent with an interaction-enhanced valley splitting, which exceeds the Zeeman spin splitting in a perpendicular field B. When tilting B the energy gap Delta E at nu=1 shows first an unexpectedly strong angular dependence and then remains constant. This suggests a crossover in the energy gap, most likely from a spin to a pseudospin gap. We attribute the strong initial dependence of Delta E on the tilt angle to skyrmion-type spin excitations. Surprisingly, the dHvA oscillation amplitudes do not display coincidence phenomena at higher filling factors. This is explained by the large valley splitting and avoided crossings of energy levels.

SPIN-RELATED TRANSPORT AFFECTED BY COMPETITION BETWEEN SPIN-ORBIT INTERACTION AND ZEEMAN EFFECT

The spin dynamics in solid state systems is governed by the competition between spin-orbit interaction (SOI) and the Zeeman effect. The SOI couples orbital motion of electron spins with an electric field. The Zeeman effect lifts the spin degeneracy in a magnetic field. In InGaAs -based 2DEGs, it is known that the Rashba SOI energy E SOI can be controlled by an electric field applied on the gate electrode.1 In the presence of SOI, weak localization (WL) due to time reversal symmetric interference changes to weak anti-localization (WAL). We have found crossover from WL to WAL by applying the gate voltage in InGaAs 2DEGs. Applying an in-plane magnetic field to the 2DEG does not affect the orbital motion of the electrons, but only modifies the Zeeman spin splitting energy E Z . This allows tuning the ratio between E SOI and E Z very accurately. We have studied how the interplay between SOI and Zeeman coupling affects the electron transport and the spin dynamics in InGaAs -based 2DEGs. From the quantitative analysis of the magnetoconductance, measured in the presence of an in-plane magnetic field, we conclude that this interplay results in a spin-induced breaking of time reversal symmetry (TRS) and in an enhancement of the spin relaxation time. Both effects are due to a partial alignment of the electron spin along the applied magnetic field, and are found to be in excellent agreement with recent theoretical predictions.2 We find that the electron dephasing time saturates when E Z becomes comparable to E SOI . Moreover, we show that the spin-induced electron dephasing time is a universal function of the ratio E Z /E SOI within the experimental accuracy, i.e. it is independent of any details of the quantum well.3 This universal behavior is explained by the recent theory.4 The suppression of WAL is observed by applying in-plane magnetic field because of the enhancement of the spin relaxation time, and this suppression also appears in narrow InGaAs wires since the effective magnetic field direction is confined by wires. In gate fitted narrow wires, the large enhancement of spin relaxation time is obtained when the Rashba SOI is decreased. The spin relaxation time is more than one order longer than that of 2DEG case. This enhancement suggests that the Rashba SOI strength approaches the Dresselhaus SOI strength. We have numerically investigated the angular dependence of in-plane magnetoconductance in disordered wires with both Rashba and Dresselhaus SOIs. A new method is proposed to determine the relative strength of Rashba and Dresselhaus SOI from transport measurements without the need of fitting parameters.5 This in-plane magnetic field measurement provides fruitful information on spin related transport. Note from Publisher: This article contains the abstract only.

Energy shell structure of a single InAs/GaAs quantum dot with a spin-orbit interaction

We study the evolution of the excited-state photoluminescence of a single self-assembled quantum dot as a function of applied magnetic field in a regime where the cyclotron energy is comparable to the confinement energy. As expected, we observe the splitting of the angular-momentum states following the Fock-Darwin scheme, but we also observe that each state further splits into a doublet which shows an unexpected evolution with increasing magnetic field. This behavior cannot be explained by a simple Zeeman spin splitting but is rather consistent with the observation of spin-orbit coupling where the spin of electrons is coupled with the envelope function orbital angular momentum. We show that the addition of this type of spin-orbit coupling to the single-particle Fock-Darwin model can account for the observed dependence. By comparison of our data with such a model, we derive a spin-orbit intensity of 3.90.310 9 eV cm 2 . DOI: 10.1103/PhysRevB.79.165427 PACS numbers: 78.67.Hc, 73.21.La, 78.55.Cr, 81.07.Ta

The interplay between one-dimensional confinement and two-dimensional crystallographic anisotropy effects in ballistic hole quantum wires

In this paper, we study the Zeeman spin-splitting in hole quantum wires aligned along the and crystallographic axes of a high-mobility (311)A undoped AlGaAs/GaAs heterostructure. We obtained measurements of the effective g-factor g* as a function of the wire width for in-plane magnetic fields aligned both parallel and perpendicular to the wire axis. We interpret our data in terms of a qualitative model that involves the interplay of two effects—1D confinement and 2D crystalline anisotropy.

Spin orientation of holes in quantum wells

This paper reviews the spin orientation of spin-3/2 holes in quantum wells. We discuss the Zeeman and Rashba spin splitting in hole systems that are qualitatively different from their counterparts in electron systems. We show how a systematic understanding of the unusual spin-dependent phenomena in hole systems can be gained using a multipole expansion of the spin density matrix. As an example we discuss spin precession in hole systems that can give rise to an alternating spin polarization. Finally, we discuss the qualitatively different regimes of hole spin polarization decay in clean and dirty samples.

Spin Hall effect in a two-dimensional electron gas in the presence of a magnetic field

We study the spin Hall effect of a two-dimensional electron gas in the presence of a magnetic field and both the Rashba and Dresselhaus spin-orbit interactions. We show that the value of the spin Hall conductivity, which is finite only if the Zeeman spin splitting is taken into account, may be tuned by varying the ratio of the in-plane and out-of-plane components of the applied magnetic field. We identify the origin of this behavior with the different role played by the interplay of spin-orbit and Zeeman couplings for in-plane and out-of-plane magnetic-field components.

Magnetic edge states in graphene in nonuniform magnetic fields

We theoretically study the electronic properties of a graphene sheet on the $xy$ plane in a spatially nonuniform magnetic field, $B={B}_{0}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ in one domain and $B={B}_{1}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ in the other domain, in the quantum Hall regime, and in the low-energy limit. We find that the magnetic edge states of the Dirac fermions, formed along the boundary between the two domains, have features strongly dependent on whether ${B}_{0}$ is parallel or antiparallel to ${B}_{1}$. In the parallel case, when the Zeeman spin splitting can be ignored, the magnetic edge states originating from the $n=0$ Landau levels of the two domains have dispersionless energy levels contrary to those from the $n\ensuremath{\ne}0$ levels. Here, $n$ is the graphene Landau-level index. They become dispersive as the Zeeman splitting becomes finite or as an electrostatic step potential is additionally applied. In the antiparallel case, the $n=0$ magnetic edge states split into electronlike and holelike current-carrying states. The energy gap between the electronlike and holelike states can be created by the Zeeman splitting or by the step potential. These features are attributed to the fact that the pseudospin of the magnetic edge states couples to the direction of the magnetic field. We propose an Aharonov--Bohm interferometry setup in a graphene ribbon for an experimental study of the magnetic edge states.

Temperature dependence of the electron Landégfactor in InSb and GaAs

We report Larmor precession in bulk InSb observed in the time domain from $77\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The optically oriented polarization precesses coherently even at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The inferred Zeeman spin splitting is strongly nonparabolic, and the electron $g$ factor $({g}^{*})$ is in good agreement with $\mathbf{k}∙\mathbf{p}$ theory (provided we take only the dilational contribution to the change in energy gap with temperature). We also show here that correct application of the 14-band $\mathbf{k}∙\mathbf{p}$ model agrees with apparently anomalous trends previously reported for GaAs and confirm that the most widely quoted formula for ${g}^{*}$ in GaAs is incomplete.

Electronic structure of paramagnetic In1-xMnx As nanowires

The electronic structure, spin splitting energies, and g factors of paramagnetic In1-xMnxAs nanowires under magnetic and electric fields are investigated theoretically including the sp-d exchange interaction between the carriers and the magnetic ion. We find that the effective g factor changes dramatically with the magnetic field. The spin splitting due to the sp-d exchange interaction counteracts the Zeeman spin splitting. The effective g factor can be tuned to zero by the external magnetic field. There is also spin splitting under an electric field due to the Rashba spin-orbit coupling which is a relativistic effect. The spin-degenerated bands split at nonzero kz (kz is the wave vector in the wire direction), and the spin-splitting bands cross at kz = 0, whose kz-positive part and negative part are symmetrical. A proper magnetic field makes the kz-positive part and negative part of the bands asymmetrical, and the bands cross at nonzero kz. In the absence of magnetic field, the electron Rashba coefficient increases almost linearly with the electric field, while the hole Rashba coefficient increases at first and then decreases as the electric field increases. The hole Rashba coefficient can be tuned to zero by the electric field.

Correlated many-electron states in a quantum dot containing a single magnetic impurity

The few-electron states of a parabolic confined quantum dot is studied in the presence of a magnetic ion. The electrons interact with a single magnetic ion $({\mathrm{Mn}}^{2+})$ which is located in the quantum dot at arbitrary position. The local Zeeman spin splitting is calculated for different numbers of electrons $({N}_{e}=1,2,3,\dots{},10)$. The effect of the position of the magnetic ion on the energy levels (both ground state and excited states) is investigated. We calculate the heat capacity as a function of temperature, the position of the impurity, and the Coulomb strength.

QUASIEXCITONS IN PHOTOLUMINESCENCE OF INCOMPRESSIBLE QUANTUM LIQUIDS

The problem of a trion (charged exciton) immersed in an incompressible quantum liquid formed by two-dimensional electrons in a high magnetic field is studied theoretically by combining the composite fermion model and exact numerical diagonalization. Laughlin correlation of the trion with the surrounding electrons is shown to lead to the formation of a family of novel many-body excitations called "quasiexcitons" (QXs). The residual charge of the most stable QX can be either zero or the fractional quantum ±e/3, depending on the presence of negative or positive Laughlin quasiparticles in the electron liquid (controlled by the Landau level filling factor ν), but also on the width of the quantum well, Zeeman spin splitting, etc. The prediction of the magnetic-field driven transition from negative to positive QXs is argued to explain the recently observed minute discontinuity in the photoluminescence spectra of sufficiently wide (w ≥ 20 nm ) asymmetric GaAs quantum wells at ν = 1/3. Conversely, the observed discontinuity is hence indirectly linked to the emergence of a fractional charge quantum in the electron liquid.

Resonant tunneling diode with spin polarized injector

The authors investigate the current-voltage characteristics of a II-VI semiconductor resonant tunneling diode coupled to a diluted magnetic semiconductor injector. As a result of an external magnetic field, a giant Zeeman splitting develops in the injector, which modifies the band structure of the device, strongly affecting the transport properties. They find a large increase in peak amplitude accompanied by a shift of the resonance to higher voltages with increasing fields. They discuss a model which shows that the effect arises from a combination of three-dimensional incident distribution, giant Zeeman spin splitting, and broad resonance linewidth.