Caspar van der Wal

• Professor (Full) at University of Groningen

Understanding the relaxation and recombination processes of excited states in two-dimensional (2D)/three-dimensional (3D) semiconductor heterojunctions is essential for developing efficient optical and (opto)electronic devices, which integrate van der Waals 2D materials with more conventional 3D ones. In this work, we unveil the carrier dynamics an...

Vanadium in silicon carbide (SiC) is emerging as an important candidate system for quantum technology due to its optical transitions in the telecom wavelength range. However, several key characteristics of this defect family including their spin relaxation lifetime (T1), charge state dynamics, and level structure are not fully understood. In this w...

Semiconductor transition metal dichalcogenides (TMDs) have equivalent dynamics for their two spin/valley species. This arises from their energy-degenerated spin states, connected via time-reversal symmetry. When an out-of-plane magnetic field is applied, time-reversal symmetry is broken and the energies of the spin-polarized bands shift, resulting...

Semiconductor transition metal dichalcogenides (TMDs) have equivalent dynamics for their two spin/valley species. This arises from their energy-degenerated spin states, connected via time-reversal symmetry. When an out-of-plane magnetic field is applied, time-reversal symmetry is broken and the energies of the spin-polarized bands shift, resulting...

Progress with quantum technology has for a large part been realized with the nitrogen-vacancy centre in diamond. Part of its properties, however, are nonideal and this drives research into other spin-active crystal defects. Several of these come with much stronger energy scales for spin-orbit and hyperfine coupling, but how this affects their spin...

Vanadium in silicon carbide (SiC) is emerging as an important candidate system for quantum technology due to its optical transitions in the telecom wavelength range. However, several key characteristics of this defect family including their spin relaxation lifetime (T1), charge state dynamics, and level structure are not fully understood. In this w...

Electromagnetically induced transparency (EIT) is a phenomenon that can provide strong and robust interfacing between optical signals and quantum coherence of electronic spins. In its archetypical form, mainly explored with atomic media, it uses a (near-)homogeneous ensemble of three-level systems, in which two low-energy spin-1/2 levels are couple...

Electromagnetically induced transparency (EIT) is a phenomenon that can provide strong and robust interfacing between optical signals and quantum coherence of electronic spins. In its archetypical form, mainly explored with atomic media, it uses a (near-)homogeneous ensemble of three-level systems, in which two low-energy spin-1/2 levels are couple...

Color-center defects in silicon carbide promise opto-electronic quantum applications in several fields, such as computing, sensing and communication. In order to scale down and combine these functionalities with the existing silicon device platforms, it is crucial to consider SiC integrated optics. In recent years many examples of SiC photonic plat...

Color-center defects in silicon carbide promise opto-electronic quantum applications in several fields, such as computing, sensing, and communication. In order to scale down and combine these functionalities with the existing silicon device platforms, it is crucial to consider SiC integrated optics. In recent years, many examples of SiC photonic pl...

Circular photocurrents (CPC), namely circular photogalvanic (CPGE) and photon drag effects, have recently been reported both in monolayer and multilayer transition metal dichalcogenide (TMD) phototransistors. However, the underlying physics for the emergence of these effects are not yet fully understood. In particular, the emergence of CPGE is not...

Transition metal defects in SiC give rise to localized electronic states that can be optically addressed in the telecom range in an industrially mature semiconductor platform. This has led to intense scrutiny of the spin and optical properties of these defect centers. For spin-1/2 defects, a combination of the defect symmetry and the strong spin–or...

Transition metal defects in SiC give rise to localized electronic states that can be optically addressed in the telecom range in an industrially mature semiconductor platform. This has led to intense scrutiny of the spin and optical properties of these defect centers. For spin-1/2 defects, a combination of the defect symmetry and the strong spin-or...

Transition metal dichalcogenides (TMDs) combine interesting optical and spintronic properties in an atomically thin material, where the light polarization can be used to control the spin and valley degrees of freedom for the development of novel optospintronic devices. These promising properties emerge due to their large spin-orbit coupling in comb...

Transition metal dichalcogenides (TMDs) combine interesting optical and spintronic properties in an atomically-thin material, where the light polarization can be used to control the spin and valley degrees-of-freedom for the development of novel opto-spintronic devices. These promising properties emerge due to their large spin-orbit coupling in com...

Spin-active color centers in solids show good performance for quantum technologies. Several transition-metal defects in SiC offer compatibility with telecom and semiconductor industries. However, whether their strong spin–orbit coupling degrades their spin lifetimes is not clear. We show that a combination of a crystal-field with axial symmetry and...

Circular photocurrents (CPC), namely circular photogalvanic (CPGE) and photon drag effects, have recently been reported both in monolayer and multilayer transition metal dichalcogenide (TMD) phototransistors. However, the underlying physics for the emergence of these effects are not yet fully understood. In particular, the emergence of CPGE is not...

Central to spintronics is the interconversion between electronic charge and spin currents, and this can arise from the chirality-induced spin selectivity (CISS) effect. CISS is often studied as magnetoresistance (MR) in two-terminal (2T) electronic nanodevices containing a chiral (molecular) component and a ferromagnet. However, fundamental underst...

Here we emphasize once more the distinction between generating CISS (spin-charge current conversion) in a chiral system and detecting it as magnetoresistance in two-terminal electronic devices. We also highlight important differences between electrical measurement results obtained in the linear response regime and those obtained in the nonlinear re...

In this Reply, we emphasize once more the distinction between generating CISS (spin-charge current conversion) in a chiral spin-orbit system and detecting it as magnetoresistance in two-terminal electronic devices. We also highlight important differences between electrical measurement results obtained in the linear response regime and those obtaine...

The chirality-induced spin selectivity (CISS) effect concerns the interconversion of electronic charge and spin currents. In two-terminal (2T) devices containing a chiral (molecular) component and a ferromagnet, CISS has been detected as magnetoresistance (MR) signals, which, however, is forbidden by Onsager reciprocity in the linear response regim...

Spin-active color centers in solids show good performance for quantum technologies. Several transition-metal defects in SiC offer compatibility with telecom and semiconductor industries. However, whether their strong spin-orbit coupling degrades their spin lifetimes is not clear. We show that a combination of a crystal-field with axial symmetry and...

Recent research discovered that charge-transfer processes in chiral molecules can be spin-selective, and the effect was named chiral-induced spin selectivity (CISS). Follow-up work studied hybrid spintronic devices with conventional electronic materials and chiral (bio)molecules. However, a theoretical foundation for the CISS effect is still in dev...

Recent research discovered that charge transfer processes in chiral molecules can be spin selective and named the effect Chiral-Induced Spin Selectivity (CISS). Follow-up work studied hybrid spintronic devices with conventional electronic materials and chiral (bio)molecules. However, a theoretical foundation for the CISS effect is still in developm...

In optically excited two-dimensional phototransistors, charge transport is often affected by photodoping effects. Recently, it was shown that such effects are especially strong and persistent for graphene/h-BN heterostructures, and that they can be used to controllably tune the charge neutrality point of graphene. In this work we investigate how th...

In optically excited two-dimensional phototransistors, charge transport is often affected by photodoping effects. Recently, it was shown that such effects are especially strong and persistent for graphene/h-BN heterostructures, and that they can be used to controllably tune the charge neutrality point of graphene. In this work we investigate how th...

Experimental observations have suggested that certain chiral molecules may be able to function as spin polarizers, an effect that promises new spintronic applications but whose mechanism remains unclear. Here, the authors bypass the microscopic origin of the effect and approach it by applying universal theorems of electrical conduction to mesoscopi...

For atoms and crystals with an ideal symmetry, the optical selection rules for electronic transitions are well covered in physics textbooks. However, in studies of material systems one often encounters systems with a weakly distorted symmetry. Insight and intuition for how optical selection rules change when an ideal symmetry is gradually distorted...

Various device-based experiments have indicated that electron transfer in certain chiral molecules may be spin-dependent, a phenomenon known as the Chiral Induced Spin Selectivity (CISS) effect. However, due to the complexity of these devices and a lack of theoretical understanding, it is not always clear to what extent the chiral character of the...

In monolayer transition metal dichalcogenides helicity-dependent charge and spin photocurrents can emerge, even without applying any electrical bias, due to circular photogalvanic and photon drag effects. Exploiting such circular photocurrents (CPC) in devices, however, requires better understanding of their behavior and physical origin. Here, we p...

In monolayer transition metal dichalcogenides helicity-dependent charge and spin photocurrents can emerge, even without applying any electrical bias, due to circular photogalvanic and photon drag effects. Exploiting such circular photocurrents (CPC) in devices, however, requires better understanding of their behavior and physical origin. Here, we p...

Color centers in wide-bandgap semiconductors are attractive systems for quantum technologies since they can combine long-coherent electronic spin and bright optical properties. Several suitable centers have been identified, most famously the nitrogen-vacancy defect in diamond. However, integration in communication technology is hindered by the fact...

Color centers in wide-bandgap semiconductors are attractive systems for quantum technologies since they can combine long-coherent electronic spin and bright optical properties. Several suitable centers have been identified, most famously the nitrogen-vacancy defect in diamond. However, integration in communication technology is hindered by the fact...

We investigate the excitonic transitions in single- and few-layer MoSe2 phototransistors by photocurrent spectroscopy. The measured spectral profiles show a well-defined peak at the optically active (bright) A0 exciton resonance. More interestingly, when a gate voltage is applied to the MoSe2 to bring its Fermi level near the bottom of the conducti...

We investigate the excitonic transitions in single- and few-layer MoSe2 phototransistors by photocurrent spectroscopy. The measured spectral profiles show a well-defined peak at the optically active (bright) A0 exciton resonance. More interestingly, when a gate voltage is applied to the MoSe2 to bring its Fermi level near the bottom of the conducti...

A new two dimensional (2D) material-germanane-has been synthesised recently with promising electrical and optical properties. In this paper we report the first realisation of germanane fieldeffect transistors fabricated from multilayer single crystal flakes. Our germanane devices show transport in both electron and hole doped regimes with on/off cu...

We experimentally demonstrate how coherent population trapping (CPT) for donor-bound electron spins in GaAs results in autonomous feedback producing stabilized states for the spin polarization of nuclei around the electrons. CPT was realized by excitation with two lasers to a bound-exciton state. Transmission studies of the spectral CPT feature on...

Divacancy defects in silicon carbide have long-lived electronic spin states and sharp optical transitions, with properties that are similar to the nitrogen-vacancy defect in diamond. We report experiments on 4H-SiC that investigate all-optical addressing of spin states with the zero-phonon-line transitions. Our magneto-spectroscopy results identify...

We analyze theoretically and experimentally how nonlinear differential-transmission spectroscopy of a lambda-system medium can provide quantitative understanding of the optical dipole moments and transition energies. We focus on the situation where two optical fields spatially overlap and co-propagate to a single detector. Nonlinear interactions gi...

We present how optical coherent population trapping (CPT) of the spin of localized semiconductor electron stabilizes the surrounding nuclear spin bath via the hyperfine interaction, resulting in a state which is more ordered than the thermal equilibrium state. We find distinct control regimes for different signs of laser detuning and examine the tr...

The study of electron transport in low-dimensional systems is of importance, not only from a fundamental point of view, but also for future electronic and spintronic devices. In this context heterostructures containing a two-dimensional electron gas (2DEG) are a key technology. In particular GaAs/AlGaAs heterostructures, with a 2DEG at typically 10...

A quantum point contact (QPC) is a basic nanometre-scale electronic device: a short and narrow transport channel between two electron reservoirs. In clean channels, electron transport is ballistic and the conductance is then quantized as a function of channel width with plateaux at integer multiples of 2e(2)/h (where e is the electron charge and h...

In a quantum computer information is stored and processed on two-state quantum systems, called qubits. Practical realization of a quantum computer requires a large number of qubits that remain co-herent on a time scale much longer than the typ-ical switching time of the qubits. We present the design of a qubit that consists of a micrometer-sized su...

We report on developing split-gate quantum point contacts (QPCs) that have a tunable length for the transport channel. The QPCs were realized in a GaAs/AlGaAs heterostructure with a two- dimensional electron gas (2DEG) below its surface. The conventional design uses 2 gate fingers on the wafer surface which deplete the 2DEG underneath when a negati...

We report the observation of electromagnetically induced transparency (EIT) with an ensemble of donor-bound electrons in low-doped n-GaAs. We used pure GaAs layers with Si doping at very low concentration in a strong magnetic field. EIT was implemented with the two optical transitions that exist for the three-level system that is formed by the two...

We present the design and operation of a fiber-based cryogenic confocal microscope. It is designed as a compact cold-finger that fits inside the bore of a superconducting magnet, and which is a modular unit that can be easily swapped between use in a dilution refrigerator and other cryostats. We aimed at application in quantum optical experiments w...

We experimentally demonstrate an ultrafast method for preparing spin states of donor-bound electrons in GaAs with single laser pulses. Each polarization state of a preparation pulse has a direct mapping onto a spin state, with bijective correspondence between the Poincar\'{e}-sphere (for photon polarization) and Bloch-sphere (for spin) state repres...

We present a new robust setup that explains and demonstrates the quantum of electrical conductance for a general audience and which is continuously available in a public space. The setup allows users to manually thin a gold wire of several atoms in diameter while monitoring its conductance in real time. During the experiment, a characteristic step-...

We present time-resolved Kerr rotation measurements of electron spin dynamics in a GaAs/AlGaAs heterojunction system that contains a high-mobility two-dimensional electron gas (2DEG). Due to the complex layer structure of this material the Kerr rotation signals contain information from electron spins in three different layers: the 2DEG layer, a GaA...

We present measurements of electromagnetically induced transparency with an ensemble of donor- bound electrons in low-doped n-GaAs. We used optical transitions from the Zeeman-split electron spin states to a bound trion state in samples with optical densities of 0.3 and 1.0. The electron spin dephasing time T* \approx 2 ns was limited by hyperfine...

We report a study of suppressed spin dephasing for quasi-one-dimensional electron ensembles in wires etched into a GaAs/AlGaAs heterojunction system. Time-resolved Kerr-rotation measurements show a suppression that is most pronounced for wires along the [110] crystal direction. This is the fingerprint of a suppression that is enhanced due to a stro...

We present studies on ensembles of single-electron systems in GaAs, realized by Si doping at very low concentration. This yields a gas of donor-bound electrons in hydrogen-like orbitals. The Bohr radius is large and each electron spin has hyperfine interaction with around 10^5 nuclear spins. We address this system with a resonant Raman scheme: The...

A compact cryogenic Kerr microscope for operation in the small volume of high-field magnets is described. It is suited for measurements both in Voigt and Faraday configurations. Coupled with a pulsed laser source, the microscope is used to measure the time-resolved Kerr rotation response of semiconductor microstructures with approximately 1 mum spa...

We present a numerical study of dephasing of electron spin ensembles in a diffusive quasi-one-dimensional GaAs wire due to the D'yakonov-Perel' spin-dephasing mechanism. For widths of the wire below the spin precession length and for equal strength of Rashba and linear Dresselhaus spin-orbit fields a strong suppression of spin-dephasing is found. T...

We describe electrical detection of spin pumping in metallic nanostructures. In the spin pumping effect, a precessing ferromagnet attached to a normal-metal acts as a pump of spin-polarized current, giving rise to a spin accumulation. The resulting spin accumulation induces a backflow of spin current into the ferromagnet and generates a dc voltage...

A compact cryogenic Kerr microscope for operation in the small volume of high-field magnets is described. It is suited for measurements both in Voigt and Faraday configuration. Coupled with a pulsed laser source, the microscope is used to measure the time-resolved Kerr rotation response of semiconductor microstructures with ~1 micron spatial resolu...

Ohmic contacts to a two-dimensional electron gas (2DEG) in GaAs/AlxGa1 − xAs heterostructures are often realized by annealing of AuGe/Ni/Au that is deposited on its surface. We studied how the quality of this type of ohmic contact depends on the annealing time and temperature, and how optimal parameters depend on the depth of the 2DEG below the sur...

We report electronic control and measurement of an imbalance between spin-up and spin-down electrons in micron-scale open quantum dots. Spin injection and detection were achieved with quantum point contacts tuned to have spin-selective transport, with four contacts per dot for realizing a nonlocal spin-valve circuit. This provides an interesting sy...

We present a numerical study of spin relaxation in a semiclassical electron ensemble in a large ballistic quantum dot. The dot is defined in a GaAs/AlGaAs heterojunction system with a two-dimensional electron gas, and relaxation occurs due to Dresselhaus and Rashba spin orbit interaction. We find that confinement in a micronscale dot can result in...

We discuss a technique and a material system that enable the controlled realization of quantum entanglement between spin-wave modes of electron ensembles in two spatially separated pieces of semiconductor material. The approach uses electron ensembles in GaAs quantum wells that are located inside optical waveguides. Bringing the electron ensembles...

We report electronic control and measurement of an imbalance between spin-up and spin-down electrons in micron-scale open quantum dots. Spin injection and detection was achieved with quantum point contacts tuned to have spin-selective transport, with four contacts per dot for realizing a non-local spin-valve circuit. This provides an interesting sy...

Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantum-mechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1/2, the physics of this system corresponds to a double well, who...

The conductance of a quantum point contact (QPC) shows several features that result from many-body electron interactions. The spin degeneracy in zero magnetic field appears to be spontaneously lifted due to the so-called 0.7 anomaly. Further, the g-factor for electrons in the QPC is enhanced, and a zero-bias peak in the conductance points to simila...

The spin degeneracy of the lowest subband that carries one-dimensional electron transport in quantum point contacts appears to be spontaneously lifted in zero magnetic field due to a phenomenon that is known as the 0.7 anomaly. We measured this energy splitting, and studied how it evolves into a splitting that is the sum of the Zeeman effect and a...

We investigate quantum fluctuations in the non-local resistance of an open quantum dot which is connected to four reservoirs via quantum point contacts. In this four-terminal quantum dot the voltage path can be separated from the current path. We measured non-local resistance fluctuations of several hundreds of Ohms, which have been characterized a...

A number of time-resolved optical experiments probing and controlling the spin and charge dynamics of the high-mobility two-dimensional electron gas in a GaAs/AlGaAs heterojunction are discussed. These include time-resolved reflectivity, luminescence, transient grating, magneto-optical Kerr effect, and electro-optical Kerr effect experiments. The o...

The on-chip resonant driving of large cone-angle magnetization precession of an individual nanoscale Permalloy element is demonstrated. Strong driving is realized by locating the element in close proximity to the shorted end of a coplanar strip waveguide, which generates a microwave magnetic field. A frequency modulation method is used to accuratel...

We report direct electrical detection of spin pumping, using a lateral normal-metal/ferromagnet/normal-metal device, where a single ferromagnet in ferromagnetic resonance pumps spin-polarized electrons into the normal metal, resulting in spin accumulation. The resulting backflow of spin current into the ferromagnet generates a dc voltage due to the...

We report direct electrical detection of spin pumping, using a lateral normal metal/ferromagnet/normal metal device, where a single ferromagnet in ferromagnetic resonance pumps spin polarized electrons into the normal metal, resulting in spin accumulation. The resulting backflow of spin current into the ferromagnet generates a d.c. voltage due to t...

We measured ferromagnetic resonance of a single submicron ferromagnetic strip, embedded in an on-chip microwave transmission line device. The method used is based on detection of the oscillating magnetic flux due to the magnetization dynamics, with an inductive pick-up loop. The dependence of the resonance frequency on applied static magnetic field...

A new method for generating spin accumulation in metals or semiconductors is by application of an rf magnetic field [1], similar to the spin battery effect induced by a ferromagnet in resonance [2]. A dc spin accumulation is produced that is in general a small fraction of phi, where phi is the rotation frequency of the rf field. When a resonant dc...

We describe a mechanism for generating nonequilibrium electron-spin accumulation in semiconductors or metals by rf magnetic field pumping. With a semiclassical model we show that a rotating applied magnetic field (or the processing magnetization inside a weak ferromagnet) generates a dc spin accumulation. For bulk systems this spin accumulation is...

The dynamics of non-equilibrium spin accumulation generated in metals or semiconductors by rf magnetic field pumping is treated within a diffusive picture. The dc spin accumulation produced in a uniform system by a rotating applied magnetic field or by a precessing magnetization of a weak ferromagnet is in general given by a (small) fraction of hba...

We demonstrate a detection method for microwave spectroscopy on magnetization reversal dynamics of nanomagnets. Measurement of the nanomagnet anisotropic magnetoresistance was used for probing how magnetization reversal is resonantly enhanced by microwave magnetic fields. We used Co strips of 2 um x 130 nm x 40 nm, and microwave fields were applied...

We describe a technique for strong, coherent interactions between spatially separated quantum systems. Using a mechanism analogous to cavity quantum electrodynamics, the state of a isolated neutral atom or a quantum dot spin or charge can be transferred to long-lived modes of a superconducting transmission line. The small mode volume of the transmi...

We describe a technique that enables a strong, coherent coupling between isolated neutral atoms and mesoscopic conductors. The coupling is achieved by exciting atoms trapped above the surface of a superconducting transmission line into Rydberg states with large electric dipole moments that induce voltage fluctuations in the transmission line. Using...

We experimentally demonstrate emission of two quantum-mechanically correlated light pulses with a time delay that is coherently controlled via temporal storage of photonic states in an ensemble of rubidium atoms. The experiment is based on Raman scattering, which produces correlated pairs of spin-flipped atoms and photons, followed by coherent conv...

On the way to solid-state quantum computing, overcoming decoherence is the central issue. In this contribution, we discuss the modeling of decoherence of a superonducting flux qubit coupled to dissipative electronic circuitry. We discuss its impact on single qubit decoherence rates and on the performance of two-qubit gates. These results can be use...

Controlled manipulation of quantum systems can lead to a number of exciting new applications in quantum information science, from quantum computation to applications in precision measurements. In many such applications, decoherence is a key factor to take into account and ultimately determines the feasibility or usefulness of the proposal. The deco...

We present experimental and theoretical studies toward demonstration of storage and retrieval of quantum states of light in warm Rb vapor. In particular, we investigate correlations between Stokes photons and atomic spin flips in Raman scattering followed by retrieval of the stored atomic excitation. Storage of spontaneous signals as well as signif...

We present experimental work that investigates whether quantum information carried by light can be stored via reversible mapping of the quantum state of such light onto a collective atomic coherence. Such a quantum memory could be utilized to allow quantum communication over long, lossy channels. Current efforts concentrate on writing a photon-numb...

We investigate the ground state properties of a system containing two superconducting islands coupled capacitively by a wire. The ground state is a macroscopic superposition of charge states, even though the islands cannot exchange charge carriers. The ground state of the system is probed by measuring the switching current of a Bloch transistor con...

We review several ideas for manipulation of quantum information using atomic ensembles and photons and describe some preliminary experiments toward their implementation. In particular, we review a technique that allows for robust transfer of quantum states between light fields and metastable states of matter. Next we discuss the use of Raman scatte...

this article we present experimental results from measuring single-charge effects in small Josephson junction arrays, with complete control over the electrostatic parameters. Results were 2e-periodic in the induced gate charges (Fig. 1a). Along with results we report on the experimental techniques that were used. The array was designed for studying...

We discuss the relaxation and dephasing rates that result from the control and the measurement setup itself in experiments on Josephson persistent-current qubits. For control and measurement of the qubit state, the qubit is inductively coupled to electromagnetic circuitry. We show how this system can be mapped on the spin-boson model, and how the s...

Superconducting quantum circuits have been proposed as qubits for developing quantum computation. The goal is to use superconducting quantum circuits to model the measurement process, understand the sources of decoherence, and to develop scalable algorithms. A particularly promising feature of using superconducting technology is the potential of de...

The SQUID used to measure the flux state of a superconducting flux-based qubit interacts with the qubit and transmits its environmental noise to the qubit, thus causing the relaxation and dephasing of the qubit state. The SQUID–qubit system is analyzed and the effect of the transmittal of environmental noise is calculated. The method presented can...

This thesis presents experimental research on Josephson junction devices that behave quantum mechanically. The devices are formed by micrometer-sized superconducting islands, that are interconnected by a Josephson tunnel junction: a thin insulating layer between two superconductors. With current microfabrication technology it is possible to make ve...

We present experimental results of a study of the coherent ground state of two superconducting single-electron transistors (SSET's) that are strongly coupled by a superconducting overlap capacitor. The SSET's have comparable Josephson coupling and charging energy, and we find that in this regime the ground state is a Bell-state-like superposition o...

Applying a small magnetic field to a superconducting loop with Josephson tunnel junctions induces a persistent supercurrent. The persistent current is a collective coordinate for the macroscopic Cooper-pair condensate, and it is only weakly coupled to the solid-state environment. This makes Josephson junction loops excellent systems for a study of...