Letter pubs.acs.org/NanoLett
Electrostatic Spin Control in InAs/InP Nanowire Quantum Dots Lorenzo Romeo, Stefano Roddaro,*,† Alessandro Pitanti, Daniele Ercolani, Lucia Sorba, and Fabio Beltram NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza S. Silvestro 12, I-56127 Pisa, Italy S Supporting Information *
ABSTRACT: Very robust voltage-controlled spin transitions in few-electron quantum dots are demonstrated. Two lateral-gate electrodes patterned on opposite sides of an InAs/InP nanowire are used to apply a transverse electric field and tune orbital energy separation down to level-pair degeneracy. Transport measurements in this regime allow us to demonstrate the breakdown of the standard alternate up/down spin filling scheme and unambiguously show singlet−triplet spin transitions. The strong confinement of the present devices leads to a large energy gain for the observed anomalous spin configurations that exceeds 4 meV. As a consequence, this behavior is well visible even at temperatures exceeding T = 20 K. KEYWORDS: Nanowire, spin, quantum dot, InAs/InP, Coulomb blockade, high temperature
D
In this Letter, we demonstrate the purely electrostatic control of the spin configuration InAs/InP QDs at temperatures up to 20 K. Well-resolved singlet−triplet transitions will be shown under suitable gating conditions and at zero magnetic field in a configuration where the usual up/down spin-filling scheme breaks down. While electrostatic spin transitions in single fewelectron QDs have been inferred in the past based on Kondo transport at very low temperatures,30 the magnitude of the effect here reported and its electrostatic control make it particularly relevant in the context of the time-resolved investigation of spin physics in semiconductor nanostructures.31 In addition, our results represent a new qualitative step forward in the effective tunability of quantum confined systems based on epitaxial InAs/InP NWs. The structure of the present devices is visible in Figure 1a. SETs were built starting from 45 ± 10 nm diameter InAs/InP nanowires that were deposited on a Si/SiO2 (250 nm thick oxide) substrate and contacted by aligned e-beam lithography. The QD region is defined by a 20 nm long InAs island sandwiched between two epitaxial 5 nm-thick InP barriers (see Supporting Information). Ohmic contacts were fabricated by thermal evaporation of two Ti/Au (10/90 nm) source (S) and drain (D) electrodes (yellow in Figure 1a) located at a nominal
evelopments in semiconductor nanowire (NW) growth1−5 have opened the way to the fabrication of diverse self-assembled nanostructures that are widely impacting research on single-electron devices obtained using homogeneous6,7 and radially8,9 or axially10,11 heterostructured nanosystems,12 on hybrid superconductor-semiconductor devices13−15 and on studies on more exotic fundamental effects.16,17 Moreover the availability of free-standing nanometric heterostructured conductors only loosely constrained by latticematching requirements has led to the realization of a great variety of innovative devices for nanoelectronics18−23 and optoelectronics.24−27 In particular, the InAs/InP heterostructure material system has shown a unique potential for the implementation of strongly confined single-electron transistors (SETs) along the axis of the NW.28 In these structures, population of quantum-dot (QD) states can be controlled down to the last free electron and clear shell structures are routinely observed10,11 at temperatures in excess of 4.2 K. Unfortunately, in these systems QD properties are fully defined during epitaxial growth and in particular electronic states typically display very limited tunability, in any specific QD geometry experimentally realized. Recently, some of us demonstrated that the electronic spectrum of an InAs/InP NW QD can exhibit enhanced tunability by exploiting a transverse electric field29 and that this can much enhance SET working temperatures up to beyond 50 K from the usual ∼10 K offered by this technology. © 2012 American Chemical Society
Received: April 21, 2012 Revised: July 31, 2012 Published: July 31, 2012 4490
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increasing separation between the first two pairs indicated in red). According to the constant interaction model,33,34 CB peaks at VSD ≈ 0 are expected to occur when source and drain electrochemical potentials (μS and μD, respectively) align to the addition energy μN of the N-th electron μN = Ek +
Ne 2 − |e|αavgVavg + c CΣ
(1)
where k labels the first available QD energy level, the lever arm αavg takes into account how the gate bias impacts QD levels for a given geometry, and c is a constant not dependent on N and Vavg. Within this approximation, the voltage separation between two consecutive peaks (ΔVavg) satifies |e|αavgΔVavg = e2/CΣ + ΔE, where ΔE is the energy difference of the levels involved in the transport process through the QD. CB peak pairs in Figure 1c thus correspond to transport resonances involving the spinup and spin-down channels of a same QD shell (ΔE = 0), while the varying separation between the doublets (red arrow in Figure 1c) is a consequence of the change in ΔE as a function of E⊥. The specific energy values were calculated using Vavg values at peak, with αavg = (29 ± 2) mV/V, as estimated from data in Figure 1b. Equation 1 provides a sufficiently accurate description of the data in most experimental conditions, but it is expected to fail when two levels in the QD are brought near degeneracy (ΔE ≈ 0). This is the case of interest here and it is known that direct and exchange Coulomb interactions govern system behavior with a contribution strongly depending on the detailed filling configuration of the QD. As discussed in the seminal work by Tarucha et al.35 and as ultimately expected from Hund’s rule, exchange interaction will indeed tend to favor higher-spin configurations and the partial filling of degenerate levels. In order to better understand this effect, it is helpful to consider the ideal case of a QD hosting two levels εa(x) and εb(x), which cross as a function of some tuning parameter x. Two separate contributions for direct (Cij) and exchange (Kij) Coulomb interactions must be taken into account between two electrons occupying levels i and j as a function of the number of electrons in the system (N). For the QD ground state energy with N = 1, it is simply U = min(εa,εb), but a number of situations can occur at N = 2 depending on the detailed filling configuration. In particular, when the two electrons occupy the same orbital one obtains U1 = 2εa + Caa or U2 = 2εb + Cbb, depending on the specific occupied level. Differently, if both levels a and b are occupied, the QD energy will depend on the spin configuration: U3 = εa + εb + Cab + |Kab| for the S = 0 singlet configuration; U4 = εa + εb + Cab − |Kab| for the S = 1 triplet configuration. Analogously to Hund’s rule in atoms, when εa and εb are sufficiently close the S = 1 configuration is energetically favored with an energy gain at degeneracy Δ1 = Caa − Cab + |Kab| and Δ2 = Cbb − Cab + |Kab|. A summary of these results is shown in Figure 2 which reports the addition energy μN = U(N) − U(N−1) as a function of N and x. The downward cusp in the secondelectron addition energy near orbital degeneracy is a clear deviation from what predicted by eq 1 and corresponds to a transition to a S = 1 configuration with a maximum energy gain Δi with respect to the ordinary up−down spin-filling scheme. Our experimental data show a behavior in line with this picture. Figure 3 reports the experimental evolution of CB peaks as a function of E⊥ (i.e., of the lateral-gate imbalance ΔV). Two unambiguous examples of the impact of orbital degeneracy on spin transitions are visible: the first one at ΔV ≈ 6 V and N = 4
Figure 1. (a) Scanning electron micrograph of one of the studied devices. The heterostructured nanowire is deposited on a SiO2/Si substrate and is contacted by two Ti/Au electrodes (yellow). Two lateral gate nanoelectrodes (blue) can be used to control the electron filling of the heterostructured quantum dot (see overlay and Supporting Information for details) and the applied transverse electric field. (b) Current ISD as a function of bias VSD and lateral gate voltage Vlg1 = Vlg2. (c,d) DC measurements at finite bias VSD = 2 mV: evolution of the Coulomb blockade peaks as a function of the lateral gate imbalance ΔV = Vlg1 − Vlg2 and gate average Vavg = (Vlg1 + Vlg2)/ 2.
distance of 800 nm. A passivation step was performed prior to evaporation in order to remove the native oxide from the NW contact areas; the sample was dipped into a highly diluted (NH4)2Sx water solution heated at 44 °C. Such fabrication step has been shown to be crucial for the realization of lowresistance ohmic contact.32 Two 200 nm wide lateral gate electrodes (blue in Figure 1a) were also fabricated at a nominal relative distance of 250 nm and were aligned with the InAs/InP heterostructure defining the QD. These gates can be used to control the QD electron filling by changing their bias (Vlg1 and Vlg2). Figure 1b shows a typical finite-bias Coulomb blockade (CB) measurement performed on one of the devices studied when the same voltage Vlg1 = Vlg2 is applied to the lateral gates. The estimated charging energy for the QD is e2/CΣ = 13 ± 1 meV, corresponding to a total capacitance CΣ = 12 ± 1aF, a value which is consistent with the geometry of the source and drain barriers in the device. QD shell filling is clearly observed and labeled in the figure. Notably, quantum confinement contributions exceed 10 meV. While the symmetric gating configuration of Figure 1b allows a straightforward control of QD filling, a gate bias imbalance ΔV = Vlg1 − Vlg2 can be used to additionally impose a transverse electric field E⊥ onto the electron island.29 In this latter case, it is useful to consider also the average lateral-gate bias defined as Vavg = (Vlg1 + Vlg2)/2. An example of the effect of E⊥ on QD transport properties is shown in Figure 1c and 1d: CB peaks at VSD = 2 mV (see Figure 1c) occur in pairs that exhibit different energy shifts as a function of the transverse field (colorplot of Figure 1d, note the 4491
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small size of the QDs, the field can be expected to have a negligible effect on the orbitals but to rather couple to the spin degree of freedom. The impact of B was investigated on the two characteristic bias configurations shown by the green and red cross-section overlays in Figure 4a (ΔV = 1.8 V and ΔV =
Figure 2. Expected evolution of the addition energy for two levels crossing as a function of a detuning parameter x. Each line corresponds to one of the four electrons sequentially added in the two nearly degenerate orbitals (εa = εb, at x = 0). Colors correspond to the lowest energy available level (a or b). In the schematic representation the energy maximum energy gain for the triplet configuration with respect to the single one is indicated as Δ1 = Caa − Cab + |Kab| and Δ2 = Cbb − Cab + |Kab|.
Figure 4. Magnetotransport measurement for two selected values of ΔV (overlay bands in panel (a)) corresponding to different spin configurations in the QD at N = 4. Panels (b−c) evolution of the Coulomb peaks as a function of the magnetic field. The standard spin up−down filling sequence observed for ΔV = 1.8 V (red band in panel (a) and color plot in panel (b)) breaks down near the level degeneracy at ΔV = 5.8 V (green band in panel (a) and colorplot in panel (c)), giving rise to a S = 1 ground state.
5.8 V). Note that one is far away from the crossing and one corresponds to the candidate S = 1 configuration. The measurements as a function of B are reported in Figure 4b and Figure 4c. In both panels, for increasing B values the two lowest energy peaks drift and their energy separation increases linearly; this is expected and is a consequence of the Zeeman splitting ΔE = g*μB|B| of the first QD orbital. A different behavior is observed for N > 2. Figure 4b (electronic configuration away from degeneracy) shows a nice example of a standard alternate spin up/down filling sequence, while in Figure 4c the two higher-energy pairs drift while maintaining a constant energy difference (third and fourth, and fifth and sixth CB resonances). This latter behavior is in disagreement with a standard sequential filling of Zeeman-split second and third orbitals. This constant energy distance between two levels indeed indicates that the two electronic levels contributing to the transport have the same spin polarization and thus confirms the presence of a triplet state at N = 4 in Figure 4c. Considering the slope of the observed energy separation between different spin levels as a function of B it is possible to estimate an effective gyromagnetic factor g* = 3.6 ± 0.5. The measured g* value is sizably smaller than the InAs bulk value. Such a deviation is not unexpexcted due to quantum confined effects.36 We also notice that in our case the presence of a strong lateral confinement might have an additional modulation effect on the observed coupling between the spin degree of freedom and the external magnetic field. In conclusion, we have demonstrated that a transverse electric field applied to an InAs/InP NW QD can be exploited to tune the energy separation between electronic orbitals and bring energy levels to degeneracy. This configuration can be used to drive very robust singlet−triplet spin transitions which are well visible up to a temperature of 20 K, as demonstrated by
Figure 3. Evolution of the Coulomb blockade peaks as a function of the lateral gate imbalance ΔV and average voltage Vavg. Two anomalous level crossings are observed for N = 4 and N = 8 at ΔV ≈ 6 V and ΔV ≈ 13 V, respectively. Observed features are consistent with a single-triplet transition driven by exchange interaction, as indicated by the ground state configurations reported on the right side of the colorplot. Measurements were performed at VSD = 2 mV and T = 7 K.
involving second and third QD orbitals and the second one at ΔV ≈ 13 V and N = 8 involving fourth and fifth orbitals. The two double cusps labeling the anomalous filling of the QD are in good agreement with the simple model discussed above and (2) were used to extract an energy gain Δ(1) 1 ≅ Δ1 = (4.4 ± 0.5) (2) meV for the first crossing at N = 4 and Δ1 ≅ Δ(2) 2 = (6.4 ± 0.6) meV for the second one at N = 8. Thanks to these high values of Δ, the experimental features shown in Figure 3 were found to be well visible even at T = 20 K (see Supporting Information). In order to confirm our description in terms of an anomalous spin configuration in the QD, we also measured the transport properties of the devices in the presence of a uniform external magnetic field B applied perpendicularly to the substrate, that is, perpendicular to both E⊥ and the NW axis. Thanks to the 4492
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our magnetotransport measurements. Anyway, beyond this rather remarkable temperature stability, we should like to stress that these transitions are obtained merely by voltage bias and with no need of an external magnetic field. Considering the extremely low stray capacitance that can be obtained with the present device structure,24 we believe that this approach can be very useful for the time-resolved study of few-spin physics in InAs/InP QDs.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Additional information and figures. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail:
[email protected]. Present Address †
Istituto Offcina dei Materiali CNR, Laboratorio TASC, Basovizza (TS), Italy.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge Giovanni Signore for support with chemical passivation of the NWs, Francesca Rossi for the NW pictures reported in the Supporting Information and Massimo Rontani for useful discussions. A.P. acknowledges funding from REA through Marie Curie Actions, project NEMO (ga 298861). The work was partly supported by Monte dei Paschi di Siena through the project “Creazione di un laboratorio per lo sviluppo di nanodispositivi optoelettronici al THz” and by MIUR under PRIN 2009 prot. 2009HS2F7N_003.
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