Coherent electron–phonon coupling in tailored quantum systems

ARTICLE Received 17 Nov 2010 | Accepted 16 Feb 2011 | Published 15 Mar 2011 DOI: 10.1038/ncomms1241 Coherent electron–phonon coupling in tailored quantum systems P. Roulleau1, S. Baer1, T. Choi1, F. Molitor1, J. Güttinger1, T. Müller1, S. Dröscher1, K. Ensslin1 & T. Ihn1 The coupling between a two-level system and its environment leads to decoherence. Within the context of coherent manipulation of electronic or quasiparticle states in nanostructures, it is crucial to understand the sources of decoherence. Here we study the effect of electron–phonon coupling in a graphene and an InAs nanowire double quantum dot (DQD). Our measurements reveal oscillations of the DQD current periodic in energy detuning between the two levels. These periodic peaks are more pronounced in the nanowire than in graphene, and disappear when the temperature is increased. We attribute the oscillations to an interference effect between two alternative inelastic decay paths involving acoustic phonons present in these materials. This interpretation predicts the oscillations to wash out when temperature is increased, as observed experimentally. Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland. Correspondence and requests for materials should be addressed to P.R. (email: ). 1 nature communications | 2:239 | DOI: 10.1038/ncomms1241 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved.  ARTICLE nature communications | DOI: 10.1038/ncomms1241 C oherent spin manipulation has already been accomplished in AlGaAs/GaAs double quantum dots (DQDs)1,2 and, more recently, also in InAs nanowires (NWs)3. Although the coherence times are usually limited by random nuclear fields4, also electron–phonon coupling can be a source of decoherence5. InAs NWs and graphene are two alternative and promising materials for achieving coherent spin manipulation. In InAs NW DQDs, spin-orbit interactions are very strong and enable a more efficient electron-spin resonance driven by spin-orbit interaction compared with AlGaAs/GaAs DQDs3. In graphene, it is expected that hyperfine coupling as a source of decoherence is very weak compared with AlGaAs/GaAs. Although electron–phonon interaction effects have been observed in carbon nanotube6,7, AlGaAs/GaAs8, or silicon quantum dots (QDs)9 and in AlGaAs/GaAs DQDs10,11, only little is known about electron–phonon interaction in graphene and InAs NWs. Almost 60 years ago, Dicke12 predicted superradiant and subradiant spontaneous emission, which was observed 40 years later with two trapped ions13. In this experiment, the spontaneous emission rate Γ(R) of a two-ion crystal excited by a short laser pulse was studied as a function of the ion–ion separation R. Superradiant (subradiant) spontaneous emission was observed with Γ(R) > Γ0 (Γ(R) < Γ0), where Γ0 is the emission rate of a single ion. In analogy to the Dicke subradiance phenomenon, Brandes et al.14 later proposed an interference effect due to electron–phonon interactions in a solid-state two-level system (DQD). Our experimental observations are interpreted in this framework. Here, we report on an effect associated with coherent electron–phonon coupling in two entirely different DQD systems and therefore different electronic and phononic environments. The very strong confinement of electronic states in these two materials, in contrast to AlGaAs/GaAs DQDs, has enabled us to observe this coherent coupling, the solid-state analogue of the Dicke subradiance phenomenon. Our measurements show periodic oscillations a in the current through both double dot systems as a function of the energy difference of the levels in the two dots. The energy dependence of these oscillations allows us to infer a coherent coupling between electrons and the phonon field. We find an enhancement of the coherent oscillations in the InAs NW compared with graphene in agreement with dimensional considerations. The temperature at which the experimentally detected oscillations disappear (≈600 mK) clearly supports the relevance of a coherent effect in the coupled electron–phonon system. Finally, this study shows new possibilities for using graphene and InAs NWs as nanoelectromechanical devices and, more specifically, as phonon detectors. Results Observation of periodic oscillations. The two investigated devices are shown in Figure 1a (graphene) and Figure 1b (InAs NW). The current through a DQD is maximal at triple points of the charge stability diagram, in which the electrochemical potentials of both dots are degenerate and aligned with the electrochemical potentials of source and drain15. The schematic configuration of the DQD is illustrated by the energy-level diagram in Figure 1c. In Figure 1d,e, we show the numerical derivative of the current with respect to VCR and VCL, ∂2I/∂VCR∂VCL, for one pair of triple points in each material system. A bias voltage Vbias = 6 mV (graphene) and 2.5 mV (NW) has been applied across the DQDs, which results in a triangular shaped region of allowed transport. Along the baseline of the triangles (in Fig. 1d,e), the two groundstate levels G(1,0) and G(0,1) are aligned and δ = 0. We can roughly estimate the number of electrons in each InAs NW dot to N~30. In graphene, a similar estimation is very difficult as we do not know exactly where the Dirac point is located. For a detuning δ≠0, inelastic transitions are probed: if energy can be exchanged with the environment, a current flows as observed in Figure 1d,e. A striking feature is the presence of periodic peaks parallel to the baseline, indicated by arrows in Figure 1d,e, with a periodicity δ0 = 430 µeV b CL SGM S d CR SGL SGR SGL 70 D c 100 nm CR CL D µL VC (mV) L R γR E(0,1) G(1,0) δ µR G(0,1) SGR –1,023 90 t 200 nm InAs δ VC (mV) γL e Graphene (1,0) S (0,1) –1,027 (0,1) (1,0) –1,031 110 –20 0 VC (mV) L 20 –867 –864 –861 VC (mV) R Figure 1 | Current in graphene and NW DQDs. (a) Schematic representation of the graphene DQD. The two dots are separated by a 30 nm wide constriction and connected to source and drain (in red) by 20 nm wide constrictions. Both constrictions, in blue and green, serve as side gates to control the electrochemical potential of the QDs as well as charge detectors for the QDs. Additional side gates are shaded in grey. (b) Tilted scanning electron microscopy image of the NW DQD. The InAs NW (in red) is deposited on an AlGaAs/GaAs heterostructure with a two-dimensional electron gas 37 nm below the surface. Again, the constrictions in blue and green serve as side gates and as charge detectors. The purple side gates offer additional tunability. Metallic top gates (in yellow) enable us to independently tune the tunnel barriers. (c) Energy-level diagram of the DQD at finite bias for non-zero detuning. (d) Graphene DQD: close-up of one pair of triple points for Vbias = 6 mV at T = 120 mK (axis VCR is upside-down). The numerical derivative of the current wit (...truncated)