Tunneling blockade and single-photon emission in GaAs double quantum wells
M. Yuan A. Hernández-Mínguez K. Biermann P. V. Santos








 
yuan@pdi-berlin.de




 Paul-Drude-Institut für Festkörperelektronik, 
Leibniz-Institut im Forschungsverbund Berlin e. V., 
Hausvogteiplatz 5-7, 10117 Berlin, Germany




             


We report on the selective excitation of single impurity-bound exciton states in a GaAs double quantum well (DQW). The structure consists of two quantum wells (QWs) coupled by  a thin tunnel barrier. The DQW  is subject to a transverse electric field to create spatially indirect inter-QW excitons with electrons and holes located in different QWs. 
We show that the presence of intra-QW charged excitons (trions) blocks carrier tunneling across the barrier to form indirect excitons, thus opening a gap in their  emission spectrum. This behavior is attributed to the low binding energy of the trions.
Within the tunneling blockade regime, emission becomes dominated by processes involving excitons bound to single shallow impurities, which behave as two-level centers  activated by resonant tunneling.  The quantum  nature of the emission is confirmed by the anti-bunched photon emission statistics. The narrow distribution of emission energies (∼ 10 meV) and the electrical connection to the QWs make these single-exciton centers interesting candidates for applications in single-photon sources. 



Valid PACS appear here
                             

                              
Tunneling blockade and single-photon emission in GaAs double quantum wells
    P. V. Santos
    December 30, 2023
==========================================================================





The interplay between resonant tunneling and inter-particle interactions in low-dimensional quantum systems gives rise to interesting phenomena in the transport of single particles. A prototype example is the Coulomb blockade, where repulsive Coulomb interaction blocks the transport through a localized state between two reservoirs. <cit.>  This blockade, which expresses itself as plateaus between steps in the current versus voltage characteristics, is a direct signature of single carrier transport.

In this paper,  we report on an analogous blockade phenomenon during the transport of exciton-related species across a thin tunnel barrier between two semiconductor quantum wells (QWs)   (cf. Fig. <ref>(a)).  Each QW supports intra-QW neutral excitons (denoted here as direct excitons, DX) as well as intra-QW charged excitons (trions, T).  A transverse electric field F_z applied across the double QW (DQW) structure controls the tunneling probability and enables the creation of spatially indirect, inter-QW excitons (IXs) consisting of electrons and holes resident in different QWs (cf. Fig. <ref>(b)). The energy of IX is tunable by F_z due to quantum-confined Stark effect (QCSE). <cit.>
We show that the low binding energy of trions blocks carrier tunneling over a range of applied fields and,  thus, the formation of IX states. 
Unlike Coulomb blockade, which arises from the repulsive interaction between electrons, the tunneling blockade reported here originates from the attractive exciton-carrier interaction leading to trion formation. 
Within the blockade regime, tunneling becomes restricted to resonant processes leading to the excitation of individual excitons bound to shallow impurities. 
These states act as electrically controlled two levels systems: their  quantum nature is evidenced by the anti-bunched photon emission statistics. 
The electric control and narrow distribution of emission energies make these bound-exciton emitters potential candidates for GaAs-based single-photon sources.












The studies were carried out on the (Al,Ga)As structure illustrated in Fig. <ref>(a). The sample was grown by molecular beam epitaxy (MBE) on n-doped GaAs(001) substrate.  The DQW consists of two 16 nm-wide GaAs QWs separated by a 4 nm-thick Al_0.33Ga_0.67As barrier. The DQW is subjected to an electric field F_z generated by a bias voltage  V_b applied between a 10 nm-thick semi-transparent top titanium contact<cit.> and the n-doped substrate. 

The optical studies were carried out at 4.2 K using a microscopic photoluminescence (μ-PL) setup with spatial and spectral resolutions of 0.6 μm and 0.08 meV, respectively.  Figure <ref>(a) displays the bias dependence of the PL intensity I_PL recorded by exciting the sample with a focused  laser beam  (diameter ϕ_L=1.2 μm) and integrating the emission over a 7.5 μm-long and 1 μm-wide slit across the Ti gate. The laser wavelength and power were λ=780 nm (1.59 eV) and P=240 nW, respectively. Further experimental details can be found in the supplementary material (SM), Sec. SM1.
The PL bias map shows the typical spectral lines from DXs, IXs, and Ts.<cit.> The strong trion signal signalizes the availability of free carriers. 
The energy and intensity of T line remain constant over a wide range of biases denoted as FB in Fig. <ref>(a) (i.e., for biases V_b between 0.5 and 1.2 V compensating the built-in potential of the Schottky junction). Within this range, the flow of free carriers between the QWs screens the applied electric field across the DQW structure, thus  inhibiting IX formation.
The transition region between the FB and IX regimes is characterized by an enhanced DX emission together with a reduction of the trion intensity. The latter is attributed to the depletion of free carriers in one of the QWs as these carriers tunnel to and accumulate in  the adjacent QW.<cit.> 
Carrier accumulation in one of the QWs also accounts for the non-linear bias dependence of the IX energy close to the FB-IX transition.<cit.>





More interesting spectral features appear when mapping the FB-IX transition range using a much lower excitation densities, as illustrated in  Fig. <ref>(b). Strikingly, the IX line does not smoothly “branch off” from  the DX and T lines but only appears  for V_b<0.25 V, thus indicating that its formation is blocked within the  bias range BR indicated in the figure. The latter results in a spectral gap between T energy and the onset of the IX emission given by Δ E_B=5.7 meV. 
Furthermore, the IX appearance at V_b∼0.25 V is accompanied by a drastic reduction of the T intensity, which indicates that the IXs result from the dissociation of T states. 
Finally, several sharp emission lines appear in the IX blockade regime BR. These lines can be grouped into two families (labeled as DX^b and IX^b and indicated by the dot-dashed lines in Fig. <ref>(b))  with bias dependence similar to the ones for free DX and IX species, respectively. The energies of the individual lines are typically between 1.5 to 10 meV lower than the T emission.

The observation of multiple sharp lines in Fig. <ref>(b) arises from the integration of the emission over an extended area on the sample surface. Figure <ref>(c) displays a similar bias map recorded by collecting the emission over a much smaller sample area (corresponding to the resolution limit of 0.4 μm^2), where individual lines can be observed (labeled as  D_1 and D_2). The energy distribution of such emission lines cover the typical energy range of excitons bound to shallow impurities. Natural candidates for the impurities are silicon (donor) and carbon (acceptor), which are the most common impurities present in the MBE growth.   Interestingly, these lines mainly appear over the narrow bias range  BR and are generally not present in the IX bias range, where their excitation should  also be energetically favorable. This behavior indicates that these individual states are  excited via a resonant process taking place over a narrow range of biases. 

The correlation between the appearance of bound exciton and IX lines, on the one hand, and the disappearance of T on the other hand, suggests that the former results from dissociation of T, governed by energy conservation. The electric field dependence of the energy E_i of the different excitonic species (i=DX, IX, T)  is summarized in Fig. <ref>(c).[we use electric field instead of bias to take into account screening effects.]  The non-monotonous electric field dependence of E_ IX (F_z)  results from the combined effect of the QCSE  and the electric field dependence of IX binding energy Δ E_ IX. <cit.> Two trion dissociation scenarios involving resonant tunneling and  IX formation can be envisaged. For simplicity, we will consider electron trions  (a similar argument  applies to hole trions). In the first, a trion dissociates via the emission of a free carrier in the same QW (with energy equal to the band gap energy E_g) and the tunneling of the extra electron to form an IX, as indicated by the solid curved arrows in Fig. <ref>(d). Energy conservation  requires that

    E_ T-E_ IX(F_z) ≥ E_ g-E_T=Δ_1.
 IX formation will thus be blocked within an energy range  Δ_1 below the trion energy.
Alternatively,  the free electron of the previous process may form a DX in the presence of a free hole.  In this case, the condition to lift the IX formation blockade reads:

    E_ T-E_ IX(F_z) ≥ E_DX-E_ T=Δ_2.

 Since this process requires a an extra particle, it is expected to be suppressed at low excitation densities.

According to the calculations in  Ref. Takahashi_JAP76_2299_94, the binding energy of DX, Δ E_ DX=E_DX- E_g≈ -5.7 meV for the DQW structure used here. From Fig. <ref>(a), we obtain Δ_2= 1.6 meV, thus yielding Δ _1=7.3 meV. The measured Δ E_B at different laser powers (cf. Fig. <ref> and SM2) typically yield Δ E_B=5± 1 meV, in reasonable agreement with Δ _1 for low excitation densities. At high excitation power and high temperature, the blockade feature cannot be identified anymore (see SM2).

The energy conservation constraint imposed by Eqs. <ref> and <ref> stabilizes trions and opens a gap in the emission spectrum of free IX species.  Within the gap, trions can still be  resonantly converted into lower energy excitons bound to an impurity, e.g. DX^b and IX^b (their energies labeled as E_ DX^b and E_ IX^b, respectively), indicated by the straight arrows in Fig. <ref>(d). We illustrate two possible mechanisms for the conversion. In the first case, the T in one QW dissociates into a free particle and a DX bound to a shallow center in the same QW (DX^b). In the second case, one of the trion particles tunnels across the barrier to form an IX^b bound to a shallow center in the adjacent QW.  (Note that the free particle can also be replaced by a DX if an extra hole is available.) These two processes yield bound species with the bias dependences corresponding to the ones for the DX^b and IX^b states<cit.> indicated by the dot-dashed lines in Fig. <ref>(b) (e.g., both D_1 and D_2 in Fig. <ref>(c) behave as DX^b). 







We now concentrate on the properties of the bound exciton states. Their spatial distribution was determined by spatially resolved PL maps recorded while biasing the structure in the BR, as illustrated in Fig. <ref>(a). The sample was excited by a focused laser spot at y=0 and the emission recorded as a function of the distance from the excitation spot.  In addition to the lines from DX and T, the figure shows localized peaks from two defect centers D_ 1 and D_ 2 at 1530.4 meV  and 1532.7 meV, respectively (the same defects as in Fig. <ref>(c)), which are populated by carriers diffusing from the excitation spot. The shallow centers are typically between 2 to 4 μm apart, thus yielding an areal density  n_d≈ 10^7cm^-2. Figure <ref>(b) displays a cross-section of Fig. <ref>(a) at the position of D_ 1 (maximum emission) at  y=1.4 μm. 
The spectral line shape is fitted by a  Gaussian profile (red) with a full width at half maximum of ħΓ_S=0.26 meV. The latter is significantly narrower than the DX and T linewidths (of 0.42 meV and 0.66 meV, respectively, cf. blue curves).
The temperature dependence of the emission intensity of the bound exciton (see SM3 for details) yields an activation energy E_A comparable to the energy red-shift with respect to T, thus indicating that the decay is caused by thermal dissociation into T. 
The PL intensity and linewidth, however, saturate for temperature lower than 5 K. The line width broadening at 4 K is probably due to charge fluctuation.<cit.>







Information about the internal structure of the bound excitons was obtained from measurements under a magnetic field B_z applied along the DQW growth axis (cf. Fig. <ref>(a)). The field splits the emission peak into a Zeeman doublet with energy splittings Δ E^(z) and average energies increasing  with B_z. The B_z dependence of the doublet energy is summarized by the blue circles in Fig. <ref>(b) and can be expressed as:

    E=Δ E^(d)±1/2Δ E^(z) = e^2/8μ⟨ρ^2⟩ B_z^2 ±1/2 g μ_B B_z.

 Here,  e is the electron charge, μ the in-plane reduced excitonic mass satisfying 1/μ=1/m_e+1/m_hh, where m_e=0.0665  m_0 and m_hh=0.34 m_0 denote the in-plane electron and heavy-hole masses, respectively, and  m_0 is the electron rest mass.<cit.> 
μ_B is the Bohr magneton and g the exciton Landé g-factor, which depends on the corresponding g-factors for holes and electrons.<cit.> The first term on the r.h.s is  the diamagnetic blue-shift Δ E^(d) resulting from the confinement of excitonic wave function by B_z, which depends on the spatial extent of the exciton wave function ρ.<cit.>

The blue dashed lines superimposed on the experimental points are fits to Eq. <ref>, which  yield g=2.2 and ρ=9 nm. This value for the effective exciton radius is in good agreement with the one reported for excitons bound to shallow donors.<cit.>. Figure <ref>(b) also shows the magnetic field dependence of the DX resonance (red squares). Due to the large spectral linewidth, the Zeeman splitting cannot be clearly resolved. From the quadratic dependence of the diamagnetic shifts (cf. Eq. <ref>), we extract an exciton radius of 12 nm. In addition to the quadratic diamagnetic behavior, one also observes small discontinuities in the field dependence, probably due to Landau quantization of the free carriers.





Motivated by the narrow linewidths of the bound excitons as well as their spectral separation from free exciton states, we investigate the bound-excitons' potential as two-level systems emitting  single photons. The two-level characteristic can be inferred by the saturation of emission intensity with increasing laser excitation powers, as indicated by the symbols in Fig. <ref> inset. The solid line is a fit to a model for light scattered by two-level systems<cit.>:


    I_PL=I_0 P/P_0+P.


Here, I_0 is the intensity limit approached at high input power and P_0 is the saturation input power, defined as the input power at which the intensity reaches 1/2I_0. 
The saturation points to a finite number of two-level centers and also  hinders the observation of bound excitons under high excitation power, as observed in Fig. <ref>(a).


In order to confirm the single-photon nature of the emission, we measured the second-order auto-correlation function g^(2)(τ) of the center D_1 of Fig. <ref>(c) using a Hanbury-Brown and Twiss setup. 
The g^(2) histogram in Fig. <ref> shows the characteristic dip at zero delay τ=0, signalizing photon anti-bunching.  
The solid line is a fit to delay dependence of the form g^(2)(τ)=1-(1/N_p) exp (-|τ|/τ_R). The fit yields an average  number of simultaneously emitted photons at zero delay  N_p<0.5,  thus confirming the single-photon nature of the emission. Finally, the fitted decay time constant τ_R=0.8 ns  is  comparable with the values measured for self-assembled  InAs/GaAs QDs.<cit.>

In conclusion, we have reported the selective excitation of  single excitons bound to shallow impurity centers via resonant tunneling in GaAs DQW structures. The observation of these centers becomes possible because of the blockade of carrier tunneling to form intrinsic exciton states over a range of applied electric fields. The latter hinders the formation of IXs, thus opening a gap in the emission spectrum. The PL within this gap is dominated by the dissociation of trions via tunneling process involving excitons bound to isolated shallow impurity centers.  These bound excitons behave as two-level systems emitting single photons, as confirmed by the observation of  anti-bunching in the photon autocorrelation histogram. 


Single-photon emitters based on shallow centers profit from the well-developed semiconductor processing techniques. 
A major advantage of these  centers is the much narrower distribution of emission energies as compared, for instance, to single-photon sources based on self-assembled quantum dots.
In contrast to previously reported impurity-based single-photon emitters on (Al,Ga)As structures,<cit.> these bound excitons  are electrically controlled and can be easily integrated with other  functionalities such as site control and spin injection. 
The electrical control enables the isolation of individual centers by in-situ fabrication of electrostatic gates.<cit.> 
The shallow centers in GaAs DQWs are promising single photon emitters with both optical and electrical controls.





 We thank S. Ludwig  and M. Ramsteiner for many helpful discussions and suggestions. We thank S. Takada, C. Bäuerle, S. Rauwerdink, S. Meister and C. Hubert for support in sample fabrication. We acknowledge financial support from the German Forschungsgemeinschaft, DFG.







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@bib@innerbibempty

[Zeller and Giaever(1969)]Zeller_PR_181_789_69
  author author H. R. Zeller and author I. Giaever, 10.1103/PhysRev.181.789 journal
  journal Phys. Rev. volume 181,  pages 789 (year 1969)NoStop
[Kastner(1992)]Kastner_RMP_64_859_92
  author author M. A. Kastner, 10.1103/RevModPhys.64.849 journal journal Rev. Mod. Phys. volume
  64, pages 849 (year 1992)NoStop
[Miller et al.(1984)Miller,
  Chemla, Damen, Gossard,
  Wiegmann, Wood, and Burrus]Miller_PRL53_1984
  author author D. A. B.  Miller, author D. S.  Chemla, author T. C.  Damen, author A. C. Gossard, author W. Wiegmann,
  author T. H. Wood,  and  author C. A. Burrus,  @noop  journal journal Phys. Rev. Lett.  volume 53, pages 2173 (year
  1984)NoStop
[Chen et al.(1987)Chen,
  Koteles, Elman, and Armiento]Chen_PRB36_1987
  author author Y. J. Chen, author E. S. Koteles,
  author B. S. Elman,  and  author C. A. Armiento,  @noop  journal journal Phys. Rev. B  volume 36, pages 4562 (year
  1987)NoStop
[Huber et al.(1998)Huber,
  Zrenner, Wegscheider, and Bichler]Huber_PSS166_1998
  author author T. Huber, author A. Zrenner,
  author W. Wegscheider,  and  author M. Bichler, @noop
   journal journal Phys. Status Solidi A  volume 166, pages R5 (year
  1998)NoStop
[Rapaport et al.(2005)Rapaport, Chen, Simon, Mitrofanov, Pfeiffer, and Platzman]Rapaport_PRB72_075428_05
  author author R. Rapaport, author G. Chen,
  author S. Simon, author O. Mitrofanov, author
  L. Pfeiffer,  and author
  P. M. Platzman, 10.1103/PhysRevB.72.075428 journal journal Phys.
  Rev. B volume 72, pages 075428
  (year 2005)NoStop
[Hammack et al.(2006)Hammack, Gippius, Yang, Andreev, Butov, Hanson, and Gossard]Hammack_JAP99_66104_06
  author author A. T. Hammack, author N. A. Gippius, author S. Yang,
  author G. O. Andreev, author L. V. Butov, author
  M. Hanson,  and author
  A. C. Gossard, http://dx.doi.org/10.1063/1.2181276 journal journal J. Appl. Phys. volume 99, eid 066104 (year 2006)NoStop
[Schinner et al.(2011)Schinner, Schubert, Stallhofer,
  Kotthaus, Schuh, Rai,
  Reuter, Wieck, and Govorov]Schinner_PRB83__11
  author author G. J. Schinner, author E. Schubert,
  author M. P. Stallhofer,
  author J. P. Kotthaus, author D. Schuh, author
  A. K. Rai, author D. Reuter, author A. D.  Wieck,  and author A. O.  Govorov, @noop  journal journal Phys. Rev. B volume 83, pages 165308 (year 2011)NoStop
[Violante et al.(2014)Violante, Cohen, Lazić, Hey, Rapaport, and Santos]PVS266
  author author A. Violante, author K. Cohen,
  author S. Lazić, author R. Hey, author
  R. Rapaport,  and author
  P. V. Santos, 10.1088/1367-2630/16/3/033035 journal journal
  New J. Phys. volume 16, pages 033035
  (year 2014)NoStop
[Schinner et al.(2013)Schinner, Repp, Kowalik-Seidl,
  Schubert, Stallhofer, Rai,
  Reuter, Wieck, Govorov,
  Holleitner, and Kotthaus]Schinner_PRB87_41303_13
  author author G. J. Schinner, author J. Repp,
  author K. Kowalik-Seidl, author E. Schubert, author
  M. P. Stallhofer, author
  A. K. Rai, author D. Reuter, author A. D.  Wieck, author A. O. Govorov, author A. W. Holleitner,  and author J. P. Kotthaus, @noop  journal journal
  Phys. Rev. B volume 87, pages 041303
  (year 2013)NoStop
[Note1()]Note1
  note We use electric field instead of bias to take into account
  screening effects.Stop
[Takahashi et al.(1994)Takahashi, Kato, Kano, Fukatsu, Shiraki, and Ito]Takahashi_JAP76_2299_94
  author author Y. Takahashi, author Y. Kato,
  author S. S. Kano, author S. Fukatsu, author
  Y. Shiraki,  and author
  R. Ito, @noop  journal journal J. Appl. Phys. volume
  76, pages 2299 (year 1994)NoStop
[Brum et al.(1985)Brum,
  Priester, and Allan]Brum_PRB32_2378_85
  author author J. A. Brum, author C. Priester,   and author G. Allan, 10.1103/PhysRevB.32.2378 journal journal Phys. Rev. B volume 32, pages 2378 (year 1985)NoStop
[Zhao et al.(1992)Zhao,
  Westgaard, Fimland, and Johannessen]Zhao_PRB45_11346_92
  author author Q. X. Zhao, author T. Westgaard,
  author B. O. Fimland,  and  author K. Johannessen, 10.1103/PhysRevB.45.11346 journal journal Phys. Rev. B volume 45, pages 11346 (year 1992)NoStop
[Bayer and Forchel(2002)]Bayer_PRB65_041308_02
  author author M. Bayer and author A. Forchel, 10.1103/PhysRevB.65.041308 journal journal Phys. Rev. B volume
  65, pages 041308 (year 2002)NoStop
[Molenkamp et al.(1988)Molenkamp, Eppenga, 't Hooft, Dawson, Foxon, and Moore]Molenkamp_PRB38_4314_88
  author author L. W. Molenkamp, author R. Eppenga,
  author G. W. 't Hooft, author P. Dawson, author
  C. T. Foxon,  and author
  K. J. Moore, 10.1103/PhysRevB.38.4314 journal journal Phys.
  Rev. B volume 38, pages 4314
  (year 1988)NoStop
[Snelling et al.(1992)Snelling, Blackwood, McDonagh,
  Harley, and Foxon]Snelling92a
  author author M. J. Snelling, author E. Blackwood,
  author C. J. McDonagh, author R. T. Harley,  and author C. T. B. Foxon, @noop 
  journal journal Phys. Rev. B volume 45, pages R3922 (year
  1992)NoStop
[Nash et al.(1989)Nash,
  Skolnick, Claxton, and Roberts]Nash_PRB_39_10943_89
  author author K. J. Nash, author M. S. Skolnick,
  author P. A. Claxton,  and  author J. S. Roberts, 10.1103/PhysRevB.39.10943 journal journal Phys. Rev. B volume 39, pages 10943 (year 1989)NoStop
[Walck and Reinecke(1998)]Walck_PRB_57_9088_98
  author author S. N. Walck and author T. L. Reinecke, 10.1103/PhysRevB.57.9088 journal journal Phys. Rev. B volume
  57, pages 9088 (year 1998)NoStop
[Brozak et al.(1989)Brozak,
  McCombe, and Larsen]Brozak_PRB_40_1265_89
  author author G. Brozak, author B. D. McCombe,
   and author D. M. Larsen,  10.1103/PhysRevB.40.1265 journal journal Phys. Rev. B volume 40, pages 1265 (year 1989)NoStop
[Mollow(1969)]Mollow_PR_188_1969
  author author B. R. Mollow, 10.1103/PhysRev.188.1969 journal
  journal Phys. Rev. volume 188,  pages 1969 (year 1969)NoStop
[Zwiller et al.(2001)Zwiller, Blom, Jonsson, Panev, Jeppesen, Tsegaye, Goobar, Pistol, Samuelson, and  Björk]Zwiller01a
  author author V. Zwiller, author H. Blom,
  author P. Jonsson, author N. Panev, author
  S. Jeppesen, author
  T. Tsegaye, author E. Goobar, author M.-E.  Pistol, author L. Samuelson,  and author B. Björk, @noop  journal journal
  Appl. Phys. Lett. volume 78, pages
  4276 (year 2001)NoStop
[Minari et al.(2012)Minari,
  Cavigli, Sarti, Abbarchi,
  Accanto, Matutano, Bietti,
  Sanguinetti, Vinattieri, and Gurioli]minari2012
  author author S. Minari, author L. Cavigli,
  author F. Sarti, author M. Abbarchi, author
  N. Accanto, author G. M. Matutano, author S. Bietti, author S. Sanguinetti, author A. Vinattieri,  and author M. Gurioli, @noop  journal journal Appl. Phys. Lett. volume 101, pages 172105 (year 2012)NoStop
[Ikezawa et al.(2012)Ikezawa, Sakuma, Zhang, Sone, Mori, Hamano, Watanabe, Sakoda, and Masumoto]Ikezawa2012
  author author M. Ikezawa, author Y. Sakuma,
  author L. Zhang, author Y. Sone, author
  T. Mori, author T. Hamano, author M. Watanabe, author K. Sakoda,  and author Y. Masumoto, @noop  journal
  journal Appl. Phys. Lett. volume
  100, pages 042106 (year 2012)NoStop
[Gschrey et al.(2013)Gschrey, Gericke, Schüßler, Schmidt, Schulze, Heindel, Rodt, Strittmatter, and Reitzenstein]Gschrey_APL102_251113_13
  author author M. Gschrey, author F. Gericke,
  author A. Schüßler, author R. Schmidt, author
  J.-H. Schulze, author
  T. Heindel, author S. Rodt, author A. Strittmatter,  and author S. Reitzenstein, @noop  journal journal
  Appl. Phys. Lett. volume 102, pages
  251113 (year 2013)NoStop











 
  
 
  
 
  





§ SUPPLEMENTARY MATERIAL  FOR:

TUNNELING BLOCKADE AND SINGLE-PHOTON EMISSION IN GAAS DOUBLE QUANTUM WELL STRUCTURES






§ SPECTROSCOPIC EXPERIMENTS



The microscopic photoluminescence (μ-PL) experiments were carried out in a helium bath cryostat at 4.2 K (Attocube Confocal Microscope) with positioning control provided by a piezoelectric stage. The incoming laser with a wavelength of 780 nm  was focused on the sample surface using an objective with numerical aperture of NA∼0.8. The laser energy lies below the band-gap of the Al_0.3Ga_0.7As barriers and thus selectively excites electron hole pairs only in the GaAs QWs. The diameter of the laser spot ϕ_L=1.2 μm sets the spatial resolution to 0.6 μm.
The PL was collected by the same objective and coupled to a monochromator using either a single-mode optical fiber (for confocal measurements) or by a fiber bundle (for spatially resolved measurements). The input slit of the monochromator was selected to yield a spectral resolution of 0.08 meV.  A liquid-nitrogen cooled CCD detector was used to detect the light at the output port of the monochromator. The dimensions of each CCD pixel corresponds to 0.35 μm on the sample.

The photon auto-correlation studies  were carried out using a Hanbury-Brown and Twiss setup. The PL from the shallow center was collected by the objective, filtered by a Semrock band-pass filter with a bandwidth of 810±1.5 nm

and then coupled to a single-mode fiber connected to a 50/50 fiber splitter. The outputs of the fiber splitters were then  sent to a pair of superconducting  single-photon detectors (Single Quantum Eos). The coincidence statistics was  performed by a PicoQuant Picoharp photon counting system with a time bin of 128 ps. 




§ BLOCKADE FEATURE UNDER VARYING POWER AND TEMPERATURE















Spatially integrated PL vs. bias voltage V_b maps were measured at 4.2 K for different laser excitation powers. A few examples are shown in Fig. <ref>. At high excitation power the blockade is no longer visible anymore. The blockade energy Δ E_B is extracted as the energy difference between T and the onset energy of the IX detected when the bias is tuned beyond the flat-band range. We plot Δ E_B for the lowest four excitation power P in Fig. <ref> and find that the blockade stays between Δ _1 and Δ _2 defined by Eqs. 1 and 2 of the main text.

As expected, rising temperature smears out the blockade feature, making it harder to identify, as shown in Fig. <ref>.





§ ACTIVATION ENERGY



By varying the sample temperature T we thermally quench the PL intensity for another bound exciton, D_3 at 1.529 eV, from which we extract the activation energy E_A for its dissociation. The probability of thermal activation obeys the Boltzmann's law


    p∝exp[-E_A/k_BT].

Here, k_B is the Boltzmann constant. The PL quantum efficiency can be expressed as

    η=1/1+ξexp(-E_A/k_BT),


where ξ is a constant. The intensity of PL is proportional to its quantum efficiency, and thus decreases with rising temperature, as can be seen in Fig. <ref>(a).

We can express the inverse of the PL intensity, letting α=1/T,  as

    1/I_PL=A+B exp(-E_A/k_B α),

where A and B are additional constants. By fitting the data with Eq. <ref> (see Fig. <ref>(b)), we extract E_A=6.5 meV, which is comparable with the energy difference between trion T and the defect center D_3, 7 meV.












§ LIST OF ABBREVIATIONS AND SYMBOLS



QW     quantum well

DQW     double quantum well

DX     direct exciton

T     trion

IX     indirect exciton

CB     conduction band

VB     valence band

QCSE       quantum-confined stark effect

MBE     molecular beam epitaxy

PL     photoluminescence

μ-PL     microscopic photoluminescence

SM     supplementary material

FB     flat-band

BR     blockade regime

DX^b     bound exciton with DX-like bias-dependence

IX^b     bound exciton with IX-like bias-dependence

D_1,2,3     individual bound excitons






F_z     transverse electric field

V_b     bias voltage

d_QW     QW thickness

d_b     barrier thickness

ϕ_c     Ti contact diameter

I_PL     PL intensity

ϕ_L     laser spot diameter

λ     laser wavelength

P     laser power

Δ E_B     energy gap between onset of IX and T

E_ IX     IX energy

E_ T    T energy

E_ DX    DX energy

E_g     bandgap energy

Δ E_ IX     IX binding energy relative to bandgap

Δ E_ T-DX     T binding energy relative to DX

Δ E_ DX     DX binding energy relative to bandgap

Δ_1     energy difference between T and bandgap

Δ_2     energy difference between T and DX

n_d     areal density of shallow impurities

Γ_S     spectral linewidth in frequency

Δ E_A     activation energy

Δ E^(d)     diamagnetic energy shift

Δ E^(z)     Zeeman splitting

e     electron charge

μ     reduced excitonic mass

m_e     electron mass

m_hh     heavy hole mass

ρ     extent of exciton wave function

B_z     transverse magnetic field

g     Landé g-factor

μ_B     Bohr magneton

g^(2)     second-order auto-correlation function

τ     time delay

N_p     number of simultaneously emitted photons

τ_R     anti-bunching time constant

Γ_R     anti-bunching linewidth in frequency






