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TWO-DIMENSIONAL ELECTRON GAS 2009Temperature effect on Coulomb pseudogap in electron tunneling betweenLandau-quantized two-dimensional gasesThe pseudogap is common effect for the tunnel structureswith two-dimensional layers. It is revealed as in high-T Csuperconductors so in semiconductor heterostructures. Experimentallya pseudogap is observed as a suppression ofthe tunnel current at the low bias voltage [Eisenstein etal., Phys. Rev. Lett. 69, 3804 (1992)] or an additionalhigh voltage shift of the resonant current peak in the I-Vcurve [Popov et al., JETP, 102, 677 (2006)]. In this caseno signature of the gap is revealed in the lateral electrontransport in the two-dimensional electron gas (2DEG). Theorigin of the pseudogap is still under investigation. For examplethere is an inhomogeneneous model [Fogler et al.,Phys. Rev. B, 54, 1853 (1996)], in which a 2DEG is segregatedon two phases with different integer filling factorsdue to the screened Coulomb interactions of the electrons.The electron spectrum is very different in the each phasedue to the different value of exchange enhancement of spinsplittingof the Landau levels (LL). Hence in the averagetunnel spectrum one should to observe two maxima correspondedto the spin-split LL. This model can explain theresonance splitting but not the high-voltage shift of the resonanceobserved in the tunnel junction between 2DEGs withdifferent electron concentrations. In other models the electrontunneling is considered as an instant event comparedwith the energy relaxation of the whole 2DEG. This meansthe tunneling electron should have some extra energy or energyof the pseudogap to organize its relaxation. Severaltypes of the collective relaxations had been considered suchas composite fermion scattering and magnetoroton excitations.The schematic conduction-band-bottom diagram of the tunneldiode is shown in the insert (a) in figure 53 with thequantum subband levels in the 2DEGs. The parametersof the 2DEGs are the following: the concentration of the2DEG with the level E 01 is n 1 = 4×10 11 cm −2 ; the concentrationof the 2DEG with level E 02 is n 2 = 6 × 10 11 cm −2 .The tunnel characteristics were measured at liquid 3 He temperaturesranged from 0.5 K up to 1.5 K. Current peakor the second derivative minimum corresponds to the firstcoherent resonance at the bias voltage V r = 6.5 mV, i.e.,E 01 (V r ) = E 02 (V r ). The second derivative maximum atV s = −14 mV associates with the second resonance, i.e.,E 01 (V s ) = E 12 (V s ). In the magnetic field directed perpendicularthe 2DEG planes the resonant features had beenshifted in voltage position (see square symbols showing positionsV r in figure 53). This voltage shift consists of twopart: first is the single-particle one that can be described inthe single-particle model (see sections of lines in figure 53)and the second part is the pseudogap shift ∆V . The pseudogapshift have been studied at temperature from 0.5 K up to10 K and unexpectable strong temperature dependence hasbeen revealed at the high magnetic field B > 12 T at lowtemperatures T < 2 K. This can be seen from insert (b) infigure 53 where the pseudogap shifts are shown by squaresymbols for T = 1.6 K and by circles for T = 0.5 K. It isinteresting to note that the temperature dependence takesplace at the fields when the cyclotron energy exceeds theintersubband one. This observation is accompanied by thedecreasing of the pseudogap growth (see insert (b) in figure53) and decreasing of the pseudogap shifts of the elasticreplicas. All this facts point on that the psedogap is forminginfluenced by intersubband plasmons. To date there isno theory considering such kind of effects.Figure 53: Topography map of the second current derivative asa function of a bias voltage and magnetic field. The experimentalvalues of the resonant voltage V r are shown as squares. Thevalues calculated in the single-particle model are shown as sectionsof lines. In the insert (a) the diagram of the conduction-bandbottom are shown with levels in the quantum wells. The diagramis shown for zero bias and zero energy corresponds to the Fermilevel. In the insert (b) the pseudogap shift ∆V is plotted versusmagnetic field as squares for T = 1.5 K and circles for T = 0.5 K.S. Wiedmann, J.-C. PortalV.G. Popov (Institute of Microelectronics Technology of RAS, Chernogolovka, Moscow district, Russia)40