St.Petersburg

1. St.Petersburg

2. Peculiarities of electrical transport in split-off impurity bands in modulated doped 2D p-GaAs/AlGaAs heterostructuresN. V. Agrinskaya In collaboration with: V. I. Kozub, Y. M. Galperin, D. V. Poloskin, A. V. Chernyaev, and D. V. ShamshurIoffe Physico-Technical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia 1.Agrinskaya N.V., Kozub V.I., Chernyaev A.V., Shamshur D.V. Manifestation of Coulomb gap in two-dimensional p-GaAs/AlGaAs structures with filled lower or upper Hubbard bands. Phys. Stat. Sol. (c) v.1, p.121-125 (2004) 2. N.V.Agrinskaya, V.I.Kozub, A. Chernyaev, D.V Shamshur Magnetoresistance of p-GaAs/AlGaAs structuresin the vicinity of metal-insulator transition: Effect of superconducting leads. Phys.Rev.B, v.72, p.085337, (2005) 3. N. V. Agrinskaya, V. I. Kozub, D. V. Poloskin, A. V. Chernyaev, and D. V. Shamshur Crossover from Strong to Weak Localization in the Split-Off Impurity Band in Two Dimensional p-GaAs/AlGaAs Structures Phys.stat.sol. (C), v.3, p.329, (2006) 4. N. V. Agrinskaya, V. I. Kozub, D. S. Poloskin, D.V.Shamshur, A.V.Chernyaev Evidences of the virtual Anderson transition in a narrow impurity band of p -GaAs/AlGaAs quantum wells: ε4 conductivity and electric breakdown at low temperatures Phys. Stat. Sol. (C), v.5, p.233, (2008) 5. N. V. Agrinskaya, Y.M.Galperin,V. I. Kozub, D.V.Shamshur Anomalous electron transport in dopeduncompensated p-GaAs/AlGaAs quantum wells: Evidence of virtualAnderson transition. ArXiv: 0710.1225v1 [Cond-mat] 5 Okt.(2007) Phys. Rev.B (in consideration)

3. Metal-insulator transition in bulk matherials: at small dopant concentration N the resistance exponentially increases with temperature decrease (insulating phase),- hopping conductivity at large N > 1018 cm-3– conductance slightlyincrease with T decrease and at T= 0 is finite-metallic behavior. That is a phase transition with the parameter N (3D)

4. As it is known, the electron interference tends to localize the electrons (emphasizes the role of trajectories returning to the starting point) – so called weak localization (decrease of conductance with temperature decrease). 1D- all states are localized 2D : the return probability increases, localization increases and there is no real MIT in 2D σ(T=0)→0 (According to scaling theory of localization with no interactions) However for high mobility samples metallic behavior of σ(T) was observed at low temperatures (Kravchenko, Pudalov) The nature is still not undrestood correctly and the nature of metallic state is not clear. Some explanations – this metallic behavior of σ(T) is related to property of disorder…but the nature of disorder for these samples is not known. Challenging problem – understanding MIT in 2D or quasi-2D devices

5. A productive approach to the problem is to start from the systems with well known disorder. This situation can be the case in a quantum well with selectively doped central part well and barrier. We report our studies of electrical transport in GaAs-AlGaAs quantum wells close to metal-insulator transition. For these doped samples only a crossover from strong to weak localization takes place: SL→ WL was observed in many structures when impurity concentration N>>Nc, ; Nca,2~0,15 -Mott . Thus in highly doped 2D samples we should discriminate between 2 regions depending on N: 1. SL region, where exponential σ(T) is observed 2. WL region where slow logaritmic dependence σ(T) is observed at low T. σ(T=0)→0

6. Problem 1- what are the evidences of the crossover from strong to weak localization for 2D- in addition to σ(T)?Problem 2- where the crossover takes place? Does IB merge with CB or it is still split-off after the transition? • Peculiarities of electrical transport in doped 2D structures : 1. The modulation doping allows in equilibrium to occupy impurity centers by one (doped only center of well-A0 ) or two carriers (doped both center of well and barriers- A+)– the latter is impossible in 3D.2.The lateral quantization leads to the lower energy position of the doubly-occupied state which allows for it to be splitted from the allowed band. For 3D case this doubly-occupied state merges with allowed band at some concentration of impurity.

7. In 2D structures binding energies of single- and double occupied impurity states increase due to lateral quantization. • This effect is more pronounced for doubly occupied states. • For A+ centers in p-GaAs/AlGaAs we have shown that its binding energy is not small and increases with a decrease of the well width (Hall and photoluminescence data, Agrinskaya et.al 2001, 2003; theory Averkiev et.al. 2003 ). theory Exp.data Hall, photoluminescence

8. Samples • Doped GaAs/Al0,3GaAs, 1-10 well (10 and 15 nm) and barriers (25-100 nm). Shallow acceptor Be (E0=28 and 30 meV for these well width). Two sorts of doping: 1 - only center wells (A0) –one hole per acceptor 2 - center wells and barriers (A+) – about two holes per acceptorE+ =7 and 10 meV for these well width Holes from the barriers fall to well

9. We observed a crossover from SL to WL for samples with A+→WL at N>6 1017cm-3 (curves 2,1)

10. Low T behavior of conductivity is in accordance to scaling theory of localization Where Lφ– phase breaking length for e-e scattering in 2D

11. According to scaling theory of localization at low T and H MR should be positive due to s-o scattering in p-GaAs (antilocalization) and negative at high H.It is completely different from MR for samples in SL regime.The latter Is negative due to interference effects for VRH conductivity.So the change of the MR sign with increasing N evidences the crossover from SL to WL regime. WL SL

12. Shubnicov de Haas oscillation observed for samples in WL region at low temperatures (0,6K) – this is signature of Fermi statistic in the metallic states.

13. Where the conductivity in WL region takes place? In conduction or impurity band? • With T increase →activation behavior both for Hall effect and conductivity, E~10 meV. Hall curve has a maximum. • We use 2-band model: • IB +VB (with higher μ )

14. Indirect estimate of mib For scattering by charged impurities (T<100K) τ~ε

15. 1. We observed crossover SL-WL with increase of impurity concentrations in modulated doped (A+) quantum wells- this is the Anderson transition in the Upper Hubbard band • Evidences: logarithmic T-dependence of conductivity; change of magnetoresistivity sign, SdH oscillation, change tunnel contact MR. • 2. WL takes place in split-off upper Hubbard impurity band. • Evidences: Activation behavior of conductivity at high T, • Maximum in T-dependence of Hall effect, • Large value of effective mass.

16. The specific feature of non-compensated intentionaly doped 2D structure is that the compensation is by background defects situated far from doped layer. As a result, rare charged defects are far from each other and the disorder potential is weak. Correspondingly, the impurity band is narrow and thus the typical interlevel spacing is much less than in typical 3D structure. Since the existence of delocalized states depends on the interlevel spacing, one expects that the delocalization of the states in Anderson sense starts at lower concentration than typical for 3D structures. At the same time, the Hubbard energy does not depend on disorder and at the concentration allowing Anderson delocalization of the single-particle states it’s double occupation is not allowed (in contrast to 3D case where the criteria of Anderson and Mott transition nearly coincide). For occupied lower band (A0) “Virtual Anderson Transition” Is observed.

17. Virtual Anderson transition Mott transition / c К<<1 Fermi level is in the IB Fermi level is in the center of Hubbard gap and coincide with mobility edge in A+ band. v v Thus in this Anderson-delocalized band there is no transition to real metallic state. Charge transport due to the delocalized states can exist only due to activation to these states of the “minority carriers” – electrons (existing due to the background compensation) from the Fermi level. c

18. Temperature dependences of conductivity and Hall mobility for samples with low impurity concentration demonstrated variable range hopping.

19. Temperature dependences of conductivity and Hall mobility for samples with high impurity concentrationdemonstrated activated behavior of resistance-e4and increasng of mobility mh with temperature decrease. e4~2-3 meV Is due to acoustic phonon scattering in 2D, (Carpus,1986)

20. Low-temperature transport in very weak fields (~3V/cm) and extremely weak currents (0.1 nA) exhibits a strong non-linearity of breakdown type with S-shaped I-V curve. Such IV curves were never observed for hopping conductivity. We explain this behavior by impact ionization of localized minority carriers (electrons) to the band of delocalized states with high enough mobility. We estimated the breakdown field as 10 V/cm. To compare: breakdown of 3D sample with deep Be dopant takes place at fields of several hundred V/cm

21. We have an unique possibility to find the parameters of these carriers - sign of charge and total concentration (equal to the concentration of the background compensating defect) by studies of the Hall coefficient for this excited metallic state.The results of corresponding studies the sign of the Hall coefficient at 300 K is opposite to its sign at small temperatures.The concentration estimated from the Hall coefficient at low temperatures appears to be 2-3 orders lower than at T = 300 K which gives an estimate of the total concentration of the electrons as 2-3 order lower than the dopant concentrations N~109cm-2 P~1012cm-2

22. The observed dependences of the conductance and Hall effect on temperature and applied voltage confirm the existence of a band of extended states in the narrow impurity band. Since the Fermi level is located below this band, the low-temperature transport is due activation of minority carriers to this band. Both the activation energy and threshold voltage for non-Ohmic behavior are anomalously small. This scenario, which we call the virtual Anderson transition, seems to be typical for relatively strongly doped intentionally non-compensated 2D materials. At larger dopant concentrations this scenario is supressed due to increase of disorder over to the conventional Mott-Anderson transition. BES

23. Conclusions 1) For occupied upper Hubbard band (A+) (resulting from the doping of both wells and barriers) we observed a crossover SL-WL (from insulator to dirty metal) with an increase of doping. The crossover took place when the impurity band was still splitted from the valence band 2) For the occupied lower band (A0) with no intentional compensation we observed only virtual Anderson transition (where a presence of extended states does not support metallic conductivity). The transition was evidenced by a weak activation behavior of conductance, by different signs of Hall coefficient for high temperature and low temperature regions and by electric breakdown at extremely low electric fields and currents.