Studies of the extreme quantum limit of 2D hole systems

We present electrical transport and photoluminecence results for high mobility p-type GaAs/(AIGa)As systems. We observe transitions into an insulating state characterized by an activation energy and a threshold electrical field at a (density-dependent) Landau level filling factor. A new line also appears in the photoluminescence spectr~ at filling factors close to those at which the insulating state occurs. All our observations are similar to those in high mobility 2D electron systems but a larger filling factors as would be expected for a Wigner solid stabilised by the larger Landau level mixing. At sufficiently low temperatures and disorder one expects two-dimensional electrons or holes to form a Wigner solid when rs, the ratio of the Coulombic energy to the Fermi energy is large, rs is proportional to m*n~-1/2 where m* is the effective mass and ns is the carrier number density. Calculation gives a critical value of rs > 37 for zero magnetic field [1]. In the magnetic quantum limit the kinetic energy of the carrier is effectively quenched and a magnetically induced Wigner crystal is predicted to occur below a critical Landau level filling factor v~ ~ 1/6.5 [2] in the limit of small r s. When rs is not small one has significant Landau level mixing which can stabilise the Wigner state leading to a larger v¢ [3]. In Fig. 1 we show a schematic zero temperature phase diagram for two-dimensional carriers drawn to be consistent with the calculated critical rs values for the fractional quantum Hall effect (FQHE~Wigner transition at i3 and 1⁄2 [3] and * Corresponding author. the insulating transitions observed in two-dihaensional electrons [4] and holes [5, 6]. For electrons[ in GaAs/ AIGaAs heterostructure r~ is always small ;ince it is proportional to the effective mass. With incre'ising field (decreasing v) one goes through a series of FQ HE states. Then for v just above i5 and again below ~ a transition into an activated insulating state occurs tl'Lough the FQHE is still the ground state at 4. Coinc:dent with the occurrence of the insulating state a new line in photoluminescence appears. Recently very high quality p-type GaAs/AIGaAs heterostructure and iquantum wells with mobilities in excess of 1 0 6 c m 2 V 1 s 1 have been produced [7, 8]. In such low disordgr samples one expects to see similar behav iour to that observed for electrons except that the r~ ~alues will be about six times higher because of the high effective mass [9]. As indicated in Fig. 1 this opens up the possibility of observing the insulating state ~t large v, re-entrance of the insulating state around othOr fractions and since r~ is inversely proportional to the square 0921-4526,/95/$09.50 ~"~ (~ 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 4 5 2 6 ( 9 4 ) 0 1 0 8 2 X 418 B.L. Gallagher et al. / Physica B 211 (1995) 417~419