Coulomb Drag in the Extreme Quantum Limit

Abstract

Coulomb drag resulting from interlayer electron-electron scattering in double layer 2D electron systems in a high magnetic field has been measured. Within the lowest Landau level the observed drag resistance exceeds its zero magnetic value by factors of typically 1000. At half-filling of the lowest Landau level in each layer (n 1͞2) the data suggest that our bilayer systems are much more strongly correlated than recent theoretical models based on perturbatively coupled composite fermion metals.[ S0031-9007(98) PACS numbers: 73.40. Hm, 72.15.Qm, 73.20.Dx Double layer two-dimensional electron systems (2DES) have been the subject of intense recent interest, especially at high magnetic fields, owing to the diversity of manybody phenomena they exhibit which are not found in ordinary single layer systems. These new phenomena arise from the interplay of the intralayer and interlayer Coulomb interactions and the tunneling amplitude in the system. A particularly interesting case arises when the individual 2D layers are at Landau level filling fraction n 1͞2. If the separation between the layers is large, the system behaves as two independent 2DES's, each of which is widely believed to be a Fermi liquidlike state of Chern-Simons composite particles. On the other hand, when the layers are close together, they behave as a single system and exhibit a ferromagnetic quantized Hall state at total Landau filling factor n tot 1͞2 1 1͞2 1. The nature of this remarkable transition from two gapless Fermi liquids to a single gapped quantum Hall phase is not well understood and remains a frontier topic in the field [1].The strength of the Coulomb interaction between electrons in opposite layers is obviously a key ingredient of the physics. Recently a technique has been developed which provides a simple way to directly obtain the interlayer electronic momentum relaxation rate and thereby assess the strength of these critical interactions. In this technique the frictional drag between the two 2DES's is measured by observing the voltage which develops in one layer when a current is driven through the other. This voltage, which exists even though the two layers are electrically isolated, is directly proportional to the interlayer momentum relaxation rate arising from the scattering of electrons in one layer off those in the other. At zero magnetic field drag studies have yielded a quantitative measure of the Coulomb scattering rate between electrons in the two layers [2], provided evidence for momentum relaxation due to the exchange of phonons [3], and revealed the predicted plasmon enhancement of the drag [4][5][6][7]. Recent drag experiments performed in magnetic fields large enough to induce the integer quantized Hall effect have given evidence for the oscillatory screening effects expected from Landau quantization [8,9].In this paper we report the first Coulomb drag results from the extreme quantum limit, focusing especially on the situation where in each 2D layer the lowest Landau level is half-filled. Our measurements show that ...

Coulomb drag

“…Moreover, there is no "Hall drag": the direction of the induced motion of charge carriers in the passive layer is expected to coincide with that of the driving current. These predictions contradict numerous experiments [see, e.g., Eisenstein and MacDonald (2004); Finck et al (2010); Lilly et al (1998); Muraki et al (2004); Nandi et al (2012);and Rubel et al (1997b)] showing that Coulomb drag is not only sensitive to mag-netic field, but in fact the drag resistivity can be greatly enhanced once the field is applied.…”

“…For realistic parameter values similar to those of the experiment of Lilly et al (1998), the drag resistivity (53) is much larger than the zero-field result (21). This fact is associated with the smallness of the typical momenta involved in the interlayer scattering processes and slow relaxation of density fluctuations in the ν = 1/2 state.…”

“…drag at ν = 1/2 is much larger that at B = 0; the temperature dependence in clean samples is subquadratic), theoretical calculations significantly underestimate the overall value of ρ D as compared to the experiment of Lilly et al (1998). Yang (1998) suggested, that the reason for the discrepancy is that the interlayer separation in the samples of Lilly et al (1998) was close to the critical value, where the system forms an incompressible interlayer state (for a detailed discussion of correlated states see Sec. VII).…”

“…In that case, as well as in "cross-talk" measurements in superconductor-insulatornormal-metal trilayers (Giordano and Monnier, 1994), the phenomenological Drude-like description of drag in terms of τ −1 D does not apply. The Drude description also fails when the system is subjected to a strong magnetic field: in contrast to the naive description, numerous experiments Hill et al, , 1998Jörger et al, 2000c;Lok et al, 2001a,b;Patel et al, 1997;Rubel et al, 1997a,b) show significant dependence of the measured drag resistivity ρ D on the applied field, especially in the extreme quantum regime (Lilly et al, 1998). More sophisticated theoretical calculations on Coulomb drag in quantum Hall states (Shimshoni and Sondhi, 1994), superfluid condensates in paired electron-hole layers (Vignale and MacDonald, 1996), drag of composite fermions (Kim and Millis, 1999;Stern, 1997, 1998;Zhou and Kim, 1999), vortex drag (Vitkalov, 1998), nondissipative drag (Rojo and Mahan, 1992), supercurrent drag (Duan and Yip, 1993), as well as drag between charged Bose gases (Tanatar and Das, 1996) and mesoscopic rings (Baker et al, 1999;Shahbazyan and Ulloa, 1997a,b) have confirmed the expectation that the drag resistivity reflects not only the exact character of interlayer interaction, but also the nature of elementary excitations in each layer and their fundamental properties.…”

“…Further experiments demonstrate interesting correlation effects such as Wigner crystallization in quantum wires (Yamamoto et al, 2006(Yamamoto et al, , 2012, exciton formation in electron-hole bilayers , or quantum Hall effect (Girvin and MacDonald, 1997;Lilly et al, 1998), see Sec. VII.A.…”