Vanishing Hall Resistance at High Magnetic Field in a Double-Layer Two-Dimensional Electron System

Abstract

At total Landau level filling factor νtot = 1 a double layer two-dimensional electron system with small interlayer separation supports a collective state possessing spontaneous interlayer phase coherence. This state exhibits the quantized Hall effect when equal electrical currents flow in parallel through the two layers. In contrast, if the currents in the two layers are equal, but oppositely directed, both the longitudinal and Hall resistances of each layer vanish in the low temperature limit. This finding supports the prediction that the ground state at νtot = 1 is an excitonic superfluid.The Hall effect is possibly the most widely observed phenomenon in solid state physics [1]. Owing to the Lorentz force, an ordinary current-carrying conductor in a magnetic field develops a voltage drop V H transverse to both the current I and the field. This Hall voltage is directly proportional to the magnetic field and offers a useful measure of the concentration and sign of the constituent particles responsible for conduction in the material. In more exotic systems the Hall resistance R H = V H /I can deviate strongly from this simple dependence. For example, in two-dimensional electron systems (2DES) R H exhibits ranges of magnetic field over which it is constant and precisely equal to the quantum of resistance h/e 2 divided by either an integer [2] or certain rational fractions [3]. These quantized Hall effects (QHE) reflect the presence of an energy gap in the system, due either to Landau quantization of the cyclotron orbits of the electrons or to the strong interactions between electrons in a partially filled Landau band. In superconductors, where a coherent collective electronic state is present, the Hall resistance vanishes altogether [4].In this paper we report low temperature measurements of the Hall and longitudinal resistances of a double layer 2DES in a strong perpendicular magnetic field B. Our focus is on the situation in which the total electron density N tot of the double layer system is equal to the degeneracy eB/h of a single spin-resolved Landau level produced by the magnetic field. It is well known [5] that in this ν tot = hN tot /eB = 1 case the system possesses an unusual strongly correlated phase when the separation between the two layers is less than a critical value. Owing to interlayer Coulomb interactions the critical layer separation remains non-zero even in the limit of arbitrarily weak tunneling between the layers. In this zero tunneling limit the electron system exhibits a quantized Hall effect [6] with R H = h/e 2 , a dramatically enhanced and sharply resonant zero bias tunneling conductance [7], and exact quantization of the Hall component of Coulomb drag between the layers [8]. It is well-established theoretically that the many-electron state responsible for these phe- nomena possesses an unusual broken symmetry: spontaneous interlayer phase coherence. This collective phase may be viewed in several equivalent ways, including as a Bose condensate of interlayer excitons [9] or a pseudospin f...

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Clausius-Clapeyron relations for first-order phase transitions in bilayer quantum Hall systems

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