Spontaneous Interlayer Phase Coherence Research Articles

Quantum theory of bilayer quantum Hall smectics

Mean-field theory predicts that bilayer quantum Hall systems at odd integer total filling factors can have stripe ground states, in which the top Landau level is occupied alternately by electrons in one of the two layers. We report on an analysis of the properties of these states based on a coupled-Luttinger-liquid description that is able to account for quantum fluctuations of charge-density and position along each stripe edge. The soft modes associated with the broken symmetries of the stripe state lead to an unusual coupled-Luttinger-liquid system with strongly enhanced low-temperature heat capacity and strongly suppressed low-energy tunneling density of states. We assess the importance of the intralayer and interlayer backscattering terms in the microscopic Hamiltonian, which are absent in the Luttinger liquid description, by employing a perturbative renormalization group approach which rescales time and length along but not transverse to the stripes. With interlayer backscattering interactions present the Luttinger-liquid states are unstable either to an incompressible striped state that has spontaneous interlayer phase coherence and a sizable charge gap even at relatively large layer separations, or to Wigner crystal states. Our quantitative estimates of the gaps produced by backscattering interactions are summarized in Fig. 11 by a schematic phase diagram intended to represent predicted experimental findings in very high mobility bilayer systems at dilution refrigerator temperatures as a function of layer separation and bilayer density balance. We predict that the bilayer will form incompressible isotropic interlayer phase-coherent states for small layer separations, say $d<~1.5\mathcal{l}.$ At larger interlayer spacings, however, the bilayer will tend to form one of several different anisotropic states depending on the layer charge balance, which we parametrize by the fractional filling factor $\ensuremath{\nu}$ contributed by one of the two layers. For large charge imbalances $(\ensuremath{\nu}$ far from $1/2),$ we predict states in which anisotropic Wigner crystals form in each of the layers. For $\ensuremath{\nu}$ closer to $1/2,$ we predict stripe states that have spontaneous interlayer phase-coherence and a gap for charged excitations. These states should exhibit the quantum Hall effect for current flowing within the layers and also the giant interlayer tunneling conductance anomalies at low bias voltages that have been observed in bilayers when the $N=0$ Landau level is partially filled. When the gaps produced by backscattering interactions are sufficiently small, the phenomenology observed at typical dilution fridge temperatures will be that of a smectic metal, anisotropic transport without a quantum Hall effect. For stripe states in the $N=2$ Landau level, this behavior is expected over a range of bilayer charge imbalances on both sides of \ensuremath{\nu}=1/2.

Evolution ofν=1bilayer quantum Hall ferromagnet

The natures of the ground state in a ${\ensuremath{\nu}}_{T}=1$ bilayer quantum Hall system at a variety of layer spacing are investigated. At small layer separations the system exhibits spontaneous interlayer phase coherence. It is claimed that the Halperin's (1,1,1) state is not relevant in the incompressible regime near the incompressible to compressible transition point in which the Josephson-like effect was observed. The two-particle correlation function shows the deflated correlation hole at this regime. An effective model that can give a good approximation to the ground state is proposed. A connection to the modified composite fermion theory is discussed.

Quantum-Hall quantum bits

Bilayer quantum Hall systems can form collective states in which electrons exhibit spontaneous interlayer phase coherence. We discuss the possibility of using bilayer quantum dot many-electron states with this property to create two-level systems that have potential advantages as quantum bits.

ZERO-BIAS CONDUCTANCE ANOMALY IN BILAYER QUANTUM HALL SYSTEMS

Bilayer quantum Hall system at total filling factor ν=1 shows a rich variety of broken symmetry ground states because of the competition between the interlayer and intralayer Coulomb interactions. When the layers are sufficiently close, a bilayer system develops spontaneous interlayer phase-coherence that manifests itself through a spectacular enhancement of the zero-bias interlayer tunneling conductance. We present a theory of this tunneling conductance anomaly, and show that the zero-bias conductance is proportional to the square of the quasiparticle tunneling amplitude.

Tunneling current characteristics in bilayer quantum Hall systems

Weakly disordered bilayer quantum Hall systems at filling factor ν=1 show spontaneous interlayer phase coherence if the layers are sufficiently close together. We study the collective modes in the system, the current–voltage characteristics and their evolution with an in-plane magnetic field in the phase-coherent regime.

Strong correlation to weak correlation phase transition in bilayer quantum Hall systems.

At small layer separations, the ground state of a nu = 1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence. The evolution of this state with increasing layer separation d has been a matter of controversy. We report on small system exact diagonalization calculations which suggest that a single-phase transition, likely of first order, separates incompressible states with strong interlayer correlations from compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.

Order parameter suppression in double layer quantum Hall ferromagnets

Double-layer quantum Hall systems at Landau level filling factor ν=1 have a broken symmetry ground state with spontaneous interlayer phase coherence and a gap between symmetric and antisymmetric subbands in the absence of interlayer tunneling. We examine the influence of quantum fluctuations on the spectral function of the symmetric Green's function, probed in optical absorption experiments. We find that as the maximum layer separation at which the ν=1 quantum Hall effect occurs is approached, absorption in the lowest Landau level grows in strength. Detailed line shapes for this absorption are evaluated and related to features in the system's collective excitation spectrum.

Broken-symmetry ground states inν=2bilayer quantum Hall systems

We report on a study of a bilayer two-dimensional electron gas at Landau level filling factor $\nu=2$. The system exhibits both magnetic and spontaneous interlayer phase coherence broken symmetries. We propose a 3-parameter Slater determinant variational wavefunction which describes the ground state over the full range of bias potential ($\Delta_V$) Zeeman coupling ($\Delta_z$) and interlayer tunneling amplitude ($\Delta_t$) strengths. Broken symmetry states occur inside a volume in this three-dimensional phase diagram near the $\Delta_z^2=\Delta_V^2+\Delta_t^2$ surface. We have obtained analytic results for the intersections of the phase diagram with the $\Delta_t=0$, $\Delta_z=0$, and $\Delta_V=0$, planes and show that the differential capacitance of the bilayer system is singular at the phase boundary.

Spontaneous interlayer coherence in double-layer quantum Hall systems: Symmetry-breaking interactions, in-plane fields, and phase solitons.

At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. The system can be mapped to an equivalent system of pseudospin $1/2$ particles with pseudospin-dependent interactions and easy-plane magnetic order. In this paper we discuss how the presence of a weak interlayer tunneling term alters the properties of double-layer systems when the broken symmetry is present. We use the energy functional and equations of motion derived earlier to evaluate the zero-temperature response functions of the double-layer system and use our results to discuss analogies between this system and Josephson-coupled superconducting films. We also present a qualitative picture of the low-energy charged excitations of this system. We show that parallel fields induce a highly collective phase transition to an incommensurate state with broken translational symmetry.

Spontaneous coherence and the quantum Hall effect in triple-layer electron systems.

We investigate spontaneous interlayer phase coherence and the occurrence of the quantum Hall effect in triple-layer electron systems. Our work is based on a simple tight-binding model that greatly facilitates calculations and whose accuracy is verified by comparison with recent experiments. By calculating the ground state in an unrestricted Hartree-Fock approximation and the collective-mode spectrum in a time-dependent Hartree-Fock approximation, we construct a phase diagram delimiting regions in the parameter space of the model where the integer quantum Hall effect occurs in the absence of interlayer tunneling. \textcopyright{} 1996 The American Physical Society.

Correlations, compressibility, and capacitance in double-quantum-well systems in the quantum Hall regime.

In the quantum Hall regime, electronic correlations in double-layer two-dimensional electron systems are strong because the kinetic energy is quenched by Landau quantization. We point out that these correlations are reflected in the way the partitioning of charge between the two layers responds to a bias potential. We report on illustrative calculations based on an unrestricted Hartree-Fock approximation, which allows for spontaneous interlayer phase coherence. The possibility of studying interlayer correlations by capacitive coupling to separately contacted two-dimensional layers is discussed in detail. \textcopyright{} 1996 The American Physical Society.

Spontaneous interlayer coherence in double-layer quantum Hall systems: Charged vortices and Kosterlitz-Thouless phase transitions.

At strong magnetic fields double-layer two-dimensional-electron-gas systems can form an unusual broken symmetry state with spontaneous inter-layer phase coherence. In this paper we explore the rich variety of quantum and finite-temperature phase transitions associated with this broken symmetry. We describe the system using a pseudospin language in which the layer degree-of-freedom is mapped to a fictional spin 1/2 degree-of-freedom. With this mapping the spontaneous symmetry breaking is equivalent to that of a spin 1/2 easy-plane ferromagnet. In this language spin-textures can carry a charge. In particular, vortices carry e/2 electrical charge and vortex-antivortex pairs can be neutral or carry charge e. We derive an effective low-energy action and use it to discuss the charged and collective neutral excitations of the system. We have obtained the parameters of the Landau-Ginzburg functional from first-principles estimates and from finite-size exact diagonalization studies. We use these results to estimate the dependence of the critical temperature for the Kosterlitz-Thouless phase transition on layer separation.