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Register a new userTunneling at $ u_T=1$ in Quantum Hall Bilayers
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James P. Eisenstein
Publication date
2013
fields
Physics
and research's language is
English
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Interlayer tunneling measurements in the strongly correlated bilayer quantized Hall phase at $ u_T=1$ are reported. The maximum, or critical current for tunneling at $ u_T=1$, is shown to be a well-defined global property of the coherent phase, insensitive to extrinsic circuit effects and the precise configuration used to measure it, but also exhibiting a surprising scaling behavior with temperature. Comparisons between the experimentally observed tunneling characteristics and a recent theory are favorable at high temperatures, but not at low temperatures where the tunneling closely resembles the dc Josephson effect. The zero-bias tunneling resistance becomes extremely small at low temperatures, vastly less than that observed at zero magnetic field, but nonetheless remains finite. The temperature dependence of this tunneling resistance is similar to that of the ordinary in-plane resistivity of the quantum Hall phase.
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Half-filled Landau levels admit the theoretically powerful fermion-vortex duality but longstanding puzzles remain in their experimental realization as $ u_T=1$ quantum Hall bilayers, further complicated by Zheng et als recent numerical discovery of an unknown phase at intermediate layer spacing. Here we propose that half-filled quantum Hall bilayers ($ u_T=1$) at intermediate values of the interlayer distance $d/ell_B$ enter a phase with textit{paired exciton condensation}. This phase shows signatures analogous to the condensate of interlayer excitons (electrons bound to opposite-layer holes) well-known for small $d$ but importantly condenses only exciton pairs. To study it theoretically we derive an effective Hamiltonian for bosonic excitons $b_k$ and show that the single-boson condensate suddenly vanishes for $d$ above a critical $d_{c1} approx 0.95 l_B$. The nonzero condensation fraction $n_0=langle b(0) rangle ^2$ at $d_{c1}$ suggests that the phase stiffness remains nonzero for a range of $d>d_{c1}$ via an intermediate phase of paired-exciton condensation, exhibiting $langle bb rangle eq 0$ while $langle b rangle =0$. Motivated by these results we derive a $K$-matrix description of the paired exciton condensates topological properties from composite boson theory. The elementary charged excitation is a half meron with $frac{1}{4}$ charge and fractional self-statistics $theta_s=frac{pi}{16}$. Finally we argue for an equivalent description via the $d=infty$ limit through topological charge-$4e$ pairing of composite fermions. We suggest graphene double layers should access this phase and propose various experimental signatures, including an Ising transition $T_{Ising}$ below the Berezinskii-Kosterlitz-Thouless transition $T_{BKT}$ at $d sim d_{c1}$.
The nature of the fractional quantum Hall effect at $ u=1/2$ observed in wide quantum wells almost three decades ago is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which makes the assumption that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, as well two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations suggest that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state supporting non-Abelian excitations. We hope that this will motivate further experimental studies of this state.
I review recent novel experimental and theoretical advances in the physics of quantum Hall effect bilayers. Of particular interest is a broken symmetry state which optimizes correlations by putting the electrons into a coherent superposition of the two different layers.
In this work we report the opening of an energy gap at the filling factor $ u=3+1/3$, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the $ u=3+1/3$ and $3+1/5$ states from the upper spin branch are reversed when compared to the $ u=2+1/3$ and $2+1/5$ counterpart states in the lower spin branch. Our findings raise the possibility that the former states have a non-conventional origin.
Measurements of the Hall and dissipative conductivity of a strained Ge quantum well on a SiGe/(001)Si substrate in the quantum Hall regime are reported. We find quantum Hall states in the Composite Fermion family and a precursor signal at filling fraction $ u=5/2$. We analyse the results in terms of thermally activated quantum tunneling of carriers from one internal edge state to another across saddle points in the long range impurity potential. This shows that the gaps for different filling fractions closely follow the dependence predicted by theory. We also find that the estimates of the separation of the edge states at the saddle are in line with the expectations of an electrostatic model in the lowest spin-polarised Landau level (LL), but not in the spin-reversed LL where the density of quasiparticle states is not high enough to accommodate the carriers required.
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