S. I. Shevchenko

On electrical phenomena in electroneutral superfluid systems

Keldysh’s theory of a rarefied superfluid electron-hole gas is extended to the case of possible pair polarization. It is established that the complex order parameter Φ(r1,r2), which is the wave function of a pair, satisfies a nonlinear, nonlocal, integrodifferential equation. The equation obtained is solved for the order parameter varying slowly over a distance of the order of the pair size. The dipole-moment density of the system is found from the known function Φ(r1,r2), and it is shown that the inhomogeneity of the system engenders a dipole moment proportional and oriented parallel to the gradient of the particle density. It is determined that an additional dipole moment associated with pair polarization due to the Lorentz force appears in a magnetic field.

Charged vortices in superfluid systems with pairing of spatially separated carriers

It is shown that in a magnetic field the vortices in superfluid electron-hole systems carry a real electrical charge. The charge value depends on the relation between the magnetic length and the Bohr radiuses of electrons and holes. In double layer systems at equal electron and hole filling factors in the case of the electron and hole Bohr radiuses much larger than the magnetic length the vortex charge is equal to the universal value (electron charge times the filling factor).

Interlayer tunneling and the problem of superfluidity in bilayer quantum Hall systems

A possibility of nondissipative transmission of electrical current from the source to the load using superfluid electron-hole pairs in bilayers is studied. The problem is considered with reference to quantum Hall bilayers with the total filling factor VT=1. At nonzero interlayer tunneling the current pattern looks as a sum of uniform planar counterflow currents and Josephson vortices. The difference of electrochemical potentials of the layers (that is required to support the current in the load circuit) causes the motion of the Josephson vortices. In such a situation the second superfluid viscosity comes into play and results in dissipation of energy. It is found that the loss power is proportional to the square of the matrix element of the interlayer tunneling and depends nonlinearly on the load resistance.

Nondissipative drag of superflow in a two-component bose gas

A microscopic theory of a nondissipative drag in a two-component superfluid Bose gas is developed. The expression for the drag current in the system with the components of different atomic masses, densities, and scattering lengths is derived. It is shown that the drag current is proportional to the square root of the gas parameter. The temperature dependence of the drag current is studied and it is shown that at temperature of order or smaller than the interaction energy the temperature reduction of the drag current is rather small. A possible way of measuring the drag factor is proposed. A toroidal system with the drag component confined in two half-ring wells separated by two Josephson barriers is considered. Under certain condition such a system can be treated as a Bose-Einstein counterpart of the Josephson charge qubit in an external magnetic field. It is shown that the measurement of the difference of number of atoms in two wells under a controlled evolution of the state of the qubit allows one to determine the drag factor.

Order parameter phase locking as a cause of a zero bias peak in the differential tunneling conductance of bilayers with electron–hole pairing

In n–p bilayer systems an exotic phase-coherent state emerges due to Coulomb pairing of n-layer electrons with p-layer holes. Unlike Josephson junctions, the order parameter phase may be locked by matrix elements of interlayer tunneling in n–p bilayers. Here we show how the phase locking phenomenon specifies the response of the electron–hole condensate to interlayer voltages. In the absence of an applied magnetic field, the phase is steady-state (locked) at low interlayer voltages, V Vc. The change in the system dynamics at V=Vc gives rise to a peak in the differential tunneling conductance. The peak width Vc is proportional to the absolute value of the tunneling matrix element |T12|, but its height does not depend on |T12|; thus the peak is sharp for small |T12|. An in-plane magnetic field reduces the peak height considerably. The present results are in qualitative agreement with the zero-bias peak behavior that has recently been obse...

On the electric polarization of inhomogeneous superfluid systems

The electric polarization appearing in superfluid systems as a result of their inhomogeneity is studied. The problem is studied using the rarefied electron-hole gas model which the authors studied previously. A microscopic calculation is performed of the polarization of quantum vortices in the absence and presence of a magnetic field. It is established that in the presence of a magnetic field vortices acquire additional polarization, which results in the appearance of a quantized charge in a vortex core. It is shown that the van-der-Waals interaction of a superfluid system with a solid surface gives rise to polarization near the surface. A relation is established between the results obtained and the prediction of possible polarization of the medium in nonuniform motion.

Collective excitations of a two-dimensional interacting Bose gas in external fields

We present a method of finding approximate analytical solutions for the spectra and eigenvectors of collective modes in a two-dimensional system of interacting bosons subjected to a linear external potential or the potential of a special form u(x,y)={mu}-u cosh{sup 2} x/l, where {mu} is the chemical potential. The eigenvalue problem is solved analytically for an artificial model allowing the unbounded density of the particles. The spectra of collective modes are calculated numerically for the stripe, the rare density valley, and the edge geometry and compared with the analytical results. It is shown that the energies of the modes localized at the rare density region and at the edge are well approximated by the analytical expressions. We discuss Bose-Einstein condensation (BEC) in the systems under investigations at T{ne}0 and find that in case of a finite number of the particles the regime of BEC can be realized, whereas the condensate disappears in the thermodynamic limit.

Oscillations of an electron–hole pair condensate in excitonic traps

A superfluid state can arise in bilayer systems as a result of pairing of spatially separated electrons and holes. In the limit of low electron–hole pair density the superfluid state can be described by a nonlinear dynamical equation. In the present paper a microscopic derivation of such an equation for the wave function of the electron–hole pair condensate in a strong magnetic field is presented. This equation is generalized to the cases where an electric field is applied to the system and where the composition of the semiconductor forming conducting layers varies in space. The solution of the dynamical equation gives the frequencies of the characteristic oscillations of the electron–hole pair condensate in excitonic traps produced by electric charge or variation of the composition of the semiconductor.

Charge ordering and interlayer phase coherence in quantum Hall superlattices

The possibility of the existence of states with a spontaneous interlayer phase coherence in multilayer electron systems in a high perpendicular magnetic field is investigated. It is shown that phase coherence can be established in such systems only within individual pairs of adjacent layers, while such coherence does not exist between layers of different pairs. The conditions for stability of a state with interlayer phase coherence against transition to a charge-ordered state are determined. It is shown that in a system with N⩽10 layers there is stability at any value of the interlayer distance d. For N>10 there are two intervals of stability: at sufficiently large and at sufficiently small d. For N→∞ the stability interval in the region of small d vanishes.

Spontaneous interlayer coherence in multilayer electron systems in strong magnetic fields

Abstract It is predicted that in multilayer system which is homogeneous in the direction normal to layers the interaction of electrons from different layers leads to spontaneous breaking of homogeneity in this direction. The alternation of paired and unpaired layers corresponds to the ground state of the system.