Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane.

We study the Sachdev-Ye-Kitaev (SYK_{4}) model with a weak SYK_{2} term of magnitude Γ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, J/N≪Γ≪J/sqrt[N], fluctuations of the Schwarzian mode are suppressed, and the SYK_{4} mean-field solution remains valid beyond the timescale t_{0}∼N/J up to t_{*}∼J/Γ^{2}. The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2πT, but its prefactor scales as T at low temperatures T≤Γ.

Low-temperature anomaly in disordered superconductors near as a vortex-glass property.

Strongly disordered superconductors in a magnetic field display many characteristic properties of type-II superconductivity-except at low temperatures, where an anomalous linear temperature dependence of the resistive critical field is routinely observed. This behavior violates the conventional theory of superconductivity, and its origin has posed a long-standing puzzle. Here we report systematic measurements of the critical magnetic field and current on amorphous indium oxide films with various levels of disorder.

Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid.

We study stability of the Sachdev-Ye-Kitaev (SYK_{4}) model with a large but finite number of fermions N with respect to a perturbation, quadratic in fermionic operators. We develop analytic perturbation theory in the amplitude of the SYK_{2} perturbation and demonstrate stability of the SYK_{4} infrared asymptotic behavior characterized by a Green function G(τ)∝1/τ^{3/2}, with respect to weak perturbation. This result is supported by exact numerical diagonalization.

Microwave Properties of Superconductors Close to the Superconductor-Insulator Transition.

Strongly disordered pseudogapped superconductors are expected to display arbitrarily high values of kinetic inductance close to the superconductor-insulator transition (SIT), which make them attractive for the implementation of large dissipationless inductance. We develop the theory of the collective modes in these superconductors and discuss associated dissipation at microwave frequencies. We obtain the collective mode spectra dependence on the disorder level and conclude that collective modes become a relevant source of dissipation and noise in the outer proximity of the SIT.

Magnetic field-induced giant enhancement of electron-phonon energy transfer in strongly disordered conductors.

Relaxation of soft modes (e.g., charge density in gated semiconductor heterostructures, spin density in the presence of magnetic field) slowed down by disorder may lead to giant enhancement of energy transfer (cooling power) between overheated electrons and phonons at low bath temperature.

Universal broadening of the Bardeen-Cooper-Schrieffer coherence peak of disordered superconducting films.

In disordered superconductors, the local pairing field fluctuates in space, leading to the smearing of the BCS peak in the density of states and the appearance of the subgap tail states. We analyze the universal mesoscopic contributions to these effects and show that they are enhanced by the Coulomb repulsion. In the vicinity of the quantum critical point, where superconductivity is suppressed by the "fermionic mechanism," strong smearing of the peak due to mesoscopic fluctuations is predicted.

Level statistics of disordered spin-1/2 systems and materials with localized Cooper pairs.

The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. Although small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce a thermal bath and excitation decay. This intrinsic decoherence is manifested by a broadening of energy levels, which aquire a finite width.

Anomalous Josephson current via Majorana bound states in topological insulators.

We propose a setup involving Majorana bound states (MBS) hosted by a vortex on a superconducting surface of a 3D topological insulator (TI). We consider a narrow channel drilled across a TI slab with both sides covered by s-wave superconductor. In the presence of a vortex pinned to such a channel, it acts as a ballistic nanowire connecting the superconducting surfaces, with a pair of MBS localized in it.

Power-law spin correlations in a perturbed spin model on a honeycomb lattice.

We consider the spin-1/2 model on the honeycomb lattice in the presence of a weak magnetic field hα << 1. Such a perturbation destroys the exact integrability of the model in terms of gapless fermions and static Z2 fluxes. We show that it results in the appearance of a long-range tail in the irreducible dynamic spin correlation function: <> ∝ h(z)(2)f(t,r), where f(t,r) ∝ [max(t,r)]-4 is proportional to the density polarization function of fermions.

Quantum spin metal state on a decorated honeycomb lattice.

We present a modification of the exactly solvable spin-(1/)2 Kitaev model on the decorated honeycomb lattice, with a ground state of "spin metal" type. The model is diagonalized in terms of Majorana fermions; the latter form a 2D gapless state with a Fermi circle whose size depends on the ratio of exchange couplings. Low-temperature heat capacity C(T) and dynamic spin susceptibility χ(ω,T) are calculated in the case of small Fermi circle.

Eigenfunction fractality and pseudogap state near the superconductor-insulator transition.

We develop a theory of a pseudogap state appearing near the superconductor-insulator (SI) transition in strongly disordered metals with an attractive interaction. We show that such an interaction combined with the fractal nature of the single-particle wave functions near the mobility edge leads to an anomalously large single-particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.

Superconductivity in disordered thin films: giant mesoscopic fluctuations.

We discuss the intrinsic inhomogeneities of superconductive properties of uniformly disordered thin films with a large dimensionless conductance g. It is shown that mesoscopic fluctuations, which usually contain a small factor 1/g, are crucially enhanced near the critical conductance g(cF) >> 1 where superconductivity is destroyed at T = 0 due to Coulomb suppression of the Cooper attraction. This leads to strong spatial fluctuations of the local transition temperature and thus to the percolative nature of the thermal superconductive transition.

Quantum percolation in granular metals.

Theory of quantum corrections to conductivity of granular metal films is developed for the realistic case of large randomly distributed tunnel conductances. Quantum fluctuations of intergrain voltages (at energies E much below the bare charging energy scale E(C)) suppress the mean conductance g (E) much more strongly than its standard deviation sigma(E). At sufficiently low energies E(*) any distribution becomes broad, with sigma(E(*)) approximately g (E(*)), leading to strong local fluctuations of the tunneling density of states.

Dephasing in disordered metals with superconductive grains.

The temperature dependence of electron dephasing time tau(phi)(T) is calculated for a disordered metal with a small concentration of superconductive grains. Above the macroscopic superconducting transition line, when electrons in the metal are normal, Andreev reflection from the grains leads to a nearly temperature-independent contribution to the dephasing rate. In a broad temperature range tau(-1)(phi)(T) strongly exceeds the prediction of the classical theory of dephasing in normal disordered conductors, whereas magnetoresistance is dominated (in two dimensions) by the Maki-Tompson correction and is positive.

Coulomb blockade of proximity effect at large conductance.

We consider the proximity effect in a normal dot coupled to a bulk superconducting reservoir by the tunnel contact with large normal conductance. Coulomb interaction in the dot suppresses the proximity minigap induced in the normal part of the system. We find exact expressions for the thermodynamic and tunneling minigaps as functions of the junction's capacitance.

Superconducting tetrahedral quantum bits.

We propose a design for a qubit with four superconducting islands in the topology of a symmetric tetrahedron, uniformly frustrated with one-half flux quantum per loop and one-half Cooper pair per island. This structure emulates a noise-resistant spin-1/2 system in a vanishing magnetic field. The flux frustration boosts quantum fluctuations and relieves the constraints on junction fabrication.

Topological order in the insulating Josephson junction array.

We propose a Josephson junction array which can be tuned into an unconventional insulating state by varying external magnetic field. This insulating state retains a gap to half-vortices; as a consequence, such an array with nontrivial global geometry exhibits a ground state degeneracy. This degeneracy is protected from the effects of external noise.

Topologically protected quantum bits using Josephson junction arrays.

All physical implementations of quantum bits (or qubits, the logical elements in a putative quantum computer) must overcome conflicting requirements: the qubits should be manipulable through external signals, while remaining isolated from their environment. Proposals based on quantum optics emphasize optimal isolation, while those following the solid-state route exploit the variability and scalability of nanoscale fabrication techniques. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation, however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task.

Defect-unbinding and the Bose-glass transition in layered superconductors.

The low-field Bose-glass transition temperature in heavy-ion irradiated Bi(2)Sr(2)CaCu(2)O(8+delta) increases progressively with increasing density n(d) of irradiation-induced columnar defects, but saturates for n(d) greater or = 1.5 x 10(9) cm(-2). The maximum Bose-glass temperature corresponds to that above which diffusion of two-dimensional pancake vortices between vortex lines becomes possible, and the "linelike" character of vortices is lost.

Quantum superconductor-metal transition in a proximity array.

A theory of the zero-temperature superconductor-metal transition is developed for an array of superconductive islands (of size d) coupled via a disordered two-dimensional conductor with the dimensionless conductance g = Planck's over 2 pi/e(2)R(square)>>1. At T = 0 the macroscopically superconductive state of the array with lattice spacing b>>d is destroyed at g View Article and Find Full Text PDF