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Quasiperiodicity and revivals in dynamics of quantum phase slips in Josephson junction chains and superconducting nanowires

Gianluca Rastelli, Mihajlo Vanević, and Wolfgang Belzig
[abstract; arXiv:1403.4565]

Quantum phase slips in superconducting loops threaded by an external magnetic field provide a coupling between macroscopic quantum states with supercurrents circulating in opposite directions. We analyze the dynamics of the phase slips as a function of the superconducting loop length, from fully coherent dynamics for short loops to dissipative dynamics for the long ones. For intermediate lengths of the superconducting loop, the phase slips are coupled to a discrete bath of oscillators with frequencies comparable to the phase-slip amplitude. This gives rise to a quasiperiodic dynamics of the phase slips which manifests itself as a decay of oscillations between the two counterpropagating current states at short times, followed by oscillation revivals at later times. We analyze possible experimental implications of this non-adiabatic regime in Josephson junction chains and superconducting nanowires.

Transmon-based simulator of nonlocal electron-phonon coupling: a platform for observing sharp small-polaron transitions

Vladimir M. Stojanović, Mihajlo Vanević, Eugene Demler, and Lin Tian
[abstract; arXiv:1401.4783; PRB 89, 144508 (2014)]

We propose an analog superconducting quantum simulator for a one-dimensional model featuring momentum-dependent (nonlocal) electron-phonon couplings of Su-Schrieffer-Heeger and "breathing-mode" types. Because its corresponding vertex function depends on both the electron- and phonon quasimomenta, this model does not belong to the realm of validity of the Gerlach-Loewen theorem that rules out any nonanalyticities in single-particle properties. The superconducting circuit behind the proposed simulator entails an array of transmon qubits and microwave resonators. By applying microwave driving fields to the qubits, a small-polaron Bloch state with an arbitrary quasimomentum can be prepared in this system within times several orders of magnitude shorter than the typical qubit decoherence times. We demonstrate that in this system -- by varying the circuit parameters -- one can readily reach the critical coupling strength required for observing the sharp transition from a nondegenerate (single-particle) ground state corresponding to zero quasimomentum (Kgs=0) to a twofold-degenerate small-polaron ground state at nonzero quasimomenta Kgs and -Kgs. Through exact numerical diagonalization of our effective Hamiltonian, we show how this nonanalyticity is reflected in the relevant single-particle properties (ground-state energy, quasiparticle residue, average number of phonons). The proposed setup provides an ideal testbed for studying quantum dynamics of polaron formation in systems with strongly momentum-dependent electron-phonon interactions.

Graphene's morphology and electronic properties from discrete differential geometry

A. P. Sanjuan, Z. Wang, H. P. Imani, M. Vanević, and S. Barraza-Lopez
[abstract; arXiv:1402.3751; PRB 89, 121403(R) (2014)]

The geometry of two-dimensional crystalline membranes dictates their mechanical, electronic, and chemical properties. The local geometry of a surface is determined from the two invariants of the metric and the curvature tensors. Here we discuss those invariants directly from atomic positions in terms of angles, areas, and vertex and normal vectors from carbon atoms on the graphene lattice, for arbitrary elastic regimes and atomic conformations, and without recourse to an effective continuum model. The geometrical analysis of graphene membranes under mechanical load is complemented with a study of the local density of states (LDOS), discrete induced gauge potentials, velocity renormalization, and nontrivial electronic effects originating from the scalar deformation potential. The asymmetric LDOS is related to sublattice-specific deformation potential differences, giving rise to the pseudomagnetic field. The results here enable the study of geometrical, mechanical, and electronic properties for arbitrarily shaped graphene membranes in experimentally relevant regimes without recourse to differential geometry and continuum elasticity.

Anomalous independence of interface superconductivity from carrier density

J. Wu, O. Pelleg, G. Logvenov, A. T. Bollinger, Y. Sun, G. S. Boebinger, M. Vanević, Z. Radović, and I. Božović
[abstract; Nature Materials 12, 877 (2013)]

The recent discovery of superconductivity at the interface of two non-superconducting materials has received much attention. In cuprate bilayers, the critical temperature (Tc) can be significantly enhanced compared with single-phase samples. Several explanations have been proposed, invoking Sr interdiffusion, accumulation and depletion of mobile charge carriers, elongation of the copper-to-apical-oxygen bond length, or a beneficial crosstalk between a material with a high pairing energy and another with a large phase stiffness. From each of these models, one would predict Tc to depend strongly on the carrier density in the constituent materials. Here, we study combinatorial libraries of La2-xSrxCuO4-La2CuO4 bilayer samples -- an unprecedentedly large set of more than 800 different compositions. The doping level x spans a wide range, 0.15 < x < 0.47, and the measured Hall coefficient varies by one order of magnitude. Nevertheless, across the entire sample set, Tc stays essentially constant at about 40 K. We infer that doping up to the optimum level does not shift the chemical potential, unlike in ordinary Fermi liquids. This result poses a new challenge to theory -- cuprate superconductors have not run out of surprises.

[Interface Superconductivity Withstands Variations in Atomic Configuration]
[Nature Materials cover; Nature Materials News & Views article]

Strain-engineering of graphene’s electronic structure beyond continuum elasticity

S. Barraza-Lopez, A. P. Sanjuan, Z. Wang, and M. Vanević
[abstract; arXiv:1310.3622; Solid State Commun. 166, 70 (2013), fast track article]

We present a new first-order approach to strain-engineering of graphene's electronic structure where no continuous displacement field u(x,y) is required. The approach is valid for negligible curvature. The theory is directly expressed in terms of atomic displacements under mechanical load, such that one can determine if mechanical strain is varying smoothly at each unit cell, and the extent to which sublattice symmetry holds. Since strain deforms lattice vectors at each unit cell, orthogonality between lattice and reciprocal lattice vectors leads to renormalization of the reciprocal lattice vectors as well, making the K and K' points shift in opposite directions. From this observation we conclude that no K-dependent gauges enter in a first-order theory. In this formulation of the theory the deformation potential and pseudo-magnetic field take discrete values at each graphene unit cell. We illustrate the formalism by providing strain-generated fields and local density of electronic states in graphene membranes with large numbers of atoms. The present method complements and goes beyond the prevalent approach, where strain engineering in graphene is based upon first-order continuum elasticity.

Early stages of magnetization relaxation in superconductors

Mihajlo Vanević, Zoran Radović, and Vladimir G. Kogan
[abstract; arXiv:1302.4312; PRB 87, 144501 (2013)]

Magnetic flux dynamics in type-II superconductors is studied within the model of a viscous nonlinear diffusion of vortices for various sample geometries. We find that time dependence of magnetic moment relaxation after the field is switched off can be accurately approximated by \( m(t)\propto 1-\sqrt{t/\tilde\tau} \) in the narrow initial time interval and by \( m(t)\propto (1+t/\tau)^{-1} \) at later times before the flux creep sets in. The characteristic times \( \tilde\tau \) and \( \tau \) are proportional to the viscous drag coefficient \( \eta \). Quantitative agreement with available experimental data is obtained for both conventional and high-temperature superconductors with \( \eta \) exceeding by many orders of magnitude the Bardeen-Stephen coefficient for free vortices. Huge enhancement of the drag, as well as its exponential temperature dependence, indicate a strong influence of pinning centers on the flux diffusion. Notwithstanding complexity of the vortex motion in the presence of pinning and thermal agitation, we argue that the initial relaxation of magnetization can still be considered as a viscous flux flow with an effective drag coefficient.

Control of electron-hole pair generation by biharmonic voltage drive of a quantum point contact

Mihajlo Vanević and Wolfgang Belzig
[abstract; arXiv:1210.7541; PRB 86, 241306(R) (2012)]

A time-dependent electromagnetic field creates electron-hole excitations in a Fermi sea at low temperature. We show that the electron-hole pairs can be generated in a controlled way using harmonic and biharmonic time-dependent voltages applied to a quantum contact and obtain the probabilities of the pair creations. For a biharmonic voltage drive, we find that the probability of a pair creation decreases in the presence of an in-phase second harmonic. This accounts for the suppression of the excess noise observed experimentally [Gabelli and Reulet, arXiv:1205.3638] proving that dynamic control and detection of elementary excitations in quantum conductors are within the reach of the present technology.

Quantum phase slips in superconducting wires with weak inhomogeneities

Mihajlo Vanević and Yuli V. Nazarov
[abstract; arXiv:1108.3553; PRL 108, 187002 (2012)]

Quantum phase slips are traditionally considered in diffusive superconducting wires which are assumed homogeneous. We present a definite estimate for the amplitude of phase slips that occur at a weak inhomogeneity in the wire where local resistivity is slightly increased. We model such a weak link as a general coherent conductor and show that the amplitude is dominated by topological part of the action. We argue that such weak links occur naturally in apparently homogeneous wires and adjust the estimate to that case. The fabrication of an artificial weak link would localize phase slips and facilitate a better control of the phase-slip amplitude.

[selected for Virtual Journal of Nanoscale Science & Technology]

Electron-phonon coupling in graphene antidot lattices: an indication of polaronic behavior

N. Vukmirović, V. M. Stojanović, and M. Vanević
[abstract; arXiv:0909.2179; PRB 81, 041408(R) (2010)]

We study graphene antidot lattices -- superlattices of perforations (antidots) in a graphene sheet -- using a model that accounts for the phonon-modulation of the pi-electron hopping integrals. We calculate the phonon spectra of selected antidot lattices using two different semi-empirical interatomic potentials. Based on the adopted model and the obtained phonon modes, we quantify the nature of charge-carriers in the system by computing the quasiparticle spectral weight due to the electron-phonon interaction for an excess electron in the conduction band. We show that the phonon-induced renormalization is much stronger than in graphene, with the effective electron masses exhibiting an interesting nonmonotonic dependence on the superlattice period for a given antidot diameter. Our study provides an indication of polaronic behavior and points to the necessity of taking into account the inelastic degrees of freedom in future studies of electronic transport in graphene antidot lattices.

[selected as PRB Editors' suggestion]

[selected for Virtual Journal of Nanoscale Science & Technology]

Effects of metallic contacts on electron transport through graphene

S. Barraza-Lopez, M. Vanević, M. Kindermann, and M. Y. Chou
[abstract; arXiv:1001.5257; PRL 104, 076807 (2010)]

We report on a first-principles study of the conductance through graphene suspended between Al contacts as a function of junction length, width, and orientation. The charge transfer at the leads and into the freestanding section gives rise to an electron-hole asymmetry in the conductance and in sufficiently long junctions induces two conductance minima at the energies of the Dirac points for suspended and clamped regions, respectively. We obtain the potential profile along a junction caused by doping and provide parameters for effective model calculations of the junction conductance with weakly interacting metallic leads.

[Georgia Tech research news: Making contact...]

Character of electronic states in graphene antidot lattices: Flat bands and spatial localization

M. Vanević, V. M. Stojanović, and M. Kindermann
[abstract; arXiv:0903.0918; PRB 80, 045410 (2009)]

Graphene antidot lattices have recently been proposed as a new breed of graphene-based superlattice structures. We study electronic properties of triangular antidot lattices, with emphasis on the occurrence of dispersionless (flat) bands and the ensuing electron localization. Apart from strictly flat bands at zero-energy (Fermi level), whose existence is closely related to the bipartite lattice structure, we also find quasi-flat bands at low energies. We predict the real-space electron density profiles due to these localized states for a number of representative antidot lattices. We point out that the studied low-energy, localized states compete with states induced by defects on the superlattice scale in this system which have been proposed as hosts for electron spin qubits. We furthermore suggest that local moments formed in these midgap zero-energy states may be at the origin of a surprising saturation of the electron dephasing length observed in recent weak localization measurements in graphene antidot lattices.

[selected for Virtual Journal of Nanoscale Science & Technology]

Elementary charge-transfer processes in mesoscopic conductors

M. Vanević, Yu. V. Nazarov, and W. Belzig
[abstract; arXiv:0808.3370; PRB 78, 245308 (2008)]

We determine charge-transfer statistics in a quantum conductor driven by a time-dependent voltage and identify the elementary transport processes. At zero temperature unidirectional and bidirectional single-charge transfers occur. The unidirectional processes involve electrons injected from the source terminal due to excess dc bias voltage. The bidirectional processes involve electron-hole pairs created by time-dependent voltage bias. This interpretation is further supported by the charge-transfer statistics in a multiterminal beam-splitter geometry in which injected electrons and holes can be partitioned into different outgoing terminals. The probabilities of elementary processes can be probed by noise measurements: the unidirectional processes set the dc noise level, while bidirectional ones give rise to the excess noise. For ac voltage drive, the noise oscillates with increasing the driving amplitude. The decomposition of the noise into the contributions of elementary processes reveals the origin of these oscillations: the number of electron-hole pairs generated per cycle increases with increasing the amplitude. The decomposition of the noise into elementary processes is studied for different time-dependent voltages. The method we use is also suitable for systematic calculation of higher-order current correlators at finite temperature. We obtain current noise power and the third cumulant in the presence of time-dependent voltage drive. The charge-transfer statistics at finite temperature can be interpreted in terms of multiple-charge transfers with probabilities which depend on energy and temperature.

[selected for Virtual Journal of Nanoscale Science & Technology]

Quantum-entanglement aspects of polaron systems

V. M. Stojanović and M. Vanević
[abstract; arXiv:0808.2632; PRB 78, 214301 (2008)]

We describe quantum entanglement inherent to the polaron ground states of coupled electron-phonon (or, more generally, particle-phonon) systems based on a model comprising both local (Holstein-type) and nonlocal (Peierls-type) couplings. We study this model using a variational method supplemented by the exact numerical diagonalization on a system of finite size. By way of subsequent numerical diagonalization of the reduced density matrix, we determine the particle-phonon entanglement as given by the von Neumann and linear entropies. Our results are strongly indicative of the intimate relationship between the particle localization/delocalization and the particle-phonon entanglement. In particular, we find a compelling evidence for the existence of a nonanalyticity in the entanglement entropies with respect to the Peierls-coupling strength. The occurrence of such nonanalyticity—not accompanied by an actual quantum phase transition—reinforces analogous conclusion drawn in several recent studies of entanglement in the realm of quantum-dissipative systems. In addition, we demonstrate that the entanglement entropies saturate inside the self-trapped region where the small-polaron states are nearly maximally mixed.

[selected as PRB Editors' suggestion]
[selected for Virtual Journal of Nanoscale Science & Technology]

Circuit theory of charge transport in mesoscopic conductors

M. Vanević (PhD Thesis, February 2008, Basel)
[summary; full text; e-Diss@UNI BASEL]

This Thesis is devoted to the circuit theory of mesoscopic transport. The emphasis is put on its extension which provides a method to obtain the complete statistics of the transferred charge. To accomplish this task, several topics have to be combined: a mathematical description of the charge transfer statistics, the scattering approach to mesoscopic transport, and the nonequilibrium Keldysh-Green's function technique. Although the underlying theory is rather complex, the circuit-theory rules which are obtained at the end are in fact very simple. They resemble Kirchhoff's laws for conventional macroscopic conductors, with currents and voltages replaced by their mesoscopic counterparts. An important difference is that the mesoscopic "currents'' and "voltages'' acquire matrix structure, and that the "current''-"voltage'' relation is in general nonlinear. The matrix structure originates from the Keldysh-Green's function formalism which is needed to account for the many-body quantum state of the electrons in the system. The circuit theory is applicable to multiterminal mesoscopic structures with terminals of different types, e.g., normal metals, superconductors, and ferromagnets. The junctions within the structure can be different also, e.g., transparent quantum point contacts, tunnel barriers, disordered interfaces, diffusive wires, etc.
The Thesis is organized as follows. In Chapter I, we provide introductory information on noise. We discuss early experiments on noise in vacuum tubes and the Schottky result which relates the spectral density of current fluctuations and the average current. We summarize some important results on noise in mesoscopic conductors which can be obtained within circuit theory. Chapters II and III are devoted to theoretical prerequisites needed for the circuit theory. In Chapter II, we define the notion of the cumulant generating function and its relation to statistically independent processes. In Chapter III, we introduce the scattering approach to mesoscopic transport and the method of Keldysh-Green's functions. The circuit theory is presented in Chapter IV focusing on the extension which provides complete information on the charge transfer statistics. The method is illustrated by calculation of the transmission distribution in 2-terminal junctions, and by studying current cross correlations in a superconductor-beam splitter geometry. In Chapters V - VII we apply the general template of the circuit theory and obtain the charge transfer statistics in several physical systems of interest: a cavity coupled to a superconductor and a normal terminal, several junctions in series, and a voltage driven mesoscopic junction. The knowledge of the charge transfer statistics enables us to identify the elementary charge transfer processes in these systems. The conclusion is given in Chapter VIII.

Elementary events of electron transfer in a voltage-driven quantum point contact

M. Vanević, Yu. V. Nazarov, and W. Belzig
[abstract; cond-mat/0701282; PRL 99, 076601 (2007)]

We show that the statistics of electron transfer in a coherent quantum point contact driven by an arbitrary time-dependent voltage is composed of elementary events of two kinds: unidirectional one-electron transfers determining the average current and bidirectional two-electron processes contributing to the noise only. This result pertains at vanishing temperature while the extended Keldysh-Green's function formalism in use also enables the systematic calculation of the higher-order current correlators at finite temperatures.

[selected for Virtual Journal of Nanoscale Science & Technology]

Quasiparticle transport in arrays of chaotic cavities

M. Vanević and W. Belzig
[abstract; cond-mat/0605329; EPL 75, 604 (2006)]

We find the distribution of transmission eigenvalues in a series of identical junctions between chaotic cavities using the circuit theory of mesoscopic transport. This distribution rapidly approaches the diffusive wire limit as the number of junctions increases, independent of the specific scattering properties of a single junction. The cumulant generating function and the first three cumulants of the charge transfer through the system are obtained both in the normal and in the superconducting state.

Full counting statistics of Andreev scattering in an asymmetric chaotic cavity

M. Vanević and W. Belzig
[abstract; cond-mat/0412320; PRB 72, 134522 (2005)]

We study the charge transport statistics in coherent two-terminal double junctions within the framework of the circuit theory of mesoscopic transport. We obtain the general solution of the circuit-theory matrix equations for the Green's function of a chaotic cavity between arbitrary contacts. As an example we discuss the full counting statistics and the first three cumulants for an open asymmetric cavity between a superconductor and a normal-metal lead at temperatures and voltages below the superconducting gap. The third cumulant shows a characteristic sign change as a function of the asymmetry of the two quantum point contacts, which is related to the properties of the Andreev reflection eigenvalue distribution.

[selected for Virtual Journal of Applications of Superconductivity]
[selected for Virtual Journal of Nanoscale Science & Technology]

Quasiparticle states in superconducting superlattices

M. Vanević and Z. Radović
[abstract; cond-mat/0502180; EPJB 46, 419 (2005)]

The energy bands and the global density of states are computed for superconductor / normal-metal superlattices in the clean limit. Dispersion relations are derived for the general case of insulating interfaces, including the mismatch of Fermi velocities and effective band masses. We focus on the influence of finite interface transparency and compare our results with those for transparent superlattices and trilayers. Analogously to the rapid variation on the atomic scale of the energy dispersion with layer thicknesses in transparent superlattices, we find strong oscillations of the almost flat energy bands (transmission resonances) in the case of finite transparency. In small-period transparent superlattices the BCS coherence peak disappears and a similar subgap peak is formed due to the Andreev process. With decreasing interface transparency the characteristic double peak structure in the global density of states develops towards a gapless BCS-like result in the tunnel limit. This effect can be used as a reliable STM probe for interface transparency.