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We present a Floquet scattering theory of electron waiting time distributions in periodically driven quantum conductors. We employ a second-quantized formulation that allows us to relate the waiting time distribution to the Floquet scattering matrix of the system. As an application we evaluate the electron waiting times for a quantum point contact, modulating either the applied voltage (external driving) or the transmission probability (internal driving) periodically in time. Lorentzian-shaped voltage pulses are of particular interest as they lead to the emission of clean single-particle excitations as recently demonstrated experimentally. The distributions of waiting times provide us with a detailed characterization of the dynamical properties of the quantum-coherent conductor in addition to what can be obtained from the shot noise or the full counting statistics., Comment: 4+ pages, 3 figures, 2 pages of Supplemental Material

We analyze a heat engine based on a hot cavity connected via quantum wells to electronic reservoirs. We discuss the output power as well as the efficiency both in the linear and nonlinear regime. We find that the device delivers a large power of about 0.18 W/cm^2 for a temperature difference of 1 K nearly doubling the power than can be extracted from a similar heat engine based on quantum dots. At the same time, the heat engine also has a good efficiency although reduced from the quantum dot case. Due to the large level spacings that can be achieved in quantum wells, our proposal opens the route towards room-temperature applications of nanoscale heat engines., Comment: 13 pages, 4 figures, published version

A double quantum dot coupled to an s-wave superconductor and subject to an inhomogeneous magnetic field can host a pair of zero-energy Majorana fermions when the dot properties are tuned appropriately. Here, we demonstrate the possibility to generate a fractional 4-pi Josephson effect in two such double dots tunnel-coupled to each other. We discuss the robustness of this effect with respect to perturbations away from the special point in parameter space where the uncoupled double dots host Majorana fermions. We demonstrate the possibility to generate Josephson effects with a period of 8-pi and 12-pi in strongly-coupled double dots., Comment: 15 pages, 6 figures, published version

We propose and analyze the use of hybrid microwave cavities as quantum heat engines. A possible realization consists of two macroscopically separated quantum dot conductors coupled capacitively to the fundamental mode of a microwave cavity. We demonstrate that an electrical current can be induced in one conductor through cavity-mediated processes by heating up the other conductor. The heat engine can reach Carnot efficiency with optimal conversion of heat to work. When the system delivers the maximum power, the efficiency can be a large fraction of the Carnot efficiency. The heat engine functions even with moderate electronic relaxation and dephasing in the quantum dots. We provide detailed estimates for the electrical current and output power using realistic parameters., Comment: 5 pages, 3 figures, final version as published in Phys. Rev. Lett

We propose a single-particle source which emits into the helical edge states of a two-dimensional quantum spin Hall insulator. Without breaking time-reversal symmetry, this source acts like a pair of noiseless single-electron emitters which each inject separately into a chiral edge state. By locally breaking time-reversal symmetry, the source becomes a proper single-particle emitter which exhibits shot noise. Due to its intrinsic helicity, this system can be used to produce time-bin entangled pairs of electrons in a controlled manner. The shot noise created by the source is related to the concurrence of the emitted state., Comment: 5 Pages, 3 figures, published version

We analyze the noise properties of both electric charge and heat currents as well as their correlations in a quantum-dot based thermoelectric engine. The engine is a three-terminal conductor with crossed heat and charge flows where heat fluctuations can be monitored by a charge detector. We investigate the mutual influence of charge and heat dynamics and how it is manifested in the current and noise properties. In the presence of energy-dependent tunneling, operating conditions are discussed where a charge current can be generated by heat conversion. In addition, heat can be pumped into the hot source by driving a charge current in the coupled conductor. An optimal configuration is found for structures in which the energy dependence of tunneling maximizes asymmetric transmission with maximal charge-heat cross-correlations. Remarkably, at a voltage that stalls the heat engine we find that in the optimal case the non-equilibrium state is maintained by fluctuations in the heat and charge current only., Comment: 17 pages, 7 figures. Published version

We investigate the current noise correlations at a quantum point contact in a quantum spin Hall structure, focusing on the effect of a weak magnetic field in the presence of disorder. For the case of two equally biased terminals we discover a robust peak: the noise correlations vanish at $B = 0 $ and are negative for $B\not = 0 $. We find that the character of this peak is intimately related to the interplay between time reversal symmetry and the helical nature of the edge states and call it the Z2 peak., Comment: 4+epsilon pages, 3 figures

We propose a nanoscale heat engine that utilizes the physics of resonant tunneling in quantum dots in order to transfer electrons only at specific energies. The nanoengine converts heat into electrical current in a multiterminal geometry which permits one to separate current and heat flows. By putting two quantum dots in series with a hot cavity, electrons that enter one lead are forced to gain a prescribed energy in order to exit the opposite lead, transporting a single electron charge. This condition yields an ideally efficient heat engine. The energy gain is a property of the composite system rather than of the individual dots. It is therefore tunable to optimize the power while keeping a much larger level spacing for the individual quantum dots. Despite the simplicity of the physical model, the optimized rectified current and power is larger than any other candidate nano-engine. The ability to scale the power by putting many such engines into a two-dimensional layered structure gives a paradigmatic system for harvesting thermal energy at the nanoscale. We demonstrate that the high power and efficiency of the layered structure persists even if the quantum dots exhibit some randomness., Comment: 7 pages, 7 figures

We investigate adiabatic and non-adiabatic emission of single particles into an edge state using an analytically solvable dynamical scattering matrix model of an on-demand source. We compare adiabatic and non-adiabatic emissions by considering two geometries: a collider geometry where two emitters are coupled to two different edge states and a series geometry where two emitters are coupled to the same edge state. Most effects observed for adiabatic emitters also occur for non-adiabatic emitters. In particular this applies to effects arising due to the overlap of wave-packets colliding at a quantum point contact. Specifically we compare the Pauli peak (the fermionic analog of the bosonic Hong-Ou-Mandel dip) for the adiabatic and non-adiabatic collider and find them to be similar. In contrast we find a striking difference between the two operating conditions in the series geometry in which particles are emitted into the same edge state. Whereas the squared average charge current can be nullified for both operating conditions, the heat current can be made to vanish only with adiabatic emitters., Comment: 19 pages, 6 figures

Recently demonstrated solid state single electron sources generate different quantum states depending on their operation condition. For adiabatic and non-adiabatic sources we determine the Glauber correlation function in terms of the Floquet scattering matrix of the source. The correlation function provides full information on the shape of the state, on its time-dependent amplitude and phase, which makes the coherence properties of single electron states essential for the production of quantum multi-particle states., Comment: 4+ pages, 4 figures

We consider a quantum dot system whose charge fluctuations are monitored by a quantum point contact allowing for the detection of both charge and transferred heat statistics. Our system consists of two nearby conductors that exchange energy via Coulomb interaction. In interfaces consisting of capacitively coupled quantum dots, energy transfer is discrete and can be measured by charge counting statistics. We investigate gate dependent deviations away from a charge fluctuation theorem in the presence of local temperature gradients (hot spots). Non universal relations are found for state dependent charge counting. A fluctuation theorem holds for coupled dot configurations with heat exchange and no net particle flow., Comment: 6 pages, 3 figures. Published version. Corrected after erratum publication

Localization of the helical edge states in quantum spin Hall insulators requires breaking time reversal invariance. In experiments this is naturally implemented by applying a weak magnetic field B. We propse a model based on scattering theory that describes the localization of helical edge states due to coupling to random magnetic fluxes. We find that the localization length is proportional to B^{2} when B is small, and saturates to a constant when B is sufficiently large. We estimate especially the localization length for the HgTe/CdTe quantum wells with known experimental parameters.

Hamiltonian systems can be classified into ten classes, in terms of the presence or absence of time-reversal symmetry, particle-hole symmetry and sublattice/chiral symmetry. We construct a quantum coherent scattering theory of linear transport for coupled electric, heat and spin transport; including the effect of Andreev reflection from superconductors. We derive a complete list of the Onsager reciprocity relations between transport coefficients for coupled electric, spin, thermoelectric and spin caloritronic effects. We apply these to all ten symmetry classes, paying special attention to specific additional relations that follow from the combination of symmetries, beyond microreversibility. We discuss these relations in several illustrative situations. We show the reciprocity between spin-Hall and inverse spin-Hall effects, and the reciprocity between spin-injection and magnetoelectric spin currents. We discuss the symmetry and reciprocity relations of Seebeck, Peltier, spin-Seebeck and spin-Peltier effects in systems with and without coupling to superconductors., Comment: 14 pages (4 figures) - typos corrected in v2

We investigate a heat- to charge-current converter consisting of a single-level quantum dot coupled to two ferromagnetic metals and one ferromagnetic insulator held at different temperatures. We demonstrate that this nano engine can act as an optimal heat to spin-polarized charge current converter in an antiparallel geometry, while it acts as a heat to pure spin current converter in the parallel case. We discuss the maximal output power of the device and its efficiency., Comment: 6 pages, 4 figures, published version, selected as Editor's choice

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a cross-over from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with energy level statistics and random matrix theory., Comment: 4+ pages, 3 figures

Using scattering theory, we investigate interferometers composed of chiral Majorana fermion modes coupled to normal metal leads. We advance an approach in which also the basis states in the normal leads are written in terms of Majorana modes. Thus each pair of electron-hole states is associated with a pair of Majorana modes. Only one lead Majorana mode couples to the intrinsic Majorana mode whereas its partner is completely reflected. Similarly the remaining Majorana modes are completely reflected but in general mix pair-wise. We demonstrate that the charge current can also be expressed in terms of interference between pairs of Majorana modes. These two basic facts permit a treatment and understanding of current and noise signatures of chiral Majorana fermion interferometry in an especially elegant way. As a particular example of applications, in Fabry-Perot-type interferometers where chiral Majorana modes form loops, resonances (anti-resonances) from such loops always lead to peaked (suppressed) Andreev differential conductances, and negative (positive) cross-correlations that originate purely from two-Majorana-fermion exchange. These investigations are intimately related to current and noise signatures of Majorana bound states.

We investigate the rectification of thermal fluctuations in a mesoscopic on-chip heat engine. The engine consists of a hot chaotic cavity capacitively coupled to a cold cavity which rectifies the excess noise and generates a directed current. The fluctuation-induced directed current depends on the energy asymmetry of the transmissions of the contacts of the cold cavity to the leads and is proportional to the temperature difference. We discuss the maximal power output of the heat engine and its efficiency., Comment: Published version, 8 pages, 4 figures

We analyze the dynamics of a single-level quantum dot with Coulomb interaction, weakly tunnel coupled to an electronic reservoir, after it has been brought out of equilibrium, e.g. by a step-pulse potential. We investigate the exponential decay towards the equilibrium state, which is governed by three time scales. In addition to the charge and spin relaxation time there is a third time scale which is independent of the level position and the Coulomb interaction. This time scale emerges in the time evolution of physical quantities sensitive to two-particle processes., Comment: Version accpeted in PRB

A new type of electron sources has emerged which permits to inject particles in a controllable manner, one at a time, into an electronic circuit. Such single electron sources make it possible to fully exploit the particles' quantum nature. We determine the single-particle coherence length from the decay of the Aharonov-Bohm oscillations as a function of the imbalance of a Mach-Zehnder interferometer connected to a single electron source. The single-particle coherence length is of particular importance as it is an intrinsic property of the source in contrast to the dephasing length., Comment: 4 pages, 4 figures

The distribution of waiting times between elementary tunneling events is of fundamental importance for understanding the stochastic charge transfer processes in nanoscale conductors. Here we investigate the waiting time distributions (WTDs) of periodically driven single-electron emitters and evaluate them for the specific example of a mesoscopic capacitor. We show that the WTDs provide a particularly informative characterization of periodically driven devices and we demonstrate how the WTDs allow us to reconstruct the full counting statistics (FCS) of charges that have been transferred after a large number of periods. We find that the WTDs are capable of describing short-time physics and correlations which are not accessible via the FCS alone., Comment: 4+ pages, 3 figures, final version as published in Phys. Rev. Lett

We review the latest progress in understanding the fundamental noise properties of a coherent single electron emitter known as the mesoscopic capacitor. The system consists of a sub-micron cavity connected to a two-dimensional electron gas via a quantum point contact. When subject to periodic gate voltage modulations, the mesoscopic capacitor absorbs and re-emits single electrons at giga-hertz frequencies as it has been demonstrated experimentally. Recent high-frequency noise measurements have moreover allowed for a precise characterization of the device in different operating regimes. Here we discuss a simple model of the basic charge transfer processes in the mesoscopic capacitor and show how the model is capable of fully reproducing the measured high-frequency noise spectrum. We extend our analysis to the counting statistics of emitted electrons during a large number of periods which we use to discuss the accuracy of the mesoscopic capacitor as a single electron source. Finally, we consider possible applications of the mesoscopic capacitor in future experiments and identify novel pathways for further theoretical research., Comment: 6 pages, 6 figures, Invited contribution to ICNF 2011, Toronto, Canada, June, 2011

Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures. Recently it has been shown that the charge transport statistics for non-interacting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent single-particle events and the zeros of the generating function are real and negative. Here we investigate how the zeros of the generating function move into the complex plane due to interactions and demonstrate that the positions of the zeros can be detected using high-order factorial cumulants. As an illustrative example we consider electron transport through a Coulomb blockade quantum dot for which we show that the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. Our findings are important for understanding the influence of interactions on counting statistics and the characterization in terms of zeros of the generating function provides us with a simple interpretation of recent experiments, where high-order statistics have been measured., Comment: 12 pages, 7 figures, Editors' Suggestion in Phys. Rev. B

We study the correspondence between the non-trivial topological properties associated with the individual valleys of gapped bilayer graphene (BLG), as a prototypical multi-valley system, and the gapless modes at its edges and other interfaces. We find that the exact connection between the valley-specific Hall conductivity and the number of gapless edge modes does not hold in general, but is dependent on the boundary conditions, even in the absence of intervalley coupling. This non-universality is attributed to the absence of a well-defined topological invariant within a given valley of BLG; yet, a more general topological invariant may be defined in certain cases, which explains the distinction between the BLG-vacuum and BLG-BLG interfaces., Comment: 7 pages, 4 figures

To analyze the state of injected carrier streams of different electron sources, we propose to use correlation measurements at a quantum point contact with the different sources connected via chiral edge states to the two inputs. In particular we consider the case of an on-demand single-electron emitter correlated with the carriers incident from a biased normal reservoir, a contact subject to an alternating voltage and a stochastic single electron emitter. The correlation can be viewed as a spectroscopic tool to compare the states of injected particles of different sources. If at the quantum point contact the amplitude profiles of electrons overlap, the noise correlation is suppressed. In the absence of an overlap the noise is roughly the sum of the noise powers due to the electron streams in each input. We show that the electron state emitted from a (dc or ac) biased metallic contact is different from a Lorentzian amplitude electron state emitted by the single electron emitter (a quantum capacitor driven with slow harmonic potential), since with these inputs the noise correlation is not suppressed. In contrast, if quantized voltage pulses are applied to a metallic contact instead of a dc (ac) bias then the noise can be suppressed. We find a noise suppression for multi-electron pulses and for the case of stochastic electron emitters for which the appearance of an electron at the quantum point contact is probabilistic., Comment: Main part: 6 pages, 5 figures. Appendices: 7 pages, 1 figure

A parity meter projects the state of two qubits onto two subspaces with different parities, the states in each parity class being indistinguishable. It has application in quantum information for its entanglement properties. In our work we consider the electronic Mach-Zehnder interferometer (MZI) coupled capacitively to two double quantum dots (DQDs), one on each arm of the MZI. These charge qubits couple linearly to the charge in the arms of the MZI. A key advantage of an MZI is that the qubits are well separated in distance so that mutual interaction between them is avoided. Assuming equal coupling between both DQDs and the arms and the same bias for each DQD, this setup usually detects three different currents, one for the odd states and two for each even state. Controlling the magnetic flux of the MZI, we can operate the MZI as a parity meter: only two currents are measured at the output, one for each parity class. In this configuration, the MZI acts as an ideal detector, its Heisenberg efficiency being maximal. For a class of initial states, the initially unentangled DQDs become entangled through the parity measurement process with probability one., Comment: 9 pages, 2 figures

A periodically driven quantum capacitor may function as an on-demand single electron source as it has recently been demonstrated experimentally. However, the accuracy at which single electrons are emitted is not yet understood. Here we consider a conceptually simple model of a quantum capacitor and find analytically the noise spectrum as well as the counting statistics of emitted electrons. We find that the failure rate of the capacitor can be arbitrarily small when operated under favorable conditions. Our theoretical predictions may be tested in future experiments., Comment: 4 pages, 3 figures, final version as published in Phys. Rev. B Rapid Comm

In the late seventies an increasing interest in the scaling theory of Anderson localization led to new efforts to understand the conductance of systems which scatter electrons elastically. The conductance and its relation to the scattering matrix emerged as an important subject. This, coupled with the desire to find explicit manifestations of single electron interference led to the emergence of mesoscopic physics. We review electron transport phenomena which can be expressed elegantly in terms of the scattering matrix. Of particular interest are phenomena which depend not only on transmission probabilities but on both amplitude and phase of scattering matrix elements., Comment: 21 pages, 5 figures

The transient response of a quantum dot with strong Coulomb interaction to a fast change in the gate potential, as well as the stationary ac-response to a slow harmonic variation of the gate potential are computed by means of a real-time diagrammatic expansion in the tunnel-coupling strength. We find that after a fast switching, the relaxation of charge and spin are governed by a single time constant each, which differ from each other due to Coulomb repulsion. We compare the response to a step potential with the $RC$ time extracted from the ac response., Comment: 5 pages, 3 figures, published version

We propose a mesoscopic circuit in the quantum Hall effect regime comprising two uncorrelated single-particle sources and two distant Mach-Zehnder interferometers with magnetic fluxes, which allows in a controllable way to produce orbitally entangled electrons. Two-particle correlations appear as a consequence of erasing of which path information due to collisions taking place at distant interferometers and in general at different times. The two-particle correlations manifest themselves as an Aharonov-Bohm effect in noise while the current is insensitive to magnetic fluxes. In an appropriate time-interval the concurrence reaches a maximum and a Bell inequality is violated., Comment: 4 pages, 2 figures, published in Phys. Rev. Lett

We consider two driven cavities (capacitors) connected in series via an edge state. The cavities are driven such that they emit an electron and a hole in each cycle. Depending on the phase lag the second cavity can effectively absorb the carriers emitted by the first cavity and nullify the total current or the set-up can be made to work as a two-particle emitter. We examine the precision with which the current can be nullified and with which the second cavity effectively counts the particles emitted by the first one. To achieve single-particle detection we examine pulsed cavities., Comment: 5 pages, 3 figures, published in Phys. Rev. B

We report on the GHz complex admittance of a chiral one dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission-independent. This shows that the relaxation time of a chiral R-L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the c cuit.