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See detailNon-Abelian parafermions in time-reversal invariant interacting helical systems
Orth, Christoph P.; Tiwari, Rakesh P.; Meng, Tobias et al

in Phys. Rev. B (2015), 91

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical ... [more ▼]

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of $e/2$, giving rise to a Josephson current with $8\pi$ periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as $Z_4$ parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems. [less ▲]

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See detailElectron transport in multiterminal networks of Majorana bound states
Weithofer, Luzie; Recher, Patrik; Schmidt, Thomas UL

in Phys. Rev. B (2014), 90

We investigate electron transport through multiterminal networks hosting Majorana bound states (MBS) in the framework of full counting statistics. In particular, we apply our general results to T-shaped ... [more ▼]

We investigate electron transport through multiterminal networks hosting Majorana bound states (MBS) in the framework of full counting statistics. In particular, we apply our general results to T-shaped junctions of two Majorana nanowires. When the wires are in the topologically nontrivial regime, three MBS are localized near the outer ends of the wires, while one MBS is localized near the crossing point, and when the lengths of the wires are finite adjacent MBS can overlap. We propose a combination of current and cross-correlation measurements to reveal the predicted coupling of four Majoranas in a topological T junction. Interestingly, we show that the elementary transport processes at the central lead are different compared to the outer leads, giving rise to characteristic nonlocal signatures in electronic transport. We find quantitative agreement between our analytical model and numerical simulations of a tight-binding model. Using the numerical simulations, we discuss the effect of weak disorder on the current and the cross-correlation functions. [less ▲]

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See detailJosephson effect in normal and ferromagnetic topological-insulator junctions: Planar, step, and edge geometries
Nussbaum, Jennifer; Schmidt, Thomas UL; Bruder, Christoph et al

in Phys. Rev. B (2014), 90

We investigate Josephson junctions on the surface of a three-dimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface ... [more ▼]

We investigate Josephson junctions on the surface of a three-dimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface states of the topological insulator results in a scaling factor in the Josephson current in a step junction as compared to the planar junction. In edge junctions, the contribution of the Andreev bound states to the Josephson current vanishes due to spin-momentum locking of the surface states. Furthermore, we consider a junction with a ferromagnetic insulator between the superconducting regions. In these ferromagnetic junctions, we find an anomalous finite Josephson current at zero phase difference if the magnetization is pointing along the junction (and perpendicular to the Josephson current). An out-of-plane magnetization with respect to the central region of the junction opens up an exchange gap and leads to a nonmonotonic behavior of the critical Josephson current for sufficiently large magnetization as the chemical potential increases. [less ▲]

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See detailStructure factor of interacting one-dimensional helical systems
Gangadharaiah, Suhas; Schmidt, Thomas UL; Loss, Daniel

in Phys. Rev. B (2014), 89

We calculate the dynamical structure factor $S(q,\omega)$ of a weakly interacting helical edge state in the presence of a magnetic field $B$. The latter opens a gap of width $2B$ in the single-particle ... [more ▼]

We calculate the dynamical structure factor $S(q,\omega)$ of a weakly interacting helical edge state in the presence of a magnetic field $B$. The latter opens a gap of width $2B$ in the single-particle spectrum, which becomes strongly nonlinear near the Dirac point. For chemical potentials $|\mu|>B$, the system then behaves as a nonlinear helical Luttinger liquid, and a mobile-impurity analysis reveals power-law singularities in $S(q,\omega)$ which depend on the interaction strength as well as on the spin texture of the edge states. For $|\mu|<B$, the low-energy excitations are gapped, and we determine $S(q,\omega)$ by using an analogy to exciton physics. [less ▲]

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See detailPoint contacts and localization in generic helical liquids
Orth, Christoph P.; Strübi, Grégory; Schmidt, Thomas UL

in Phys. Rev. B (2013), 88

We consider two helical liquids on opposite edges of a two-dimensional topological insulator, which are connected by one or several local tunnel junctions. In the presence of spatially inhomogeneous ... [more ▼]

We consider two helical liquids on opposite edges of a two-dimensional topological insulator, which are connected by one or several local tunnel junctions. In the presence of spatially inhomogeneous Rashba spin-orbit coupling, the spin of the helical edge states is momentum dependent, and this spin texture can be different on opposite edges. We demonstrate that this has a strong impact on the electron transport between the edges. In particular, in the case of many random tunnel contacts, the localization length depends strongly on the spin textures of the edge states. [less ▲]

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See detailStrongly correlated dynamics in multichannel quantum RC circuits
Dutt, Prasenjit; Schmidt, Thomas UL; Mora, Christophe et al

in Phys. Rev. B (2013), 87

We examine dissipation effects in a multichannel quantum RC circuit, comprising a cavity or single-electron box capacitively coupled to a gate and connected to a reservoir lead via several conducting ... [more ▼]

We examine dissipation effects in a multichannel quantum RC circuit, comprising a cavity or single-electron box capacitively coupled to a gate and connected to a reservoir lead via several conducting channels. Depending on the engineering details of the quantum RC circuit, the number of channels contributing to transport varies, as does the form of the interchannel couplings. For low-frequency ac transport, the charge-relaxation resistance (Rq) is a nontrivial function of the parameters of the system. However, in the vicinity of the charge-degeneracy points and for weak tunneling, we find as a result of cross-mode mixing or channel asymmetry that Rq becomes universal for a metallic cavity at low temperatures, and equals the unit of quantum resistance. To prove this universality, we map the system to an effective one-channel Kondo model, and construct an analogy with the Coulomb gas. Next, we probe the opposite regime of near-perfect transmission using a bosonization approach. Focusing on the two-channel case, we study the effect of backscattering at the lead-dot interface, more specifically, the role of an asymmetry in the backscattering amplitudes, and make a connection with the weak-tunneling regime near the charge-degeneracy points. [less ▲]

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See detailTransport properties of double quantum dots with electron-phonon coupling
Walter, Stefan; Trauzettel, Björn; Schmidt, Thomas UL

in Phys. Rev. B (2013), 88

We study transport through a double quantum dot system in which each quantum dot is coupled to a phonon mode. Such a system can be realized, e.g., using a suspended carbon nanotube. We find that the ... [more ▼]

We study transport through a double quantum dot system in which each quantum dot is coupled to a phonon mode. Such a system can be realized, e.g., using a suspended carbon nanotube. We find that the interplay between strong electron-phonon coupling and interdot tunneling can lead to a negative differential conductance at bias voltages exceeding the phonon frequency. Various transport properties are discussed, and we explain the physics of the occurrence of negative differential conductance in this system. [less ▲]

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See detailFinite-temperature conductance of interacting quantum wires with Rashba spin-orbit coupling
Schmidt, Thomas UL

in Phys. Rev. B (2013), 88

We calculate the finite-temperature conductance of clean, weakly interacting one-dimensional quantum wires subject to Rashba spin-orbit coupling and a magnetic field. For chemical potentials near the ... [more ▼]

We calculate the finite-temperature conductance of clean, weakly interacting one-dimensional quantum wires subject to Rashba spin-orbit coupling and a magnetic field. For chemical potentials near the center of the Zeeman gap ($\mu=0$), two-particle scattering causes the leading deviation from the quantized conductance at finite temperatures. On the other hand, for $|\mu| > 0$, three-particle scattering processes become more relevant. These deviations are a consequence of the strongly nonlinear single-particle spectrum, and are thus not accessible using Luttinger liquid theory. We discuss the observability of these predictions in current experiments on InSb nanowires and in ``spiral liquids,'' where a spontaneous ordering of the nuclear spins at low temperatures produces an effective Rashba coupling. [less ▲]

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See detailDetecting Majorana bound states by nanomechanics
Walter, Stefan; Schmidt, Thomas UL; Borkje, Kjetil et al

in Phys. Rev. B (2011), 84

We propose a nanomechanical detection scheme for Majorana bound states, which have been predicted to exist at the edges of a one-dimensional topological superconductor, implemented, for instance, using a ... [more ▼]

We propose a nanomechanical detection scheme for Majorana bound states, which have been predicted to exist at the edges of a one-dimensional topological superconductor, implemented, for instance, using a semiconducting wire placed on top of an s-wave superconductor. The detector makes use of an oscillating electrode, which can be realized using a doubly clamped metallic beam, tunnel coupled to one edge of the topological superconductor. We find that a measurement of the nonlinear differential conductance provides the necessary information to uniquely identify Majorana bound states. [less ▲]

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See detailCharge transfer statistics of a molecular quantum dot with strong electron-phonon interaction
Maier, S.; Schmidt, Thomas UL; Komnik, A.

in Phys. Rev. B (2011), 83

We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics. By using the ... [more ▼]

We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics. By using the Lang-Firsov (polaron) transformation, we construct a diagrammatic scheme to calculate the cumulant generating function. The electron-phonon interaction is taken into account exactly, and the employed approximation represents a summation of a diagram subset with respect to the tunneling amplitude. By comparison to Monte Carlo data, the formalism is shown to capture the basic properties of the strong-coupling regime. [less ▲]

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See detailSpin-charge separation in one-dimensional fermion systems beyond Luttinger liquid theory
Schmidt, Thomas UL; Imambekov, Adilet; Glazman, Leonid I.

in Phys. Rev. B (2010), 82

We develop a nonperturbative zero-temperature theory for the dynamic response functions of interacting one-dimensional spin-1/2 fermions. In contrast to the conventional Luttinger liquid theory, we take ... [more ▼]

We develop a nonperturbative zero-temperature theory for the dynamic response functions of interacting one-dimensional spin-1/2 fermions. In contrast to the conventional Luttinger liquid theory, we take into account the nonlinearity of the fermion dispersion exactly. We calculate the power-law singularities of the spectral function and the charge- and spin-density structure factors for arbitrary momenta and interaction strengths. The exponents characterizing the singularities are functions of momenta and differ significantly from the predictions of the linear Luttinger liquid theory. We generalize the notion of the spin-charge separation to the nonlinear spectrum. This generalization leads to phenomenological relations between threshold exponents and the threshold energy. [less ▲]

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See detailTransport properties of a superconducting single-electron transistor coupled to a nanomechanical oscillator
Koerting, V.; Schmidt, Thomas UL; Doiron, C. B. et al

in Phys. Rev. B (2009), 79

We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent ... [more ▼]

We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooper-pair tunneling events is shown to lead to pronounced back action effects. Measuring the current and the shot noise provides a direct way of gaining information on the state of the oscillator. In addition to an analytical discussion of the linear-response regime, we discuss and compare results of higher-order approximation schemes and a fully numerical solution. We find that cooling of the mechanical resonator is possible and that there are driven and bistable oscillator states at low couplings. Finally, we also discuss the frequency dependence of the charge noise and the current noise of the superconducting single electron transistor. [less ▲]

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See detailCharge transfer statistics of a molecular quantum dot with a vibrational degree of freedom
Schmidt, Thomas UL; Komnik, A.

in Phys. Rev. B (2009), 80

We analyze the full counting statistics (FCS) of a single-site quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electron-phonon coupling. We identify explicitly the ... [more ▼]

We analyze the full counting statistics (FCS) of a single-site quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electron-phonon coupling. We identify explicitly the contributions due to quasielastic and inelastic transport processes in the cumulant generating function and discuss their influence on the transport properties of the dot. We find that in the low-energy sector, the inelastic term causes a sign change in the shot noise correction at certain universal values of the transmission. Furthermore, we show that when the correction to the current due to inelastic processes vanishes, all odd order cumulants vanish as well. [less ▲]

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See detailTransient dynamics of a molecular quantum dot with a vibrational degree of freedom
Riwar, Roman-Pascal; Schmidt, Thomas UL

in Phys. Rev. B (2009), 80

We investigate the transient effects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian, which is instantly coupled to two fermionic leads biased by a finite voltage. In ... [more ▼]

We investigate the transient effects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian, which is instantly coupled to two fermionic leads biased by a finite voltage. In the limit of weak electron-phonon interaction, we use perturbation theory to determine the time dependence of the dot population and the average current. The limit of strong coupling is accessed by means of a self-consistent time-dependent mean-field approximation. These complementary approaches allow us to investigate the dynamics of the inelastic effects occurring when the applied bias voltage exceeds the phonon frequency and the emergence of bistability. [less ▲]

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See detailTransient dynamics of the Anderson impurity model out of equilibrium
Schmidt, Thomas UL; Werner, P.; Mühlbacher, L. et al

in Phys. Rev. B (2008), 78

We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the ... [more ▼]

We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant-level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material. [less ▲]

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See detailNonlinear transport through a dynamic impurity in a strongly interacting one-dimensional electron gas
Schmidt, Thomas UL; Komnik, A.

in Phys. Rev. B (2007), 76

We analyze the transport properties of a Luttinger liquid with an embedded impurity of explicitly time-dependent strength. We employ a radiative boundary condition formalism to describe the coupling to ... [more ▼]

We analyze the transport properties of a Luttinger liquid with an embedded impurity of explicitly time-dependent strength. We employ a radiative boundary condition formalism to describe the coupling to the voltage sources. Assuming the impurity time dependence to be oscillatory, we present a full analytic perturbative result in impurity strength for arbitrary interaction parameter calculated with the help of Coulomb gas expansion (CGE). Moreover, a full analytic solution beyond the above restriction is possible for a special nontrivial interaction strength which has been achieved independently by full resummation of CGE series as well as via refermionization technique. The resulting nonlinear current-voltage characteristic turns out to be very rich due to the presence of the additional energy scale associated with the impurity oscillation frequency. In accordance with the previous studies, we also find an enhancement of the linear conductance of the wire to values above the unitary limit G0=2e2/h. [less ▲]

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See detailFull counting statistics of spin transfer through the Kondo dot
Schmidt, Thomas UL; Gogolin, A. O.; Komnik, A.

in Phys. Rev. B (2007), 75

We calculate the spin current distribution function for a Kondo dot in two different regimes. In the exactly solvable Toulouse limit the linear response, zero temperature statistics of the spin transfer ... [more ▼]

We calculate the spin current distribution function for a Kondo dot in two different regimes. In the exactly solvable Toulouse limit the linear response, zero temperature statistics of the spin transfer is trinomial, such that all the odd moments vanish and the even moments follow a binomial distribution. On the contrary, the corresponding spin-resolved distribution turns out to be binomial. The combined spin and charge statistics is also determined. In particular, we find that in the case of a finite magnetic field or an asymmetric junction the spin and charge measurements become statistically dependent. Furthermore, we analyzed the spin counting statistics of a generic Kondo dot at and around the strong coupling fixed point (the unitary limit). Comparing these results with the Toulouse limit calculation we determine which features of the latter are generic and which ones are artifacts of the spin symmetry breaking. [less ▲]

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See detailFull counting statistics of spin transfer through ultrasmall quantum dots
Schmidt, Thomas UL; Komnik, A.; Gogolin, A. O.

in Phys. Rev. B (2007), 76

We analyze the spin-resolved full counting statistics of electron transfer through an ultrasmall quantum dot coupled to metallic electrodes. Modeling the setup by the Anderson Hamiltonian, we explicitly ... [more ▼]

We analyze the spin-resolved full counting statistics of electron transfer through an ultrasmall quantum dot coupled to metallic electrodes. Modeling the setup by the Anderson Hamiltonian, we explicitly take into account the on-site Coulomb repulsion U. We calculate the cumulant generating function for the probability to transfer a certain number of electrons with a preselected spin orientation during a fixed time interval. With the cumulant generating function at hand, we are then able to calculate the spin current correlations, which are of utmost importance in the emerging field of spintronics. We confirm the existing results for the charge statistics and report the discovery of a different type of correlation between the spin-up and -down polarized electron flows, which has the potential to become a powerful instrument for the investigation of the Kondo effect in nanostructures. [less ▲]

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