Nonsymmetrized Correlations in Quantum Noninvasive Measurements

Adam Bednorz, Christoph Bruder, Bertrand Reulet, Wolfgang Belzig
Physical Review Letters 110, 250404 (2013)
A long-standing problem in quantum mesoscopic physics is how to order operators in quantum noise expressions like <I(-\omega)I(\omega)> where I(\omega) is the measured current at frequency \omega. Symmetrized ordering of operators describes a classical measurement while nonsymmetrized ordering corresponds to a quantum detector, sensitive to either emission or absorption of photons. We show that both ordering schemes can be embedded in quantum weak-measurement theory taking into account a finite interaction time between the system and the detector. Importantly, the nonsymmetrized ordering reveals its nonclassical nature already in second-order correlations, contrary to symmetrized ordering. This feature can be related to the squeezing of the many-body state of the transported electrons in a ac-driven tunnel junction. our predictions have in the meantime been confirmed experimentally: arXiv:1306.3913

The quantum correlation functions in tunnel junctions at T = 0. The emission noise, at Td = 0, (red line) violates an classical inequality for a certain range of eVac (shaded region). The violation is equivalent to a squeezing condition for the symmetrized noise (blue line). The experimental realization has been recently achieved (left plot, see the paper by Gasse, Gabelli, and Reulet, arXiv:1306.3913):




Nonlocal Thermoelectric Effects and Nonlocal Onsager relations in a Three-Terminal Proximity-Coupled Superconductor-Ferromagnet Device
Peter Machon, Matthias Eschrig, and Wolfgang Belzig
Phys. Rev. Lett. 110, 047002 (2013)

We study thermal and charge transport in a three-terminal setup consisting of a superconducting and two ferromagnetic contacts. We predict that the simultaneous presence of spin-filtering and of spin-dependent scattering phase shifts at each of the two interfaces will lead to very large nonlocal thermoelectric effects both in clean and in disordered systems. The symmetries of thermal and electric transport coefficients are related to fundamental thermodynamic principles by the Onsager reciprocity. Our results show that a nonlocal version of the Onsager relations for thermoelectric currents holds in a three terminal quantum coherent ferromagnet-superconductor heterostructure including spin-dependent crossed Andreev reflection and coherent electron transfer processes.

Nonlocal thermopower S for a symmetric setup as a function of the polarization and the spin-mixing parameter in the clean (a) and the dirty (b) limit for T=0.1Tc.

Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure
Christian Wickles and W. Belzig

Starting from a general N-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows us to systematically construct the unitary transformation that brings the Hamiltonian into band-diagonal form. We address the issue of gauge invariance and discuss the necessity of using kinetic variables in order to obtain a low energy effective description that is consistent with the original theory. Essentially, our analysis is a semiclassical one and quantum corrections appear as Berry curvatures in addition to quantities that are related to the appearance of persistent currents. We develop a transport framework which is manifestly gauge invariant and it is based on a quantum Boltzman formulation along with suitable definitions of current density operators such that Liouville's theorem is satisfied. Finally, we incorporate the effects of an external electromagnetic field into our theory.

Spin-precession-assisted supercurrent in a superconducting point contact coupled to a single-molecule magnet
C. Holmqvist, W. Belzig, and M. Fogelström
Physical Review B 86, 054519 (2012)

 The supercurrent through a quantum point contact coupled to a nanomagnet strongly depends on the dynamics of the nanomagnet's spin. We employ a fully microscopic model to calculate the transport properties of a junction coupled to a spin whose dynamics is modeled as Larmor precession brought about by an external magnetic field and find that the dynamics affects the charge and spin currents by inducing transitions between the continuum states outside the superconducting gap region and the Andreev levels. This redistribution of the quasiparticles leads to a nonequilibrium population of the Andreev levels and an enhancement of the supercurrent which is visible as a modified current-phase relation as well as a nonmonotonous critical current as function of temperature. The nonmonotonous behavior is accompanied by a corresponding change in spin-transfer torques acting on the precessing spin and leads to the possibility of using temperature as a means to tune the back-action on the spin.

Reflectionless Transport of Surface Dirac Fermions on Topological Insulators with Induced Ferromagnetic Domain Walls
Christian Wickles and Wolfgang Belzig
Phys. Rev. B 86, 035151

The interplay between Dirac quasi-particles on the surface of a topological insulator and proximity induced ferromagnetism with inhomogenoues order parameter gives rise to interesting physics. Here we study ballistic transport through a domain wall (DW) of in- and out-of-plane configurations by using an exact analytical treatment. Essentially, the out-of-plane DW provides constitutes the Jackiw-Rebbi model in two dimensions for which an analytical solution is provided. Interestingly, in the out-of-plane case we find oscilations in the DW resistance and for certain widths of the DW, ballistic transport through the DW is completely reflectionless. We establish a link to supersymmetry in order to explain these surprising features.

Mesoscopic transport of fermions through an engineered optical lattice connecting two reservoirs
Martin Bruderer and Wolfgang Belzig
Phys. Rev. A 85, 013623 (2012)

In this recent article the flow of a Fermi gas between two reservoirs connected by a short optical lattice is examined. We show how the flow of the fermions can be controlled by modulating the optical lattice and derive the equations that govern the full equilibration between the reservoirs. In contrast to classical fluids, the particle current exhibits measurable quantum fluctuations caused by the probabilistic nature of the transmission through the optical lattice. Moreover, even weak interactions between fermions have a strong blocking effect on the current. The described setup is a versatile testbed for studying non-equilibrium quantum many-body effects owing to the slow dynamics of the equilibration process and the possibility to detect fermions in small numbers.


Interferometric and noise signaturess of Majorana fermion edge states in transport experiments
Grégory Strübi, Wolfgang Belzig, Mahn-Soo Choi, and Christoph Bruder
Phys.Rev.Lett. 107, 136403 (2011)

Domain walls between superconducting and magnetic regions placed on top of a topological insulator support transport channels for Majorana fermions. We propose to study noise correlations in a Hanbury Brown–Twiss type interferometer and find three signatures of the Majorana nature of the channels. First, the average charge current in the outgoing leads vanishes. Furthermore, we predict an anomalously large shot noise in the output ports for a vanishing average current signal. Adding a quantum point contact to the setup, we find a surprising absence of partition noise which can be traced back to the Majorana nature of the carriers.