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A. Schroer, B. Braunecker, A. Levy Yeyati, and P. Recher
We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLL) realized, e.g., as two crossed nanowires or quantum Hall edge states. When injecting into each TLL one electron of an opposite spin pair, the dc-current measured after the crossing differs for singlet, triplet or product states. This is a striking new non-Fermi liquid feature because the (mean) current in a non-interacting beam splitter is insensitive to spin-entanglement. It can be understood in terms of collective excitations subject to spin-charge separation. This behavior may offer an easier alternative to traditional entanglement detection schemes based on current noise, which we show to be suppressed by the interactions.
F. Mazza, B. Braunecker, P. Recher, and A. Levy Yeyati
Phys. Rev. B 88, 195403 (2013) [arXiv:1307.7992] [PDF]
We demonstrate that, due to their spin-orbit interaction, carbon nanotube cross-junctions have attractive spin projective properties for transport. First, we show that the junction can be used as a versatile spin filter as a function of a backgate and a static external magnetic field. Switching between opposite spin filter directions can be achieved by small changes of the backgate potential, and a full polarization is generically obtained in an energy range close to the Dirac points. Second, we discuss how the spin filtering properties affect the noise correlators of entangled electron pairs, which allows us to obtain signatures of the type of entanglement that are different from the signatures in conventional semiconductor cross-junctions.
B. Braunecker, P. Burset, and A. Levy Yeyati
Phys. Rev. Lett. 111, 136806 (2013) [arXiv:1303.6196] [PDF] [Supplement]
Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube, the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through a Bell-like inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and does not demand a full knowledge of the spin-orbit strength. Using a microscopic calculation we demonstrate that entanglement detection by violation of the Bell-like inequality is within the reach of current experimental setups.
B. Braunecker and P. Simon
Phys. Rev. Lett. 111, 147202 (2013) [arXiv:1307.2431] [PDF] [Supplement]
We study a one-dimensional interacting electronic liquid coupled to a 1D array of classical magnetic moments and to a superconductor. We show that at low energy and temperature the magnetic moments and the electrons become strongly entangled and that a magnetic spiral structure emerges. For strong enough coupling between the electrons and magnetic moments, the 1D electronic liquid is driven into a topological superconducting phase supporting Majorana fermions without any fine-tuning of external parameters. Our analysis applies at low enough temperature to a quantum wire in proximity to a superconductor when the hyperfine interaction between electrons and nuclear spins is taken into account, or to a chain of magnetic adatoms adsorbed on a superconducting surface.
R. Hützen, A. Zazunov, B. Braunecker, A. Levy Yeyati, and R. Egger,
Phys. Rev. Lett. 109, 166403 (2012) [arXiv:1206.3912] [PDF] [Supplement]
We study transport through a Coulomb blockaded topologically nontrivial superconducting wire (with Majorana end states) contacted by metallic leads. An exact formula for the current through this interacting Majorana single-charge transistor is derived in terms of wire spectral functions. A comprehensive picture follows from three different approaches. We find Coulomb oscillations with universal halving of the finite-temperature peak conductance under strong blockade conditions, where the valley conductance mainly comes from elastic cotunneling. The nonlinear conductance exhibits finite-voltage sidebands due to anomalous tunneling involving Cooper pair splitting.
S. Gangadharaiah, B. Braunecker, P. Simon, and D. Loss
Phys. Rev. Lett. 107, 036801 (2011) [arXiv:1101.0094] [PDF]
We show that one-dimensional electron systems in proximity of a superconductor that support Majorana edge states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime, in which the Majorana edge states persist. We present strategies how this regime can be reached.
A. Zazunov, R. Egger, A. Levy Yeyati, R. Hützen, and B. Braunecker,
in Low-Dimensional Functional Materials,
NATO Science for Peace and Security Series B: Physics and Biophysics,
ed. by R. Egger, D. Matrasulov, and K. Rakhimov (Springer, 2013), pp 63-76
In one-dimensional (1D) quantum wires with strong spin-orbit coupling and a Zeeman field, a superconducting substrate can induce zero-energy Majorana bound states located near the ends of the wire. We study electronic properties when such a wire is contacted by normal metallic or superconducting electrodes. A special attention is devoted to Coulomb blockade effects. We analyze the "Majorana single-charge transistor" (MSCT), i.e., a floating Majorana wire contacted by normal metallic source and drain contacts, where charging effects are important. We describe Coulomb oscillations in this system and predict that Majorana fermions could be unambiguously detected by the emergence of sideband peaks in the nonlinear differential conductance. We also study a superconducting variant of the MSCT setup with s-wave superconducting (instead of normal-conducting) leads. In the noninteracting case, we derive the exact current-phase relation (CPR) and find π-periodic behavior with negative critical current for weak tunnel couplings. Charging effects then cause the anomalous CPR I(φ) = Ic cos(φ), where the parity-sensitive critical current Ic provides a signature for Majorana states.
B. Braunecker, A. Ström, and G. I. Japaridze
Phys. Rev. B 87, 075151 (2013) [arXiv:1206.5844] [PDF]
We study Anderson localization in disordered helical conductors that are obtained from one-dimensional conductors with spin-orbit interaction and a magnetic field, or from equivalent systems. We call such conductors "quasihelical" because the spins of the counterpropagating modes are not perfectly antiparallel and have a small spin-wave-function overlap that is tunable by the magnetic field. Due to the overlap, disorder backscattering is possible and allows a localization transition. A conductor can pass through two localization transitions with increasing field, one from the conventionally localized system to the quasihelical conductor (with localization length exceeding the system length), and one at a higher field again to a localized state, due now, however, to backscattering below the magnetic-field induced pseudogap. We investigate these transitions using a unified two-step renormalization group approach.
B. Braunecker, C. Bena, and P. Simon
Phys. Rev. B 85, 035136 (2012) [arXiv:1110.5171] [PDF]
We provide analytic expressions for the Green's functions in position-frequency space as well as for the tunneling density of states of various Luttinger liquids at zero temperature: the standard spinless and spinful Luttinger liquids, the helical Luttinger liquid at the edge of a topological insulator, and the Luttinger liquid that appears either together with an ordering transition of nuclear spins in a one-dimensional conductor or in spin-orbit split quantum wires in an external magnetic field. The latter system is often used to mimic a helical Luttinger liquid, yet we show here that it exhibits significantly different response functions and, to discriminate, we call it the spiral Luttinger liquid. We give fully analytic results for the tunneling density of state of all the Luttinger liquids as well as for most of the Green's functions. The remaining Green's functions are expressed by simple convolution integrals between analytic results.
J. Klinovaja, M. J. Schmidt, B. Braunecker, and D. Loss
Phys. Rev. B 84, 085452 (2011) [arXiv:1106.3332] [PDF]
Editor's suggestion of PRB and display of one figure on the "Kaleidoscope" section of the PRB web front page.
We derive an effective low-energy theory for metallic (armchair and nonarmchair) single-wall nanotubes in the presence of an electric field perpendicular to the nanotube axis, and in the presence of magnetic fields, taking into account spin-orbit interactions and screening effects on the basis of a microscopic tight-binding model. The interplay between electric field and spin-orbit interaction allows us to tune armchair nanotubes into a helical conductor in both Dirac valleys. Metallic nonarmchair nanotubes are gapped by the surface curvature, yet helical conduction modes can be restored in one of the valleys by a magnetic field along the nanotube axis. Furthermore, we discuss electric dipole spin resonance in carbon nanotubes, and find that the Rabi frequency shows a pronounced dependence on the momentum along the nanotube.
J. Klinovaja, M. J. Schmidt, B. Braunecker, and D. Loss
Phys. Rev. Lett. 106, 156809 (2011) [arXiv:1011.3630] [PDF]
Helical modes, conducting opposite spins in opposite directions, are shown to exist in metallic armchair nanotubes in an all-electric setup. This is a consequence of the interplay between spin-orbit interaction and strong electric fields. The helical regime can also be obtained in chiral metallic nanotubes by applying an additional magnetic field. In particular, it is possible to obtain helical modes at one of the two Dirac points only, while the other one remains gapped. Starting from a tight-binding model we derive the effective low-energy Hamiltonian and the resulting spectrum.
B. Braunecker, G. I. Japaridze, J. Klinovaja, and D. Loss
Phys. Rev. B 82, 045127 (2010) [arXiv:1004.0467] [PDF]
Interacting one-dimensional conductors with Rashba spin-orbit coupling are shown to exhibit a spin-selective Peierls-type transition into a mixed spin-charge-density-wave state. The transition leads to a gap for one-half of the conducting modes, which is strongly enhanced by electron-electron interactions. The other half of the modes remains in a strongly renormalized gapless state and conducts opposite spins in opposite directions, thus providing a perfect spin filter. The transition is driven by magnetic field and by spin-orbit interactions. As an example we show for semiconducting quantum wires and carbon nanotubes that the gap induced by weak magnetic fields or intrinsic spin-orbit interactions can get renormalized by 1 order of magnitude up to 10 - 30 K.
R. Zielke, B. Braunecker, and D. Loss
Phys. Rev. B 86, 235307 (2012) [arXiv:1204.4400] [PDF]
We show that cotunneling in the 5/2 fractional quantum Hall regime allows us to test the Moore-Read wave function, proposed for this regime, and to probe the nature of the fractional charge carriers. We calculate the cotunneling current for electrons that tunnel between two quantum Hall edge states via a quantum dot and for quasiparticles with fractional charges e/4 and e/2 that tunnel via an antidot. While electron cotunneling is strongly suppressed, the quasiparticle tunneling shows signatures characteristic of the Moore-Read state. For comparison, we also consider cotunneling between Laughlin states, and find that electron transport between Moore-Read states and between Laughlin states at filling factor 1/3 have identical voltage dependences.
B. Braunecker, P. Simon, and D. Loss
Phys. Rev. B 80, 165119 (2009) [arXiv:0908.0904] [PDF]
The interaction between localized magnetic moments and the electrons of a one-dimensional conductor can lead to an ordered phase in which the magnetic moments and the electrons are tightly bound to each other. We show here that this occurs when a lattice of nuclear spins is embedded in a Luttinger liquid. Experimentally available examples of such a system are single wall carbon nanotubes grown entirely from 13C and GaAs-based quantum wires. In these systems the hyperfine interaction between the nuclear spin and the conduction electron spin is very weak, yet it triggers a strong feedback reaction that results in an ordered phase consisting of a nuclear helimagnet that is inseparably bound to an electronic density wave combining charge and spin degrees of freedom. This effect can be interpreted as a strong renormalization of the nuclear Overhauser field and is a unique signature of Luttinger liquid physics. Through the feedback the order persists up into the millikelvin range. A particular signature is the reduction of the electric conductance by the universal factor 2.
B. Braunecker, P. Simon, and D. Loss
Phys. Rev. Lett. 102, 116403 (2009) [arXiv:0808.1685] [PDF]
Single wall carbon nanotubes grown entirely from 13C form an ideal system to study the effect of electron interaction on nuclear magnetism in one dimension. If the electrons are in the metallic, Luttinger liquid regime,we show that even a very weak hyperfine coupling to the 13C nuclear spins has a striking effect: The system is driven into an ordered phase, which combines electron and nuclear degrees of freedom, and which persists up intothe millikelvin range. In this phase the conductance is reduced by a universal factor of 2, allowing for detection by standard transport experiments.
P. Simon, B. Braunecker, and D. Loss
Phys. Rev. B 77, 045108 (2008) [arXiv:0709.0164] [PDF]
We investigate the magnetic behavior of nuclear spins embedded in a two-dimensional (2D) interacting electron gas using a Kondo lattice model description. We derive an effective magnetic Hamiltonian for the nuclear spins, which is of the Rudermann-Kittel-Kasuya-Yosida type and where the interactions between the nuclear spins are strongly modified by the electron-electron interactions. We show that the nuclear magnetic ordering at finite temperature relies on the (anomalous) behavior of the 2D static electron spin susceptibility and thus provides a connection between low-dimensional magnetism and nonanalyticities in interacting 2D electron systems. Using various perturbative and nonperturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as a function of its wave vector, we show that the nuclear spins locally order ferromagnetically and that this ordering can become global in certain regimes of interest. We demonstrate that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range.
P. Simon, B. Braunecker, and D. Loss
International conference Frontiers of Quantum and Mesoscopic Thermodynamics FQMT '08 (Prague, Czech Republic, July/Aug. 2008)
Physica E 42, 634 (2010) [PDF]
Updated version of the 2008 Taiwan conference proceedings below.
We focus on nuclear spins embedded in a two-dimensional (2D) electron gas. The nuclear spins interact with each other through the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which is carried by the electron gas. We show that a nuclear magnetic order at finite temperature relies on the anomalous behaviour of the 2D static electron spin susceptibility due to electron-electron interactions. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. We discuss the conditions for nuclear magnetism, and show that the associated Curie temperature increases with the electron-electron interactions and may reach up into the millikelvin regime. We also shortly discussed what happens when the dimensionality is further reduced to one dimension.
B. Braunecker, P. Simon, and D. Loss
2nd International Workshop on Solid-State Quantum Computing (Taipei, Taiwan, June 2008)
AIP Conf. Proc., Vol. 1074, pp. 62-67 (2008) [arXiv:0808.4063] [PDF]
This is a short (6 pages) review of the coupled nuclear spin/electron order in (mostly) 2D and (a bit of) 1D.
The hyperfine interaction between the electron spin and the nuclear spins is one of the main sources of decoherence for spin qubits when the nuclear spins are disordered. An ordering of the latter largely suppresses this source of decoherence. Here we show that such an ordering can occur through a thermodynamic phase transition in two-dimensional (2D) Kondo-lattice type systems. We specifically focus on nuclear spins embedded in a 2D electron gas. The nuclear spins interact with each other through the RKKY interaction, which is carried by the electron gas. We show that a nuclear magnetic order at finite temperature relies on the anomalous behavior of the 2D static electron spin susceptibility due to electron-electron interactions. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. We discuss the conditions for nuclear magnetism, and show that the associated Curie temperature increases with the electron-electron interactions and may reach up into the millikelvin regime. The further reduction of dimensionality to one dimension is shortly discussed.
P. Simon, B. Braunecker, and D. Loss
Yukawa International Seminar 2007 (YKIS2007); Interaction and Nanostructural Effects in Low-Dimensional Systems
Prog. Theor. Phys. Suppl. 176, 302 (2008)
Review of the nuclear spin order in a 2DEG.
We consider whether nuclear spins embedded in a two-dimensional (2D) interacting electron gas can sustain some ordering at finite temperatures. We start with a Kondo lattice model description and derive an effective magnetic Hamiltonian for the nuclear spins, which is of the RKKY type. The interactions between the nuclear spins are strongly modified by electron-electron interactions. We show that the nuclear magnetic ordering at finite temperature relies on the anomalous behavior of the 2D static electron spin susceptibility. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. Based on various perturbative and non-perturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as function of its wave vector, we show that the nuclear spins locally order ferromagnetically, and that this ordering can become global in certain samples. We also argue that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range.
B. Braunecker, P. A. Lee, and Z. Wang
Phys. Rev. Lett. 95, 017004 (2005) [arXiv:cond-mat/0501125] [PDF]
We analyze edge currents and edge bands at the surface of a time-reversal symmetry breaking dx2-y2 + idxy superconductor. We show that the currents have large Friedel oscillations with two interfering frequencies: √ 2 kF from subgap states, and 2kF from the continuum. The results are based independently on a self-consistent slave-boson mean-field theory for the t - J model on a triangular lattice, and on a T-matrix scattering theory calculation. The shape of the edge-state band, as well as the particular frequency √ 2 kF of the Friedel oscillations, are attributes unique for the dx2-y2 + idxy case, and may be used as a fingerprint for its identification. Extensions to different time-reversal symmetry breaking superconductors can be achieved within the same approach.
H. E. Türeci, M. Hanl, M. Claassen, A. Weichselbaum, T. Hecht, B. Braunecker, A. Govorov, L. Glazman, J. von Delft, and A. Imamoglu
Phys. Rev. Lett. 106, 107402 (2011) [arXiv:0907.3854] [PDF]
selected for a Synopsis in Physics
We study a quantum quench for a semiconductor quantum dot coupled to a Fermionic reservoir, induced by the sudden creation of an exciton via optical absorption. The subsequent emergence of correlations between spin degrees of freedom of dot and reservoir, culminating in the Kondo effect, can be read off from the absorption line shape and understood in terms of the three fixed points of the singleimpurity Anderson model. At low temperatures the line shape is dominated by a power-law singularity, with an exponent that depends on gate voltage and, in a universal, symmetric fashion, on magnetic field, indicative of a tunable Anderson orthogonality catastrophe.
Phys. Rev. B 73, 075122 (2006) [arXiv:cond-mat/0510680] [PDF]
We provide an exact finite temperature extension to the recently developed Riemann-Hilbert approach for the calculation of response functions in nonadiabatically perturbed (multichannel) Fermi gases. We give a precise definition of the finite temperature Riemann-Hilbert problem and show that it is equivalent to a zero temperature problem. Using this equivalence, we discuss the solution of the nonequilibrium Fermi-edge singularity problem at finite temperatures.
B. Muzykantskii, N. d'Ambrumenil, and B. Braunecker
Phys. Rev. Lett. 91, 266602 (2003) [arXiv:cond-mat/0304583] [PDF]
We report exact nonperturbative results for the Fermi-edge singularity in the absorption spectrum of an out-of-equilibrium tunnel junction. We consider two metals with chemical potential difference V separated by a tunneling barrier containing a defect, which exists in one of two states. When it is in its excited state, tunneling through the otherwise impermeable barrier is possible. Our nonperturbative solution of this nonequilibrium many-body problem shows that, as well as extending below the equilibrium threshold, the line shape depends on the difference in the phase of the reflection amplitudes on the two sides of the barrier. These results have a surprisingly simple interpretation in terms of known results for the equilibrium case but with (in general complex-valued) combinations of elements of the scattering matrix replacing the equilibrium phase shifts.
Phys. Rev. B 68, 153104 (2003) [arXiv:cond-mat/0211511] [PDF]
We rediscuss a nonequilibrium x-ray edge problem which in recent publications led to discrepancies between the results of the perturbative and of an extended Nozières-De Dominicis approach. We show that this problem results from an uncritical separation of momenta of the scattering potential, and we propose a corrected Nozières-De Dominicis solution.
C. Ferrari and B. Braunecker
Am. J. Phys. 78, 792 (2010) [arXiv:0911.2072] [PDFCopyright (2010) American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers.]
We present a didactical approach to expose the so-called which-way experiment and the counterintuitive effect of a quantum eraser for one-particle quantum interferences. The fundamental concept of entanglement plays a central role and highlights the complementarity between quantum interference and knowledge of which path was followed by the quantum particle.
O. Zilberberg, B. Braunecker, and D. Loss
Phys. Rev. A 77, 012327 (2008) [arXiv:0708.1062] [PDF]
We discuss a measurement-based implementation of a controlled-NOT (CNOT) quantum gate. Such a gate has recently been discussed for free electron qubits. Here we extend this scheme for qubits encoded in product states of two (or more) spins 1/2 or in equivalent systems. The key to such an extension is to find a feasible qubit-parity meter. We present a general scheme for reducing this qubit-parity meter to a local spin-parity measurement performed on two spins, one from each qubit. Two possible realizations of a multiparticle CNOT gate are further discussed: electron spins in double quantum dots in the singlet-triplet encoding, and nu=5/2 Ising non-Abelian anyons using topological quantum computation braiding operations and nontopological charge measurements.
B. Braunecker, D. E. Feldman, and Feifei Li
Phys. Rev. B 76, 085119 (2007) [arXiv:0706.2761] [PDF]
short version (preprint): B. Braunecker and D. E. Feldman, arXiv:cond-mat/0610847 (2006) [PDF]
We demonstrate that spin current can be generated by an ac voltage in a one-channel quantum wire with strong repulsive electron interactions in the presence of a nonmagnetic impurity and uniform static magnetic field. In a certain range of voltages, the spin current can exhibit a power dependence on the ac voltage bias with a negative exponent. The spin current expressed in units of ℏ/2 per second can become much larger than the charge current in units of the electron charge per second. The spin current generation requires neither spin-polarized particle injection nor time-dependent magnetic fields.
B. Braunecker, D. E. Feldman, and J. B. Marston
Phys. Rev. B 72, 125311 (2005) [arXiv:cond-mat/0506095] [PDF]
Asymmetric current-voltage [I(V)] curves, known as the diode or rectification effect, in one-dimensional electronic conductors can have their origin from scattering off a single asymmetric impurity in the system. We investigate this effect in the framework of the Tomonaga-Luttinger model for electrons with spin. We show that electron interactions strongly enhance the diode effect and lead to a pronounced current rectification even if the impurity potential is weak. For strongly interacting electrons and not too small voltages, the rectification current Ir = [I(V)+I(-V)], measuring the asymmetry in the current-voltage curve, has a power-law dependence on the voltage with a negative exponent, Ir ~ V -|z| , leading to a bump in the current-voltage curve.
B. Braunecker and C. Bruder
SPG Mitteilungen 31, p. 28, May 2010 [journal (PDF)]
B. Braunecker and B. Braunecker
SPG Mitteilungen 27, p. 17, May 2009 [web link] [journal (PDF)]