University of St Andrews

Publications by the group members

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2023

2022

2021

• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description
  C. J. F. Carroll, B. Braunecker
  Phys. Rev. B 104, 245133 (2021)   [arXiv:1709.06093]   [PDF]
  We consider subgap bands induced in a two-dimensional superconductor by a densely packed chain of magnetic moments with ferromagnetic or spiral alignments. We show that by contrast with sparsely packed chains a consistent description requires that all wavelengths are taken into account for the scattering at the magnetic moments. The resulting subgap states are a composition of Yu-Shiba-Rusinov-type states and magnetic scattering states, whose mixture becomes especially important to understand the nature and dimensional renormalization of gap closures for spiral magnetic alignments under increasing scattering strength, particularly as the spiral becomes commensurate with the Fermi wavelength. The results are fully analytic in the form of Green’s functions and provide the tools for further analysis of the properties of the subgap states.
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. II. Topological classification
  C. J. F. Carroll, B. Braunecker
  Phys. Rev. B 104, 245134 (2021)   [arXiv:2108.05768]   [PDF]
  We investigate the topological classification of the subgap bands induced in a two-dimensional superconductor by a densely packed chain of magnetic moments with ferromagnetic or spiral alignments. The wave functions for these bands are composites of Yu-Shiba-Rusinov-type states and magnetic scattering states and have a significant spatial extension away from the magnetic moments. We show that this spatial structure prohibits a straightforward extraction of a Hamiltonian useful for the topological classification. To address the latter correctly, we construct a family of spatially varying topological Hamiltonians for the subgap bands adapted for the broken translational symmetry caused by the chain. The spatial dependence in particular captures the transition to the topologically trivial bulk phase when moving away from the chain by showing how this, necessarily discontinuous, transition can be understood from an alignment of zeros with poles of Green’s functions. Through the latter, the topological Hamiltonians reflect a characteristic found otherwise primarily in strongly interacting systems.
• Decoupled heat and charge rectification as a many-body effect in quantum wires
  C. Stevenson, B. Braunecker
  Phys. Rev. B 103, 115413 (2021)   [arXiv:2002.03593]   [PDF]
  We show that for a quantum wire with a local asymmetric scattering potential the principal channels for charge and heat rectification decouple and renormalize differently under electron interactions, with heat rectification generally being more relevant. The polarization of the rectification results from quantum interference and is tunable through external gating. Furthermore, for spin-polarized or helical electrons and sufficiently strong interactions a regime can be obtained in which heat transport is strongly rectified but charge rectification is very weak.

2020

• Current correlations of Cooper-pair tunneling into a quantum Hall system
  A. B. Michelsen, T. L. Schmidt, E. G. Idrisov
  Phys. Rev. B 102, 125402 (2020)   [arXiv:2004.10279]   [PDF]
  We study Cooper-pair transport through a quantum point contact between a superconductor and a quantum Hall edge state at integer and fractional filling factors. We calculate the tunneling current and its finite-frequency noise to the leading order in the tunneling amplitude for dc and ac bias voltage in the limit of low temperatures. At zero temperature and in the case of tunneling into a single edge channel both the conductance and differential shot noise vanish as a result of the Pauli exclusion principle. In contrast, in the presence of two edge channels, this Pauli blockade is softened and a nonzero conductance and shot noise are revealed.

2019

• Spin liquid mediated RKKY interaction
  H. F. Legg, B. Braunecker
  Sci. Rep. 9, 17697 (2019)   [arXiv:1612.06868]   [PDF]   [Supplement]
  We propose an RKKY-type interaction that is mediated by a spin liquid. If a spin liquid exists such an interaction could leave a fingerprint by ordering underlying localised moments such as nuclear spins. This interaction has a unique phenomenology that is distinct from the RKKY interaction found in fermionic systems; most notably the lack of a Fermi surface and absence of the requirement for itinerant electrons, since most spin liquids are insulators. We demonstrate that the interaction is predominately shaped by the lattice symmetries of the underlying spin liquid. As a working example we investigate the possible ordering of nuclear spins that interact through an underlying lattice of the two-dimensional spin-1/2 kagome antiferromagnet (KHAF), although the treatment remains general and can be extended to other spin liquids and dimensions. We find that several different nuclear spin orderings minimise the RKKY-type energy induced by the KHAF but are unstable due to a zero-energy flat magnon band in linear spin-wave theory. Despite this we show that a small magnetic field is able to gap out this magnon spectrum resulting in an intricate nuclear magnetism.
• Coherent backaction between spins and an electronic bath: Non-Markovian dynamics and low temperature quantum thermodynamic electron cooling
  S. Matern, D. Loss, J. Klinovaja, B. Braunecker
  Phys. Rev. B 100, 134308 (2019)   [arXiv:1905.11422]   [PDF]
  We provide a versatile analytical framework for calculating the dynamics of a spin system in contact with a fermionic bath beyond the Markov approximation. The approach is based on a second-order expansion of the Nakajima-Zwanzig master equation but systematically includes all quantum coherent memory effects leading to non-Markovian dynamics. Our results describe, for the free induction decay, the full time range from the non-Markovian dynamics at short times, to the well-known exponential thermal decay at long times. We provide full analytic results for the entire time range using a bath of itinerant electrons as an archetype for universal quantum fluctuations. Furthermore, we propose a quantum thermodynamic scheme to employ the temperature insensitivity of the non-Markovian decay to transport heat out of the electron system and thus, by repeated reinitialization of a cluster of spins, to efficiently cool the electrons at very low temperatures.
• Majorana mediated non-local charge dynamics in topological superconductors
  I. J. van Beek, PhD thesis   [DOI: 10.17630/10023-19248]
  Topology has enjoyed great success as a paradigm for the classification and understanding of condensed matter outside the framework of spontaneously broken symmetry. This success is all the more remarkable considering that the impact of interactions, in particular the Coulomb interaction between electrons, has been neglected in most analyses. Experience in topologically trivial systems demonstrates that, beyond simply leading to quantitative modifications, interactions can give rise to qualitatively new physics in condensed matter. This thesis explores the interplay between interaction effects and topologically non-trivial states and demonstrates how this interplay can lead to novel physics which is fundamentally contingent upon both a system's topological character and interactions. The prototypical example of a topological state in condensed matter is the Majorana bound state (MBS). In the work presented here, MBSs are significant because they lead to non-local fermionic states in superconductors that are bound to near-zero energy, inside the superconducting gap. The new physics arising from the synergy of MBSs and electron-electron interactions is illustrated by two examples. A Majorana-based analogue of the Kondo system is found to exhibit signs of a delocalised many-body state consisting of electrons from both metallic leads and a superconducting condensate. The presence of MBSs in a current driven capacitive Josephson junction enables excitation of the system to a non-equilibrium state and profoundly affects the overall charge dynamics of the junction. This thesis offers compelling evidence for the importance of interactions in the context of topologically non-trivial systems, not only with regard to determining the topology of the system per se, but also as the means by which new physics is realised.
• Designed topological states from hybrid spiral magnet-superconductor heterostructures
  C. J. Carroll, PhD thesis   [DOI: 10.17630/10023-17497]
  In this thesis a Green's function based, analytical formalism is developed to describe dense chains of spiral ordered classical magnetic moments embedded in superconducting substrates. I demonstrate that an understanding of the dimensional mismatch between the substrate and impurity chain is crucial to understand the physics at play. Renormalised gap closures are discovered by exact, analytic solution for a ferromagnetic chain and insights gleaned are used to understand the spiral ordered case to which it can be smoothly tuned. I investigate the topological characteristics of this model and find an ambiguity in defining effective Hamiltonians due to the dimensional embedding of the chain in the substrate. To aid in resolving this ambiguity I develop formalism which allows one to write down Green's functions for bounded, semi infinite systems in terms of more easily attainable, exact solutions for infinite systems. I derive simple expressions to identify the presence of topological bound states which agrees with purely one dimensional models and changes suggestively when applied to the aforementioned two dimensional model. I then work to extend the formalism to allow the exact solution of two or three parallel chains, taking into account all possible interactions with the classical magnetic impurities. The solutions are decoupled so that they can be written in terms of the T matrices for a single chain, with additional levels of resummation. I find that the induced sub-gap spectrum for the two chain solution completely replaces those from each individual chain, leading to oscillating, helix like band structures. I use the complicated solution of the three chain solution to inform a potential ansatz to solve the N chain case.

2018

• Non-Equilibrium Charge Dynamics in Majorana-Josephson Devices
  I. J. van Beek, A. Levy Yeyati, B. Braunecker
  Phys. Rev. B 98, 224502 (2018)   [arXiv:1809.04701]   [PDF]
  We investigate the impact of introducing Majorana bound states, formed by a proximitized semiconducting nanowire in the topological regime, into a current biased capacitive Josephson junction, thereby adding delocalized states below the superconducting gap. We find that this qualitatively changes the charge dynamics of the system, diminishing the role of Bloch oscillations and causing single-particle tunneling effects to dominate. We fully characterize the resulting charge dynamics and the associated voltage and current signals. Our work reveals a rich landscape of behaviors in both the static and time-varying driving modes. This can be directly attributed to the presence of Majorana bound states, which serve as a pathway for charge transport and enable nonequilibrium excitations of the Majorana-Josephson device.
• Kinetic Stabilization of 1D Surface States near Twin Boundaries in Noncentrosymmetric BiPd
  C. M. Yim, C. Trainer, A. Maldonado, B. Braunecker, A. Yaresko, D. C. Peets, P. Wahl
  Phys. Rev. Lett. 121, 206401 (2018)   [arXiv:1811.02832]   [PDF]
  The search for one-dimensional (1D) topologically protected electronic states has become an important research goal for condensed matter physics owing to their potential use in spintronic devices or as a building block for topologically nontrivial electronic states. Using low temperature scanning tunneling microscopy, we demonstrate the formation of 1D electronic states at twin boundaries at the surface of the noncentrosymmetric material BiPd. These twin boundaries are topological defects that separate regions with antiparallel orientations of the crystallographic b axis. We demonstrate that the formation of the 1D electronic states can be rationalized by a change in effective mass of two-dimensional surface states across the twin boundary. Our work therefore reveals a novel route towards designing 1D electronic states with strong spin-orbit coupling.
• Tunneling spectroscopy between one-dimensional helical conductors
  B. Braunecker, P. Simon
  Phys. Rev. B 98, 115146 (2018)   [arXiv:1807.00052]   [PDF]
  We theoretically investigate the tunneling spectroscopy of a system of two parallel one-dimensional helical conductors in the interacting, Luttinger liquid regime. We calculate the non-linear differential conductance as a function of the voltage bias between the conductors and the orbital momentum shift induced on tunneling electrons by an orthogonal magnetic field. We show that the conductance map exhibits an interference pattern which is characteristic to the interacting helical liquid. This can be contrasted with the different interference pattern from tunneling between regular Luttinger liquids which is governed by the spin-charge separation of the elementary collective excitations.
• Entanglement in 3D Kitaev spin liquids
  S. Matern, M. Hermanns
  J. Stat. Mech.: Theor. Exp. P063101 (2018)   [arXiv:1712.07715]  
  Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids are the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures—ranging from topologically protected Weyl semi-metals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.

2016

• Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot
  M. C. Hels, B. Braunecker, K. Grove-Rasmussen, J. Nygård
  Phys. Rev. Lett. 117, 276802 (2016)   [arXiv:1606.01065]   [PDF]   [Data]
  We demonstrate experimentally that noncollinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near fourfold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements.
• Non-Kondo many-body physics in a Majorana-based Kondo type system
  I. J. van Beek, B. Braunecker
  Phys. Rev. B 94, 115416 (2016)   [arXiv:1606.08634]   [PDF]
  We carry out a theoretical analysis of a prototypical Majorana system, which demonstrates the existence of a Majorana-mediated many-body state and an associated intermediate low-energy fixed point. Starting from two Majorana bound states, hosted by a Coulomb-blockaded topological superconductor and each coupled to a separate lead, we derive an effective low-energy Hamiltonian, which displays a Kondo-like character. However, in contrast to the Kondo model which tends to a strong- or weak-coupling limit under renormalization, we show that this effective Hamiltonian scales to an intermediate fixed point, whose existence is contingent upon teleportation via the Majorana modes. We conclude by determining experimental signatures of this fixed point, as well as the exotic many-body state associated with it.

2015

• Self-stabilizing temperature-driven crossover between topological and non-topological ordered phases in one-dimensional conductors
  B. Braunecker and P. Simon
  Phys. Rev. B 92, 241410(R) (2015)   [arXiv:1510.06339]   [PDF]
  We present a self-consistent analysis of the topological superconductivity arising from the interaction between self-ordered localized magnetic moments and electrons in one-dimensional conductors in contact with a superconductor. We show that due to a gain in entropy there exists a magnetically ordered yet non-topological phase at finite temperatures that is relevant for systems of magnetic adatom chains on a superconductor. Spin-orbit interaction is taken into account, and we show that it causes a modification of the magnetic order yet without affecting the topological properties.
• Intrinsic Metastabilities in the Charge Configuration of a Double Quantum Dot
  D. E. F. Biesinger, C. P. Scheller, B. Braunecker, J. Zimmerman, A. C. Gossard, D. M. Zumbühl
  Phys. Rev. Lett. 115, 105804 (2015)   [arXiv:1505.03195]   [PDF]   [Data]
  We report a thermally activated metastability in a GaAs double quantum dot exhibiting real-time charge switching in diamond shaped regions of the charge stability diagram. Accidental charge traps and sensor back action are excluded as the origin of the switching. We present an extension of the canonical double dot theory based on an intrinsic, thermal electron exchange process through the reservoirs, giving excellent agreement with the experiment. The electron spin is randomized by the exchange process, thus facilitating fast, gate-controlled spin initialization. At the same time, this process sets an intrinsic upper limit to the spin relaxation time.
• Probing charge fluctuator correlations using quantum dot pairs
  V. Purohit, B. Braunecker, B. W. Lovett
  Phys. Rev. B 91, 245301 (2015)   [arXiv:1501.02111]   [PDF]
  We study a pair of quantum dot exciton qubits interacting with a number of fluctuating charges that can induce a Stark shift of both exciton transition energies. We do this by solving the optical master equation using a numerical transfer matrix method. We find that the collective influence of the charge environment on the dots can be detected by measuring the correlation between the photons emitted when each dot is driven independently. Qubits in a common charge environment display photon bunching, if both dots are driven on resonance or if the driving laser detunings have the same sense for both qubits, and antibunching if the laser detunings have in opposite signs. We also show that it is possible to detect several charges fluctuating at different rates using this technique. Our findings expand the possibility of measuring qubit dynamics in order to investigate the fundamental physics of the environmental noise that causes decoherence.

2014

• Spontaneous Helical Order of Electron and Nuclear Spins in a Luttinger Liquid
  C. P. Scheller, B. Braunecker, D. Loss, D. M. Zumbühl
  SPG Mitteilungen 44, p. 23, May 2014   [journal (PDF)]
• Detection of spin entanglement via spin-charge separation in crossed Tomonaga-Luttinger liquids
  A. Schroer, B. Braunecker, A. Levy Yeyati, and P. Recher
  Phys. Rev. Lett. 113, 266401 (2014)   [arXiv:1404.4524]   [PDF]   [Supplement]
  We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLLs) realized, e.g., as two crossed nanowires or quantum Hall edge states. When injecting into each TLL one electron of opposite spin, 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 noninteracting 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.

2013

• Spin filtering and entanglement detection due to spin-orbit interaction in carbon nanotube cross-junctions
  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.
• Entanglement detection from conductance measurements in carbon nanotube Cooper pair splitters
  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.
• Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase
  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.
• Magnetic-field switchable metal-insulator transitions in a quasihelical conductor
  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.
• Transport through a Coulomb blockaded Majorana nanowire
  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) = I_c cos(φ), where the parity-sensitive critical current I_c provides a signature for Majorana states.

2012

• Cotunneling in the ν=5/2 fractional quantum Hall regime
  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.
• Majorana single-charge transistor
  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.

2011

• Majorana edge states in interacting one-dimensional systems
  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.
• Carbon nanotubes in electric and magnetic fields
  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.
• Helical modes in carbon nanotubes generated by strong electric fields
  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.
• Many-Body Dynamics of Exciton Creation in a Quantum Dot by Optical Absorption: A Quantum Quench towards Kondo Correlations
  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.

2010

• Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction
  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.
• Entanglement, which-way experiment, and a quantum erasure
  C. Ferrari and B. Braunecker
  Am. J. Phys. 78, 792 (2010)   [arXiv:0911.2072]   [PDF]
  
  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.
• 550 Jahre Universität Basel – Geschichte des Departements Physik (in German)
  B. Braunecker and C. Bruder
  SPG Mitteilungen 31, p. 28, May 2010 [web link]   [journal (PDF)]
• Magnetic order in nuclear spin two-dimensional lattices due to electron-electron interactions
  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.

2009

• Nuclear magnetism and electron order in interacting one-dimensional conductors
  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.
• Nuclear Magnetism and Electronic Order in ¹³C Nanotubes
  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.
• Physics, Society, and the Promotion of Young Physicists
  B. Braunecker and B. Braunecker
  SPG Mitteilungen 27, p. 17, May 2009   [web link]   [journal (PDF)]

2008

• Magnetic ordering of nuclear spins in an interacting two-dimensional electron gas
  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.
• Magnetic order in Kondo-lattice systems due to electron-electron interactions
  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.
• Magnetic ordering of nuclear spins in an interacting 2D electron gas as a consequence of non-analyticities in the 2D Fermi liquid
  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.
• Controlled-NOT gate for multiparticle qubits and topological quantum computation based on parity measurements
  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.

2007

• Spin current and rectification in one-dimensional electronic systems
  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.
• The Pleasures on the Road to a Quantum Computer
  B. Braunecker and D. Loss
  SPG Mitteilungen 20, p. 18, April 2007   [web link]   [journal (PDF)]

2006

• Response of a Fermi gas to time-dependent perturbations: Riemann-Hilbert approach at non-zero temperatures
  B. Braunecker
  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.

2005

• Rectification in one-dimensional electronic systems
  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 I_r = [I(V)+I(-V)], measuring the asymmetry in the current-voltage curve, has a power-law dependence on the voltage with a negative exponent, I_r ~ V ^-|z|, leading to a bump in the current-voltage curve.
• Edge-currents in superconductors with a broken time-reversal symmetry
  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 d_x²-y² + id_xy superconductor. We show that the currents have large Friedel oscillations with two interfering frequencies: √ 2 k_F from subgap states, and 2k_F 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 k_F of the Friedel oscillations, are attributes unique for the d_x²-y² + id_xy 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.

2003

• Fermi edge singularity in a non-equilibrium system
  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.
• On solutions of the nonequilibrium x-ray edge problem
  B. Braunecker
  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.