Publications of the Group
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2018

NonEquilibrium Charge Dynamics in MajoranaJosephson Devices
I. J. van Beek, A. Levy Yeyati, B. Braunecker
arXiv:1809.04701
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 singleparticle tunnelling effects to dominate. We fully
characterize the resulting charge dynamics and the associated voltage and current signals. Our work reveals a rich
landscape of behaviours in both the static and timevarying 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 MajoranaJosephson device.

Tunneling spectroscopy between onedimensional helical conductors
B. Braunecker, P. Simon
arXiv:1807.00052 (to appear in PRB)
We theoretically investigate the tunneling spectroscopy of a system of two parallel onedimensional helical
conductors in the interacting, Luttinger liquid regime. We calculate the nonlinear 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 spincharge 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, threedimensional Kitaev spin liquids. Their
fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band
structures—ranging from topologically protected Weyl semimetals over nodal semimetals 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.
2017

Continuum description for subgap states at ferromagnetic and spiral ordered magnetic chains in twodimensional superconductors
C. J. F. Carroll, B. Braunecker
arXiv:1709.06093
We consider subgap bands induced in a twodimensional superconductor by a densely packed chain of magnetic moments with ferromagnetic
or spiral alignments. We show that crucially all wavelengths must be taken into account in the calculation of the subgap properties,
and that in particular gap closings can occur at high momentum due to a mix of Shiba type and magnetic scattering states. The subgap
bands are always connected to the bulk bands such that it is impossible to single out a fully onedimensional subband as required for
distinct topological properties. To obtain the latter a finite spacing between the impurities needs to be reintroduced such that by zone
folding the bands can disconnect from the continuum.
2016

Spin liquid mediated RKKY interaction
H. F. Legg, B. Braunecker
arXiv:1612.06868
We propose an RKKYtype interaction that is mediated by a spin liquid. If a spin liquid ground state exists such an
interaction could leave a fingerprint by ordering underlying localized 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.
As a working example we investigate the twodimensional spin1/2 kagome antiferromagnet (KAFM), although the treatment
remains general and can be extended to other spin liquids and dimensions. We find that several different nuclear spin
orderings minimize the RKKYtype energy induced by the KAFM but are unstable due to a zeroenergy flat magnon band.
Despite this we show that a small magnetic field is able to gap out this magnon spectrum for some of the orderings
resulting in an intricate nuclear magnetism.

Noncollinear SpinOrbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot
M. C. Hels, B. Braunecker, K. GroveRasmussen, J. Nygård
Phys. Rev. Lett. 117, 276802 (2016)
[arXiv:1606.01065]
[PDF]
[Data]
We demonstrate experimentally that noncollinear intrinsic spinorbit magnetic fields can be realized in a
curved carbon nanotube twosegment device. Each segment, analyzed in the quantum dot regime, shows
near fourfold degenerate shell structure allowing for identification of the spinorbit 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.

NonKondo manybody physics in a Majoranabased 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
Majoranamediated manybody state and an associated intermediate lowenergy fixed point. Starting from two
Majorana bound states, hosted by a Coulombblockaded topological superconductor and each coupled to a separate
lead, we derive an effective lowenergy Hamiltonian, which displays a Kondolike character. However, in contrast
to the Kondo model which tends to a strong or weakcoupling 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 manybody state associated with it.
2015

Selfstabilizing temperaturedriven crossover between topological and nontopological ordered phases in onedimensional conductors
B. Braunecker and P. Simon
Phys. Rev. B 92, 241410(R) (2015)
[arXiv:1510.06339]
[PDF]
We present a selfconsistent analysis of the topological superconductivity arising from the interaction between selfordered localized magnetic moments and electrons in onedimensional conductors in contact with a superconductor. We show that due to a gain in entropy there exists a magnetically ordered yet nontopological phase at finite temperatures that is relevant for systems of magnetic adatom chains on a superconductor. Spinorbit 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 realtime 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, gatecontrolled 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 spincharge separation in crossed TomonagaLuttinger 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 TomonagaLuttinger 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 nonFermi 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 spincharge 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 spinorbit interaction in carbon nanotube crossjunctions
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 spinorbit interaction, carbon
nanotube crossjunctions 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 crossjunctions.

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]
Spinorbit 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 Belllike 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 spinorbit strength. Using a microscopic calculation we
demonstrate that entanglement detection by violation of the Belllike
inequality is within the reach of current experimental setups.

Interplay between classical magnetic moments and superconductivity in
quantum onedimensional conductors: toward a selfsustained topological
Majorana phase
B. Braunecker and P. Simon
Phys. Rev. Lett. 111, 147202 (2013)
[arXiv:1307.2431]
[PDF]
[Supplement]
We study a onedimensional 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
finetuning 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.

Magneticfield switchable metalinsulator 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 onedimensional conductors with spinorbit 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 spinwavefunction
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 magneticfield induced
pseudogap. We investigate these transitions using a unified twostep
renormalization group approach.

Transport through a Coulomb blockaded Majorana nanowire
A. Zazunov, R. Egger, A. Levy Yeyati, R. Hützen, and B. Braunecker
in
LowDimensional 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 6376
In onedimensional (1D) quantum wires with strong spinorbit coupling and a Zeeman field,
a superconducting substrate can induce zeroenergy 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 singlecharge 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
swave superconducting (instead of normalconducting) leads. In the noninteracting case,
we derive the exact currentphase relation (CPR) and find πperiodic behavior with
negative critical current for weak tunnel couplings. Charging effects then cause the
anomalous CPR I(φ) = I_{c} cos(φ), where the paritysensitive
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 MooreRead 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 MooreRead state. For
comparison, we also consider cotunneling between Laughlin states, and
find that electron transport between MooreRead states and between
Laughlin states at filling factor 1/3 have identical voltage
dependences.

Majorana singlecharge 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 singlecharge 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
finitetemperature peak conductance under strong blockade conditions,
where the valley conductance mainly comes from elastic cotunneling. The
nonlinear conductance exhibits finitevoltage sidebands due to anomalous
tunneling involving Cooper pair splitting.
Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids
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
positionfrequency 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
onedimensional conductor or in spinorbit 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.
2011

Majorana edge states in interacting onedimensional systems
S. Gangadharaiah, B. Braunecker, P. Simon, and D. Loss
Phys. Rev. Lett. 107, 036801 (2011)
[arXiv:1101.0094]
[PDF]
We show that onedimensional electron systems in proximity of a
superconductor that support Majorana edge states are extremely
susceptible to electronelectron 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 lowenergy theory for metallic (armchair and
nonarmchair) singlewall nanotubes in the presence of an electric field
perpendicular to the nanotube axis, and in the presence of magnetic
fields, taking into account spinorbit interactions and screening
effects on the basis of a microscopic tightbinding model. The interplay
between electric field and spinorbit 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 allelectric setup.
This is a consequence of the interplay between spinorbit 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
tightbinding model we derive the effective lowenergy Hamiltonian and
the resulting spectrum.

ManyBody 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 powerlaw
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

Spinselective Peierls transition in interacting onedimensional conductors with spinorbit interaction
B. Braunecker, G. I. Japaridze, J. Klinovaja, and D. Loss
Phys. Rev. B 82, 045127 (2010)
[arXiv:1004.0467]
[PDF]
Interacting onedimensional conductors with Rashba spinorbit coupling
are shown to exhibit a spinselective Peierlstype transition into a
mixed spinchargedensitywave state. The transition leads to a gap for
onehalf of the conducting modes, which is strongly enhanced by
electronelectron 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 spinorbit interactions.
As an example we show for semiconducting quantum wires and carbon
nanotubes that the gap induced by weak magnetic fields or intrinsic
spinorbit interactions can get renormalized by 1 order of magnitude up
to 10  30 K.

Entanglement, whichway experiment, and a quantum erasure
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 socalled whichway
experiment and the counterintuitive effect of a quantum eraser for
oneparticle 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 twodimensional lattices due to electronelectron 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 twodimensional (2D) electron
gas. The nuclear spins interact with each other through the
RudermanKittelKasuyaYosida (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 electronelectron interactions. This provides
a connection between lowdimensional magnetism and nonanalyticities in
interacting 2D electron systems. We discuss the conditions for nuclear
magnetism, and show that the associated Curie temperature increases with
the electronelectron 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 onedimensional 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
onedimensional 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 ^{13}C
and GaAsbased 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 ^{13}C 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 ^{13}C 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 ^{13}C 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 twodimensional 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
twodimensional (2D) interacting electron gas using a Kondo lattice
model description. We derive an effective magnetic Hamiltonian for the
nuclear spins, which is of the RudermannKittelKasuyaYosida type and
where the interactions between the nuclear spins are strongly modified
by the electronelectron 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 lowdimensional 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 electronelectron interactions up to the
millikelvin range.

Magnetic order in Kondolattice systems due to electronelectron interactions
B. Braunecker, P. Simon, and D. Loss
2nd International Workshop on SolidState Quantum Computing (Taipei, Taiwan, June 2008)
AIP Conf. Proc., Vol. 1074, pp. 6267 (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
twodimensional (2D) Kondolattice 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 electronelectron interactions. This provides
a connection between lowdimensional magnetism and nonanalyticities in
interacting 2D electron systems. We discuss the conditions for nuclear
magnetism, and show that the associated Curie temperature increases with
the electronelectron 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 nonanalyticities in the 2D Fermi liquid
P. Simon, B. Braunecker, and D. Loss
Yukawa International Seminar 2007 (YKIS2007); Interaction and Nanostructural Effects in LowDimensional 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 twodimensional (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 electronelectron 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 lowdimensional magnetism and nonanalyticities in
interacting 2D electron systems. Based on various perturbative and
nonperturbative 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 electronelectron interactions up to the millikelvin
range.

ControlledNOT 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 measurementbased implementation of a controlledNOT (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 qubitparity meter. We present a
general scheme for reducing this qubitparity meter to a local
spinparity 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 singlettriplet
encoding, and nu=5/2 Ising nonAbelian anyons using topological quantum
computation braiding operations and nontopological charge measurements.
2007

Spin current and rectification in onedimensional 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:condmat/0610847 (2006)
[PDF]
We demonstrate that spin current can be generated by an ac voltage in a
onechannel 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 spinpolarized particle
injection nor timedependent 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 timedependent perturbations: RiemannHilbert approach at nonzero temperatures
B. Braunecker
Phys. Rev. B 73, 075122 (2006)
[arXiv:condmat/0510680]
[PDF]
We provide an exact finite temperature extension to the recently
developed RiemannHilbert approach for the calculation of response
functions in nonadiabatically perturbed (multichannel) Fermi gases. We
give a precise definition of the finite temperature RiemannHilbert
problem and show that it is equivalent to a zero temperature problem.
Using this equivalence, we discuss the solution of the nonequilibrium
Fermiedge singularity problem at finite temperatures.
2005

Rectification in onedimensional
electronic systems
B. Braunecker, D. E. Feldman, and J. B. Marston
Phys. Rev. B 72, 125311 (2005)
[arXiv:condmat/0506095]
[PDF]
Asymmetric currentvoltage [I(V)] curves, known as the
diode or rectification effect, in onedimensional 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
TomonagaLuttinger 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 currentvoltage curve, has a powerlaw dependence
on the voltage with a negative exponent,
I_{r} ~ V^{ z},
leading to a bump in the currentvoltage curve.

Edgecurrents in superconductors with a broken timereversal symmetry
B. Braunecker, P. A. Lee, and Z. Wang
Phys. Rev. Lett. 95, 017004 (2005)
[arXiv:condmat/0501125]
[PDF]
We analyze edge currents and edge bands at the surface of a timereversal symmetry breaking
d_{x2y2} + 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 selfconsistent slaveboson meanfield theory for the t  J model on a triangular
lattice, and on a Tmatrix scattering theory calculation. The shape of the edgestate band,
as well as the particular frequency √ 2 k_{F}
of the Friedel oscillations, are attributes unique for the
d_{x2y2} + id_{xy} case,
and may be used as a fingerprint for its identification.
Extensions to different timereversal symmetry breaking superconductors
can be achieved within the same approach.
2003

Fermi edge singularity in a nonequilibrium system
B. Muzykantskii, N. d'Ambrumenil, and B. Braunecker
Phys. Rev. Lett. 91, 266602 (2003)
[arXiv:condmat/0304583]
[PDF]
We report exact nonperturbative results for the Fermiedge singularity
in the absorption spectrum of an outofequilibrium 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 manybody 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 complexvalued) combinations of elements of the
scattering matrix replacing the equilibrium phase shifts.

On solutions of the nonequilibrium xray edge problem
B. Braunecker
Phys. Rev. B 68, 153104 (2003)
[arXiv:condmat/0211511]
[PDF]
We rediscuss a nonequilibrium xray edge problem which in recent
publications led to discrepancies between the results of the
perturbative and of an extended NozièresDe Dominicis approach. We show
that this problem results from an uncritical separation of momenta of
the scattering potential, and we propose a corrected NozièresDe
Dominicis solution.