Luka Trifunovic
ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland

Short CV
2005  2009  Undergraduate studies at the University of Belgrade, Faculty of Physics 
2009  2010  Master of Physics at University of Belgrade, Faculty of Physics 
Since September 2010  PhD student in the Condensed Matter Theory group at the University of Basel, under the supervision of Prof. Dr. Daniel Loss 
Publications
Show all abstracts.1.  From Coupled Rashba Electron and Hole Gas Layers to 3D Topological Insulators 
Luka Trifunovic, Daniel Loss, and Jelena Klinovaja. arXiv:1511.01742
We introduce a system of stacked twodimensional electron and hole gas layers with Rashba spin orbit interaction and show that the tunnel coupling between the layers induces a strong three dimensional (3D) topological insulator phase. At each of the twodimensional bulk boundaries we find the spectrum consisting of a single anistropic Dirac cone, which we show by analytical and numerical calculations. Our setup has a unitcell consisting of four tunnel coupled Rashba layers and presents a synthetic strong 3D topological insulator and is distinguished by its rather high experimental feasibility.
 
2.  Highefficiency resonant amplification of weak magnetic fields for single spin magnetometry 
Luka Trifunovic, Fabio Pedrocchi (Aachen), Silas Hoffman, Patrick Maletinsky, Amir Yacoby (Harvard), and Daniel Loss. Nature Nanotechnology 10, 541 (2015); arXiv:1409.1497.
We demonstrate theoretically that by placing a ferromagnetic particle between a nitrogenvacancy (NV) magnetometer and a target spin, the magnetometer sensitivity is increased dramatically. Specifically, using materials and techniques already experimentally available, we find that by taking advantage of the ferromagnetic resonance the minimum magnetic moment that can be measured is smaller by four orders of magnitude in comparison to current stateoftheart magnetometers. As such, our proposed setup is sensitive enough to detect a single nuclear spin at a distance of 30~nm from the surface within less than one second of data acquisition at room temperature. Our proposal opens the door for nanoscale NMR on biological material under ambient conditions.
 
3.  Transport signature of fractional Fermions in Rashba nanowires 
Diego Rainis, Arijit Saha, Jelena Klinovaja, Luka Trifunovic, and Daniel Loss. Phys. Rev. Lett. 112, 196803 (2014); arXiv:1309.3738.
We study theoretically transport through a semiconducting nanowire (NW) in
the presence of Rashba spin orbit interaction, uniform magnetic field, and
spatially modulated magnetic field. The system is fully gapped, and the
interplay between the spin orbit interaction and the magnetic fields leads to
fractionally charged fermion (FF) bound states of JackiwRebbi type at each end
of the nanowire. We investigate the transport and noise behavior of a N/NW/N
system, where the wire is contacted by two normal leads (N), and we look for
possible signatures that could help in the experimental detection of such
states. We find that the differential conductance and the shot noise exhibit a
subgap structure which fully reveals the presence of the FF state. Our
predictions can be tested in standard twoterminal measurements through
InSb/InAs nanowires.
 
4.  LongRange Interaction of SingletTriplet Qubits via Ferromagnets 
Luka Trifunovic, Fabio L. Pedrocchi, and Daniel Loss. arXiv:1305.2451
We propose a mechanism of a longrange coherent interaction between two
singlettriplet qubits dipolarly coupled to a dogboneshaped ferromagnet. An
effective qubitqubit interaction Hamiltonian is derived and the coupling
strength is estimated. Furthermore we derive the effective coupling between two
spin1/2 qubits that are coupled via dipolar interaction to the ferromagnet and
that lie at arbitrary positions and deduce the optimal positioning. We consider
hybrid systems consisting of spin1/2 and ST qubits and derive the effective
Hamiltonian for this case. We then show that operation times vary between 1MHz
and 100MHz and give explicit estimates for GaAs, Silicon, and NVcenter based
spin qubits. Finally, we explicitly construct the required sequences to
implement a CNOT gate. The resulting quantum computing architecture retains all
the single qubit gates and measurement aspects of earlier approaches, but
allows qubit spacing at distances of order 1$\,\mu$m for twoqubit gates,
achievable with current semiconductor technology.
 
5.  LongRange Interaction of SpinQubits via Ferromagnets 
Luka Trifunovic, Fabio L. Pedrocchi, and Daniel Loss. Phys. Rev. X 3, 041023 (2013); arXiv:1302.4017.
We propose a mechanism of longrange coherent coupling between spins coupled
to a ferromagnet by exchnage or dipolar coupling. An effective twospin
interaction Hamiltonian is derived and the coupling strength is estimated. We
also discuss mechanisms of decoherence and consider possibilities for gate
control of the interaction between neighboring spinqubits. The resulting
quantum computing architecture retains all the single qubit gates and
measurement aspects of earlier approaches, but allows qubit spacing at
distances of order 1$\,\mu$m for twoqubit gates, achievable with current
semiconductor technology. The clock speed depends strongly on the
dimensionality of the ferromagnet and is between MHz and GHz.
 
6.  Realistic transport modeling for a superconducting nanowire with Majorana fermions 
Diego Rainis, Luka Trifunovic, Jelena Klinovaja, and Daniel Loss. Phys. Rev. B 87, 024515 (2013); arXiv:1207.5907.
Motivated by recent experiments searching for Majorana fermions (MFs) in
hybrid semiconductingsuperconducting nanostructures and by subsequent
theoretical interpretations, we consider the so far most realistic model
(including disorder) and analyze its transport behavior numerically. In
particular, we include in the model superconducting contacts used in the
experiments to extract the current. We show that important new features emerge
that are absent in simpler models, such as the enhanced visibility of the
topological gap for increased spinorbit interaction. We find oscillations of
the zero bias peak as function of magnetic field and explain their origin. Even
taking into account all the possible (known) ingredients of the experiments and
exploring many parameter regimes for MFs, we are not able to reach a
satisfactory agreement with the reported data. Thus, a different physical
origin for the observed zerobias peak cannot be excluded.
 
7.  Localized end states in density modulated quantum wires and rings 
Suhas Gangadharaiah, Luka Trifunovic, and Daniel Loss. Phys. Rev. Lett. 108, 136803 (2012); arXiv:1111.5273.
We study finite quantum wires and rings in the presence of a charge density
wave gap induced by a periodic modulation of the chemical potential. We show
that the TammShockley bound states emerging at the ends of the wire are stable
against weak disorder and interactions, for discrete open chains and for
continuum systems. The lowenergy physics can be mapped onto the JackiwRebbi
equations describing massive Dirac fermions and bound end states. We treat
interactions via the continuum model and show that they increase the charge gap
and further localize the end states. In an AharonovBohm ring with weak link,
the bound states give rise to an unusual $4\pi$peridodicity in the spectrum
and persistent current as function of an external flux. The electrons placed in
the two localized states on the opposite ends of the wire can interact via
exchange interactions and this setup can be used as a double quantum dot
hosting spinqubits.
 
8.  Signature of the long range triplet proximity effect in the density of states 
Milos Knezevic, Luka Trifunovic, and Zoran Radovic. Phys. Rev. B 85, 094517 (2012); arXiv:1112.4450.
We study the impact of the longrange spintriplet proximity effect on the
density of states (DOS) in planar SF1F2S Josephson junctions that consist of
conventional superconductors (S) connected by two metallic monodomain
ferromagnets (F1 and F2) with transparent interfaces. We determine the
electronic DOS in F layers and the Josephson current for arbitrary orientation
of the magnetizations using the solutions of Eilenberger equations in the clean
limit and for a moderate disorder in ferromagnets. We find that fully developed
longrange proximity effect can occur in highly asymmetric ferromagnetic
bilayer Josephson junctions with orthogonal magnetizations. The effect
manifests itself as an enhancement in DOS, and as a dominant second harmonic in
the Josephson currentphase relation. Distinctive variation of DOS in
ferromagnets with the angle between magnetizations is experimentally observable
by tunneling spectroscopy. This can provide an unambiguous signature of the
longrange spintriplet proximity effect.
 
9.  Longdistance spinspin coupling via floating gates 
Luka Trifunovic, Oliver Dial (Harvard), Mircea Trif (UCLA), James R. Wootton, Rediet Abebe (Harvard), Amir Yacoby (Harvard), and Daniel Loss. ( See accompanying Physics Synopsis ) Phys. Rev. X 2, 011006 (2012); arXiv:1110.1342.
The electron spin is a natural twolevel system that allows a qubit to be encoded. When localized in a gatedefined quantum dot, the electron spin provides a promising platform for a future functional quantum computer. The essential ingredient of any quantum computer is entanglement  for the case of electronspin qubits considered here  commonly achieved via the exchange interaction. Nevertheless, there is an immense challenge as to how to scale the system up to include many qubits. In this paper, we propose a novel architecture of a largescale quantum computer based on a realization of longdistance quantum gates between electron spins localized in quantum dots. The crucial ingredients of such a longdistance coupling are floating metallic gates that mediate electrostatic coupling over large distances. We show, both analytically and numerically, that distant electron spins in an array of quantum dots can be coupled selectively, with coupling strengths that are larger than the electronspin decay and with switching times on the order of nanoseconds.
 
10.  Josephson effect and spintriplet pairing correlations in SF1F2S junctions 
Luka Trifunovic, Zorica Popovic (Belgrade), and Zoran Radovic (Belgrade). Phys. Rev. B 84, 064511 (2011); arXiv:1103.0293.
We study theoretically the Josephson effect and pairing correlations in planar SF1F2S junctions that consist of conventional superconductors (S) connected by two metallic monodomain ferromagnets (F1 and F2) with transparent interfaces. We obtain both spinsinglet and triplet pair amplitudes and the Josephson currentphase relations for arbitrary orientation of the magnetizations using the selfconsistent solutions of Eilenberger equations in the clean limit and for a moderate disorder in ferromagnets. We find that the longrange triplet correlations cannot prevail in symmetric junctions with equal ferromagnetic layers. Surprisingly, the longrange spintriplet correlations give the dominant second harmonic in the Josephson currentphase relation of highly asymmetric SF1F2S junctions. The effect is robust against moderate disorder and variations in the layers thickness and exchange energy of ferromagnets.
 
11.  LongRange Superharmonic Josephson Current 
Luka Trifunovic Phys. Rev. Lett. 107, 047001 (2011); arXiv:1101.5416.
We consider a long superconductorferromagnetsuperconductor junction with one spinactive region. It is shown that an odd number of Cooper pairs cannot have a longrange propagation when there is only one spinactive region. When the temperature is much lower than the Thouless energy, the coherent transport of two Cooper pairs becomes the dominant process and the superharmonic currentphase relation is obtained ($I\propto\sin2\phi$).
 
12.  Longrange spintriplet proximity effect in Josephson junctions with multilayered ferromagnets 
Luka Trifunovic and Zoran Radovic (Belgrade). Phys. Rev. B 82, 020505(R) (2010); arXiv:1005.1867.
We study the proximity effect in SF'(AF)F'S and SF'(F)F'S planar junctions,
where S is a clean conventional (swave) superconductor, while F' and middle
layers are clean or moderately diffusive ferromagnets. Middle layers consist of
two equal ferromagnets with antiparallel (AF) or parallel (F) magnetizations
that are not collinear with magnetizations in the neighboring F' layers. We use
fully selfconsistent numerical solutions of the Eilenberger equations to
calculate the superconducting pair amplitudes and the Josephson current for
arbitrary thickness of ferromagnetic layers and the angle between inplane
magnetisations. For moderate disorder in ferromagnets the triplet proximity
effect is practically the same for AF and F structures, like in the dirty
limit. Triplet Josephson current is dominant for $d'\approx\hbar v_F/2h'$,
where $d'$ is the F' layer thickness and $h'$ is the exchange energy. Our
results are in a qualitative agreement with the recent experimental
observations [T. S. Khaire, M. A. Khasawneh, W. P. Pratt, and N. O. Birge,
Phys. Rev. Lett. \textbf{104}, 137002 (2010)].
