Christoph Kloeffel
ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland

Short CV
Since July 2014  Postdoctoral associate in the group of Prof. Dr. Daniel Loss at the University of Basel 
2010  2014  PhD student in the Condensed Matter Theory group at the University of Basel, under the supervision of Prof. Dr. Daniel Loss 
2009  2010  Research in the NanoPhotonics group of Prof. Dr. Richard J. Warburton (University of Basel and HeriotWatt) 
2008  2009  Master of Physics at HeriotWatt University in Edinburgh 
2005  2008  Undergraduate studies at the University of Wuerzburg 
Further information can be found on my website
Publications
Show all abstracts.1.  The Germanium Quantum Information Route 
G. Scappucci, C. Kloeffel, F. A. Zwanenburg, D. Loss, M. Myronov, J.J. Zhang, S. De Franceschi, G. Katsaros, and M. Veldhorst. arXiv:2004.08133
In the worldwide endeavor for disruptive quantum technologies, germanium is emerging as a versatile material to realize devices capable of encoding, processing, or transmitting quantum information. These devices leverage special properties of the germanium valenceband states, commonly known as holes, such as their inherently strong spinorbit coupling and the ability to host superconducting pairing correlations. In this Review, we initially introduce the physics of holes in lowdimensional germanium structures with key insights from a theoretical perspective. We then examine the material science progress underpinning germaniumbased planar heterostructures and nanowires. We review the most significant experimental results demonstrating key building blocks for quantum technology, such as an electrically driven universal quantum gate set with spin qubits in quantum dots and superconductorsemiconductor devices for hybrid quantum systems. We conclude by identifying the most promising prospects toward scalable quantum information processing.
 
2.  Exchange interaction of holespin qubits in double quantum dots in highly anisotropic semiconductors 
Bence Hetényi, Christoph Kloeffel, and Daniel Loss. Phys. Rev. Research 2, 033036 (2020); arXiv:2004.07658.
We study the exchange interaction between two holespin qubits in a double quantum dot setup in a silicon nanowire in the presence of magnetic and electric fields. Based on symmetry arguments we show that there exists an effective spin that is conserved even in highly anisotropic semiconductors, provided that the system has a twofold symmetry with respect to the direction of the applied magnetic field. This finding facilitates the definition of qubit basis states and simplifies the form of exchange interaction for twoqubit gates in coupled quantum dots. If the magnetic field is applied along a generic direction, cubic anisotropy terms act as an effective spinorbit interaction introducing novel exchange couplings even for an inversion symmetric setup. Considering the example of a silicon nanowire double dot, we present the relative strength of these anisotropic exchange interaction terms and calculate the fidelity of the squarerootofSWAP gate. Furthermore, we show that the anisotropyinduced spinorbit effects can be comparable to that of the direct Rashba spinorbit interaction for experimentally feasible electric field strengths.
 
3.  SiteControlled Uniform Ge/Si Hut Wires with Electrically Tunable SpinOrbit Coupling 
F. Gao, J.H. Wang, H. Watzinger, H. Hu, M. J. Rancic, J.Y. Zhang, T. Wang, Y. Yao, G.L. Wang, J. Kukucka, L. Vukusic, C. Kloeffel, D. Loss, F. Liu, G. Katsaros, and J.J. Zhang. Adv. Mater. 32, 1906523 (2020); arXiv:2001.11305.
Semiconductor nanowires have been playing a crucial role in the development of nanoscale devices for the realization of spin qubits, Majorana fermions, single photon emitters, nanoprocessors, etc. The monolithic growth of sitecontrolled nanowires is a prerequisite towards the next generation of devices that will require addressability and scalability. Here, combining topdown nanofabrication and bottomup selfassembly, we report on the growth of Ge wires on prepatterned Si (001) substrates with controllable position, distance, length and structure. This is achieved by a novel growth process which uses a SiGe strainrelaxation template and can be generalized to other material combinations. Transport measurements show an electrically tunable spinorbit coupling, with a spinorbit length similar to that of IIIV materials. Also, capacitive coupling between closely spaced wires is observed, which underlines their potential as a host for implementing two qubit gates. The reported results open a path towards scalable qubit devices with Si compatibility.
 
4.  Lowsymmetry nanowire crosssections for enhanced Dresselhaus spinorbit interaction 
Miguel J. Carballido, Christoph Kloeffel, Dominik M. Zumbühl, and Daniel Loss. arXiv:1910.00562
We study theoretically the spinorbit interaction of lowenergy electrons in semiconducting nanowires with a zincblende lattice. The effective Dresselhaus term is derived for various growth directions, including <11(2)>oriented nanowires. While a specific configuration exists where the Dresselhaus spinorbit coupling is suppressed even at confinement potentials of low symmetry, many configurations allow for a strong Dresselhaus coupling. In particular, we discuss qualitative and quantitative results for nanowire crosssections modeled after sectors of rings or circles. The parameter dependence is analyzed in detail, enabling predictions for a large variety of setups. For example, we gain insight into the spinorbit coupling in recently fabricated GaAsInAs nanomembranenanowire structures. By combining the effective Dresselhaus and Rashba terms, we find that such structures are promising platforms for applications where an electrically controllable spinorbit interaction is needed. If the nanowire crosssection is scaled down and InAs replaced by InSb, remarkably high Dresselhausbased spinorbit energies of the order of millielectronvolt are expected. A Rashba term that is similar to the effective Dresselhaus term can be induced via electric gates, providing means to switch the spinorbit interaction on and off. By varying the central angle of the circular sector, we find, among other things, that particularly strong Dresselhaus couplings are possible when nanowire crosssections resemble halfdisks.
 
5.  Direct Rashba spinorbit interaction in Si and Ge nanowires with different growth directions 
Christoph Kloeffel, Marko J. Rancic, and Daniel Loss. Phys. Rev. B 97, 235422 (2018); arXiv:1712.03476.
We study theoretically the lowenergy hole states in Si, Ge, and Ge/Si core/shell nanowires (NWs). The NW core in our model has a rectangular cross section, the results for a square cross section are presented in detail. In the case of Ge and Ge/Si core/shell NWs, we obtain very good agreement with previous theoretical results for cylindrically symmetric NWs. In particular, the NWs allow for an unusually strong and electrically controllable spinorbit interaction (SOI) of Rashba type. We find that the dominant contribution to the SOI is the "direct Rashba spinorbit interaction" (DRSOI), which is an important mechanism for systems with heavyholelighthole mixing. Our results for Si NWs depend significantly on the orientation of the crystallographic axes. The numerically observed dependence on the growth direction is consistent with analytical results from a simple model, and we identify a setup where the DRSOI enables spinorbit energies of the order of millielectronvolts in Si NWs. Furthermore, we analyze the dependence of the SOI on the electric field and the cross section of the Ge or Si core. A helical gap in the spectrum can be opened with a magnetic field. We obtain the largest g factors with magnetic fields applied perpendicularly to the NWs.
 
6.  Heavy Hole States in Germanium Hut Wires 
H. Watzinger, C. Kloeffel, L. Vukusic, M. D. Rossell, V. Sessi, J. Kukucka, R. Kirchschlager, E. Lausecker, A. Truhlar, M. Glaser, A. Rastelli, A. Fuhrer, D. Loss, and G. Katsaros. Nano Lett. 16, 6879 (2016); arXiv:1607.02977.
Hole spins have gained considerable interest in the past few years due to their potential for fast electrically controlled qubits. Here, we study holes confined in Ge hut wires, a sofar unexplored type of nanostructure. Lowtemperature magnetotransport measurements reveal a large anisotropy between the inplane and outofplane gfactors of up to 18. Numerical simulations verify that this large anisotropy originates from a confined wave function of heavyhole character. A lighthole admixture of less than 1% is estimated for the states of lowest energy, leading to a surprisingly large reduction of the outofplane gfactors compared with those for pure heavy holes. Given this tiny lighthole contribution, the spin lifetimes are expected to be very long, even in isotopically nonpurified samples.
 
7.  LongRange Interaction between Charge and Spin Qubits in Quantum Dots 
Marcel Serina, Christoph Kloeffel, and Daniel Loss. Phys. Rev. B 95, 245422 (2017); arXiv:1601.03564.
We analyze and give estimates for the longdistance coupling via floating metallic gates between different types of spin qubits in quantum dots made of different commonly used materials. In particular, we consider the hybrid, the singlettriplet, and the spin1/2 qubits, and the pairwise coupling between each type of these qubits with another hybrid qubit in GaAs, InAs, Si, and Si_{0.9}Ge_{0.1}. We show that hybrid qubits can be capacitively coupled strongly enough to implement twoqubit gates, as long as the dimensions of the dots and their distance from the metallic gates are small enough. Thus, hybrid qubits are good candidates for scalable implementations of quantum computing in semiconducting nanostructures.
 
8.  PhononAssisted Relaxation and Decoherence of SingletTriplet Qubits in Si/SiGe Quantum Dots 
Viktoriia Kornich, Christoph Kloeffel, and Daniel Loss. Quantum 2, 70 (2018); arXiv:1511.07369.
We study theoretically the phononinduced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlettriplet spin qubits and calculate their relaxation and the decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using BlochRedfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may suppress the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of onephonon and twophonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Sibased quantum dots are significantly longer than the ones reported for their GaAs counterparts.
 
9.  Strong SpinOrbit Interaction, Helical Hole States, and Spin Qubits in Nanowires and Quantum Dots 
Christoph Kloeffel PhD Thesis, University of Basel (2014)  
10.  Acoustic Phonons and Strain in Core/Shell Nanowires 
Christoph Kloeffel, Mircea Trif, and Daniel Loss. Phys. Rev. B 90, 115419 (2014); arXiv:1405.4834.
We study theoretically the lowenergy phonons and the static strain in cylindrical core/shell nanowires (NWs). Assuming pseudomorphic growth, isotropic media, and a forcefree wire surface, we derive algebraic expressions for the dispersion relations, the displacement fields, and the stress and strain components from linear elasticity theory. Our results apply to NWs with arbitrary radii and arbitrary elastic constants for both core and shell. The expressions for the static strain are consistent with experiments, simulations, and previous analytical investigations; those for phonons are consistent with known results for homogeneous NWs. Among other things, we show that the dispersion relations of the torsional, longitudinal, and flexural modes change differently with the relative shell thickness, and we identify new terms in the corresponding strain tensors that are absent for uncapped NWs. We illustrate our results via the example of Ge/Si core/shell NWs and demonstrate that shellinduced strain has large effects on the hole spectrum of these systems.
 
11.  PhononMediated Decay of SingletTriplet Qubits in Double Quantum Dots 
Viktoriia Kornich, Christoph Kloeffel, and Daniel Loss. Phys. Rev. B 89, 085410 (2014); arXiv:1311.2197.
We study theoretically the phononinduced relaxation (T_1) and decoherence times (T_2) of singlettriplet qubits in lateral GaAs double quantum dots (DQDs). When the DQD is biased, Pauli exclusion enables strong dephasing via twophonon processes. This mechanism requires neither hyperfine nor spinorbit interaction and yields T_2 << T_1, in contrast to previous calculations of phononlimited lifetimes. When the DQD is unbiased, we find T_2 \simeq 2 T_1 and much longer lifetimes than in the biased DQD. For typical setups, the decoherence and relaxation rates due to onephonon processes are proportional to the temperature T, whereas the rates due to twophonon processes reveal a transition from T^2 to higher powers as T is decreased. Remarkably, both T_1 and T_2 exhibit a maximum when the external magnetic field is applied along a certain axis within the plane of the twodimensional electron gas. We compare our results with recent experiments and analyze the dependence of T_1 and T_2 on system properties such as the detuning, the spinorbit parameters, the hyperfine coupling, and the orientation of the DQD and the applied magnetic field with respect to the main crystallographic axes.
 
12.  Circuit QED with HoleSpin Qubits in Ge/Si Nanowire Quantum Dots 
Christoph Kloeffel, Mircea Trif, Peter Stano, and Daniel Loss. Phys. Rev. B 88, 241405(R) (2013); arXiv:1306.3596.
We propose a setup for universal and electrically controlled quantum
information processing with hole spins in Ge/Si core/shell nanowire quantum
dots (NW QDs). Singlequbit gates can be driven through electricdipoleinduced
spin resonance, with spinflip times shorter than 100 ps. Longdistance
qubitqubit coupling can be mediated by the cavity electric field of a
superconducting transmission line resonator, where we show that operation times
below 20 ns seem feasible for the entangling squarerootofiSWAP gate. The
absence of Dresselhaus spinorbit interaction (SOI) and the presence of an
unusually strong Rashbatype SOI enable precise control over the transverse
qubit coupling via an externally applied, perpendicular electric field. The
latter serves as an onoff switch for quantum gates and also provides control
over the g factor, so single and twoqubit gates can be operated
independently. Remarkably, we find that idle qubits are insensitive to charge
noise and phonons, and we discuss strategies for enhancing noiselimited gate
fidelities.
 
13.  Tunable g factor and phononmediated hole spin relaxation in Ge/Si nanowire quantum dots 
Franziska Maier, Christoph Kloeffel, and Daniel Loss. Phys. Rev. B 87, 161305(R) (2013); arXiv:1302.5027.
We theoretically consider g factor and spin lifetimes of holes in a
longitudinal Ge/Si core/shell nanowire quantum dot that is exposed to external
magnetic and electric fields. For the ground states, we find a large anisotropy
of the g factor which is highly tunable by applying electric fields. This
tunability depends strongly on the direction of the electric field with respect
to the magnetic field. We calculate the singlephonon hole spin relaxation
times T1 for zero and small electric fields and propose an optimal setup in
which very large T1 of the order of tens of milliseconds can be reached.
Increasing the relative shell thickness or the longitudinal confinement length
prolongs T1 further. In the absence of electric fields, the dephasing vanishes
and the decoherence time T2 is determined by T2 = 2 T1.
 
14.  Prospects for SpinBased Quantum Computing in Quantum Dots 
Christoph Kloeffel and Daniel Loss. Annu. Rev. Condens. Matter Phys. 4, 51 (2013); arXiv:1204.5917.
Experimental and theoretical progress toward quantum computation with spins
in quantum dots (QDs) is reviewed, with particular focus on QDs formed in GaAs
heterostructures, on nanowirebased QDs, and on selfassembled QDs. We report
on a remarkable evolution of the field where decoherence, one of the main
challenges for realizing quantum computers, no longer seems to be the stumbling
block it had originally been considered. General concepts, relevant quantities,
and basic requirements for spinbased quantum computing are explained;
opportunities and challenges of spinorbit interaction and nuclear spins are
reviewed. We discuss recent achievements, present current theoretical
proposals, and make several suggestions for further experiments.
 
15.  Strong SpinOrbit Interaction and Helical Hole States in Ge/Si Nanowires 
Christoph Kloeffel, Mircea Trif, and Daniel Loss. Phys. Rev. B 84, 195314 (2011); arXiv:1107.4870.
We study theoretically the lowenergy hole states of Ge/Si core/shell nanowires. The lowenergy valence band is quasidegenerate, formed by two doublets of different orbital angular momenta, and can be controlled via the relative shell thickness and via external fields. We find that direct (dipolar) coupling to a moderate electric field leads to an unusually large spinorbit interaction of Rashba type on the order of meV which gives rise to pronounced helical states enabling electrical spin control. The system allows for quantum dots and spin qubits with energy levels that can vary from nearly zero to several meV, depending on the relative shell thickness.
 
16.  Controlling the Interaction of Electron and Nuclear Spins in a TunnelCoupled Quantum Dot 
C. Kloeffel, P. A. Dalgarno, B. Urbaszek, B. D. Gerardot, D. Brunner, P. M. Petroff, D. Loss, and R. J. Warburton. Phys. Rev. Lett. 106, 046802 (2011); arXiv:1010.3330.
We present a technique for manipulating the nuclear spins and the emission
polarization from a single optically active quantum dot. When the quantum dot
is tunnel coupled to a Fermi sea, we have discovered a natural cycle in which
an electron spin is repeatedly created with resonant optical excitation. The
spontaneous emission polarization and the nuclear spin polarization exhibit a
bistability. For a sigma(+) pump, the emission switches from sigma(+) to
sigma() at a particular detuning of the laser. Simultaneously, the nuclear
spin polarization switches from positive to negative. Away from the
bistability, the nuclear spin polarization can be changed continuously from
negative to positive, allowing precise control via the laser wavelength.
