Silas Hoffman
ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland

Research Interests
 Spin transport
 Kondo physics in magnetic systems
 Superconductorferromagnet heterostructures
CV
2014Present  Postdoc in the group of Daniel Loss, University of Basel 
2012  2013  Postdoc in the group of Yaroslav Tserkovnyak, University of California, Los Angeles 
2007  2012  PhD in Physics under the supervision of Yaroslav Tserkovnyak, University of California, Los Angeles 
2004  2007  Master of Science in Physics, University of California, Los Angeles 
2001  2004  Bachelor of Science in Physics, University of Illinois at UrbanaChampaign 
2000  2001  Worcester Polytechnic Institute 
Publications
Show all abstracts.1.  Topological Phase Detection in Rashba Nanowires with a Quantum Dot 
Denis Chevallier, Pawel Szumniak, Silas Hoffman, Daniel Loss, and Jelena Klinovaja. Phys. Rev. B 97, 045404 (2018); arXiv:1710.05576.  
2.  Lowfield Topological Threshold in Majorana Double Nanowires 
Constantin Schrade, Manisha Thakurathi, Christopher Reeg, Silas Hoffman, Jelena Klinovaja, and Daniel Loss. Phys. Rev. B 96, 035306 (2017); arXiv:1705.09364.
A hard proximityinduced superconducting gap has recently been observed in semiconductor nanowire systems at low magnetic fields. However, in the topological regime at high magnetic fields, a soft gap emerges and represents a fundamental obstacle to topologically protected quantum information processing with Majorana bound states. Here we show that in a setup of double Rashba nanowires that are coupled to an swave superconductor and subjected to an external magnetic field along the wires, the topological threshold can be significantly reduced by the destructive interference of direct and crossedAndreev pairing in this setup, precisely down to the magnetic field regime in which current experimental technology allows for a hard superconducting gap. We also show that the resulting Majorana bound states exhibit sufficiently short localization lengths, which makes them ideal candidates for future braiding experiments.
 
3.  Spindependent coupling between quantum dots and topological quantum wires 
Silas Hoffman, Denis Chevallier, Daniel Loss, and Jelena Klinovaja. Phys. Rev. B 96, 045440 (2017); arXiv:1705.03002.
Considering Rashba quantum wires with a proximityinduced superconducting gap as physical realizations of Majorana bound states and quantum dots, we calculate the overlap of the Majorana wave functions with the local wave functions on the dot. We determine the spindependent tunneling amplitudes between these two localized states and show that we can tune into a fully spin polarized tunneling regime by changing the distance between dot and Majorana bound state. Upon directly applying this to the tunneling model Hamiltonian, we calculate the effective magnetic field on the quantum dot flanked by two Majorana bound states. The direction of the induced magnetic field on the dot depends on the occupation of the nonlocal fermion formed from the two Majorana end states which can be used as a readout for such a Majorana qubit.
 
4.  Quantum Dynamics of Skyrmions in Chiral Magnets 
Christina Psaroudaki, Silas Hoffman, Jelena Klinovaja, and Daniel Loss. Phys. Rev. X 7, 041045 (2017); arXiv:1612.01885.
We study the quantum propagation of a Skyrmion in chiral magnetic insulators by generalizing the micromagnetic equations of motion to a finitetemperature path integral formalism, using field theoretic tools. Promoting the center of the Skyrmion to a dynamic quantity, the fluctuations around the Skyrmionic configuration give rise to a timedependent damping of the Skyrmion motion. From the frequency dependence of the damping kernel, we are able to identify the Skyrmion mass, thus providing a microscopic description of the kinematic properties of Skyrmions. When defects are present or a magnetic trap is applied, the Skyrmion mass acquires a finite value proportional to the effective spin, even at vanishingly small temperature. We demonstrate that a Skyrmion in a confined geometry provided by a magnetic trap behaves as a massive particle owing to its quasionedimensional confinement. An additional quantum mass term is predicted, independent of the effective spin, with an explicit temperature dependence which remains finite even at zero temperature.
 
5.  Dynamical Shiba states by precessing magnetic moments in an swave superconductor 
Vardan Kaladzhyan, Silas Hoffman, and Mircea Trif. Phys. Rev. B 95, 195403 (2017); arXiv:1611.09722.
We study theoretically the dynamics of a Shiba state forming around precessing classical spin in an swave superconductor. Utilizing a rotating wave description for the precessing magnetic impurity, we find the resulting Shiba bound state quasienergy and the spatial extension of the Shiba wavefunction. We show that such a precession pertains to dc charge and spin currents flowing through a normal STM tip tunnel coupled to the superconductor in the vicinity of the impurity. We calculate these currents and find that they strongly depend on the magnetic impurity precession frequency, precession angle, and on the position of the Shiba energy level in the superconducting gap. The resulting charge current is found to be proportional to the difference between the electron and hole wavefunctions of the Shiba state, being a direct measure for such an asymmetry. By dynamically driving the impurity one can infer the spin dependence of the Shiba states in the absence of a spinpolarized STM tip.
 
6.  Detecting Topological Superconductivity with \phi_0 Josephson Junctions 
Constantin Schrade, Silas Hoffman, Jelena Klinovaja, and Daniel Loss. Phys. Rev. B 95, 195421 (2017); arXiv:1607.07794.
The interplay of superconductivity, magnetic fields, and spinorbit interaction lies at the heart of topological superconductivity. Remarkably, the recent experimental discovery of \varphi_0 Josephson junctions by Szombati et al., Nat. Phys. 12, 568 (2016), characterized by a finite phase offset in the supercurrent, require the same ingredients as topological superconductors, which suggests a profound connection between these two distinct phenomena. Here, we theoretically show that a quantum dot \varphi_0 Josephson junction can serve as a new qualitative indicator for topological superconductivity: Microscopically, we find that the phase shift in a junction of s−wave superconductors is due to the spinorbit induced mixing of singly occupied states on the qantum dot, while for a topological superconductor junction it is due to singlettriplet mixing. Because of this important difference, when the spinorbit vector of the quantum dot and the external Zeeman field are orthogonal, the swave superconductors form a \pi Josephson junction while the topological superconductors have a finite offset \varphi_0 by which topological superconductivity can be distinguished from conventional superconductivity. Our prediction can be immediately tested in nanowire systems currently used for Majorana fermion experiments and thus offers a new and realistic approach for detecting topological bound states.
 
7.  Universal Quantum Computation with Hybrid SpinMajorana Qubits 
Silas Hoffman, Constantin Schrade, Jelena Klinovaja, and Daniel Loss. Phys. Rev. B 94, 045316 (2016); arXiv:1602.06923.
We theoretically propose a set of universal quantum gates acting on a hybrid qubit formed by coupling a quantum dot spin qubit and Majorana fermion qubit. First, we consider a quantum dot tunnelcoupled to two topological superconductors. The effective spinMajorana exchange facilitates a hybrid CNOT gate for which either qubit can be the control or target. The second setup is a modular scalable network of topological superconductors and quantum dots. As a result of the exchange interaction between adjacent spin qubits, a CNOT gate is implemented that acts on neighboring Majorana qubits, and eliminates the necessity of interqubit braiding. In both setups the spinMajorana exchange interaction allows for a phase gate, acting on either the spin or the Majorana qubit, and for a SWAP or hybrid SWAP gate which is sufficient for universal quantum computation without projective measurements.
 
8.  Topological Phases of Inhomogeneous Superconductivity 
Silas Hoffman, Jelena Klinovaja, and Daniel Loss. Phys. Rev. B 93, 165418 (2016); arXiv:1601.04270.
We theoretically consider the effect of a spatially periodic modulation of the superconducting order parameter on the formation of Majorana fermions induced by a onedimensional system with magnetic impurities brought into close proximity to an swave superconductor. When the magnetic exchange energy is larger than the interimpurity electron hopping we model the effective system as a chain of coupled Shiba states. While in the opposite regime, the effective system is accurately described by a quantum wire model. Upon including a spatially modulated superconducting pairing, we find, for sufficiently large magnetic exchange energy, the system is able to support a single pair of Majorana fermions with one Majorana fermion on the left end of the system and one on the right end. When the modulation of superconductivity is large compared to the magnetic exchange energy, the Shiba chain returns to a trivially gapped regime while the quantum wire enters a new topological phase capable of supporting two pairs of Majorana fermions.
 
9.  Impurity Induced Quantum Phase Transitions and Magnetic Order in Conventional Superconductors: Competition between Bound and Quasiparticle states 
Silas Hoffman, Jelena Klinovaja, Tobias Meng, and Daniel Loss. Phys. Rev. B 92, 125422 (2015); arXiv:1503.08762.
We theoretically study bound states generated by magnetic impurities within conventional swave superconductors, both analytically and numerically. In determining the effect of the hybridization of two such bound states on the energy spectrum as a function of magnetic exchange coupling, relative angle of magnetization, and distance between impurities, we find that quantum phase transitions can be modulated by each of these parameters. Accompanying such transitions, there is a change in the preferred spin configuration of the impurities. Although the interaction between the impurity spins is overwhelmingly dominated by the quasiparticle contribution, the ground state of the system is determined by the boundstate energies. Selfconsistently calculating the superconducting order parameter, we find a discontinuity when the system undergoes a quantum phase transition as indicated by the boundstate energies.
 
10.  Superconducting Gap Renormalization around two Magnetic Impurities: From Shiba to Andreev Bound States 
Tobias Meng, Jelena Klinovaja, Silas Hoffman, Pascal Simon, and Daniel Loss. Phys. Rev. B 92, 064503 (2015); arXiv:1501.07901.
We study the renormalization of the gap of an swave superconductor in the presence of two magnetic impurities. For weakly bound Shiba states, we analytically calculate the part of the gap renormalization that is sensitive to the relative orientation of the two impurity spins. For impurities with a strong exchange coupling to the conduction electrons, we solve the gap equation selfconsistently by numerics and find that the subgap Shiba state turns into a supragap Andreev state when the local gap parameter changes sign under the impurities.
 
11.  Magnetic exchange and nonequilibrium spin current through interacting quantum dots 
Silas Hoffman and Yaroslav Tserkovnyak. Phys. Rev. B 91, 245427 (2015); arXiv:1412.4663.
We develop a theory for charge and spin currents between two canted magnetic leads flowing through a quantum dot with an arbitrary local interaction. For a noncollinear magnetic configuration, we calculate equilibrium and nonequilibrium currents biased by voltage or temperature difference or pumped by magnetic dynamics. We are able to explicitly separate the equilibrium and nonequilibrium contributions to the spin current, both of which can be written in terms of the full retarded Green's function on the dot. Taking the specific example of a singlelevel quantum dot with a large onsite Coulomb interaction, we calculate the total spin current near the Kondo regime, which we find to be generally enhanced in magnitude as compared to the noninteracting case.
 
12.  Highefficiency resonant amplification of weak magnetic fields for single spin magnetometry 
Luka Trifunovic, Fabio L. Pedrocchi, Silas Hoffman, Patrick Maletinsky, Amir Yacoby, 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.
 
13.  Electricfield induced domainwall dynamics: depinning and chirality switching 
Pramey Upadyaya, Ritika Dusad, Silas Hoffman, Yaroslav Tserkovnyak, Juan G. Alzate, Pedram Khalili Amiri, and Kang L. Wang. Phys. Rev. B 88, 224422 (2013); arXiv:1309.3693.
We theoretically study the equilibrium and dynamic properties of nanoscale magnetic tunnel junctions (MTJs) and magnetic wires, in which an electric field controls the magnetic anisotropy through spinorbit coupling. By performing micromagnetic simulations, we construct a rich phase diagram and find that, in particular, the equilibrium magnetic textures can be tuned between Néel and Bloch domain walls in an elliptical MTJ. Furthermore, we develop a phenomenological model of a quasionedimensional domain wall confined by a parabolic potential and show that, near the NéeltoBlochwall transition, a pulsed electric field induces precessional domainwall motion which can be used to reverse the chirality of a Néel wall and even depin it. This domainwall motion controlled by electric fields, in lieu of applied current, may provide a model for ultralowpower domainwall memory and logic devices.
 
14.  LandauLifshitz theory of the longitudinal spin Seebeck effect 
Silas Hoffman, Koji Sato, and Yaroslav Tserkovnyak. Phys. Rev. B 88, 064408 (2013); arXiv:1304.7295.
Thermalbiasinduced spin angular momentum transfer between a paramagnetic metal and ferromagnetic insulator is studied theoretically based on the stochastic LandauLifshitzGilbert (LLG) phenomenology. Magnons in the ferromagnet establish a nonequilibrium steady state by equilibrating with phonons via bulk Gilbert damping and electrons in the paramagnet via spin pumping, according to the fluctuationdissipation theorem. Subthermal magnons and the associated spin currents are treated classically, while the appropriate quantum crossover is imposed on highfrequency magnetic fluctuations. We identify several length scales in the ferromagnet, which govern qualitative changes in the dependence of the thermally induced spin current on the magnetic film thickness.
 
15.  Spintorque ac impedance in magnetic tunnel junctions 
Silas Hoffman, Pramey Upadhyaya, and Yaroslav Tserkovnyak. Phys. Rev. B 86, 214420 (2012); arXiv:1209.1072.
Subjecting a magnetic tunnel junction (MTJ) to a spintransfer torque and/or electric voltageinduced magnetic anisotropy induces magnetic precession, which can reciprocally pump current through the circuit. This results in an ac impedance, which is sensitive to the magnetic field applied to the MTJ. Measurement of this impedance can be used to characterize the nature of the coupling between the magnetic free layer and the electric input as well as a readout of the magnetic configuration of the MTJ.
 
16.  Magnetic bit stability: Competition between domainwall and monodomain switching 
Silas Hoffman, Yaroslav Terskovnyak, Pedram Khalili Amiri, and Kang L. Wang. Appl. Phys. Lett. 100, 212406 (2012); arXiv:1202.2901.
We numerically study the thermal stabilityproperties of computer memory storage realized by a magnetic ellipse. In the case of practical magnetic randomaccess memory devices, the bit can form a spin texture during switching events. To study the energy barrier for thermally induced switching, we develop a variational procedure to force the bit to traverse a smooth path through configuration space between the points of stability. We identify textured configurations realizing domainwall propagation, which may have an energy barrier less than that of the corresponding monodomain model. We contrast the emergence of such micromagnetic effects in thermal versus fieldinduced switching.
 
17.  Nonlinear Dynamics in a Magnetic Josephson Junction 
Silas Hoffman, Ya. M. Blanter, and Yaroslav Tserkovnyak. Phys. Rev B 86, 054427 (2012); arXiv:1110.1680.
We theoretically consider a Josephson junction formed by a ferromagnetic spacer with a strong spinorbit interaction or a magnetic spin valve, i.e., a bilayer with one static and one free layer. Electron spin transport facilitates a nonlinear dynamical coupling between the magnetic moment and charge current, which consists of normal and superfluid components. By phenomenologically adding reactive and dissipative interactions (guided by structural and Onsager symmetries), we construct magnetic torques and charge pumping, whose microscopic origins are also discussed. A stability analysis of our coupled nonlinear systems generates a rich phase diagram with fixed points, limit cycles, and quasiperiodic states. Our findings reduce to the known phase diagrams for currentbiased nonmagnetic Josephson junctions, on the one hand, and spintorque driven magnetic films, on the other, in the absence of coupling between the magnetic and superconducting order parameters.
