arXiv subjects

Karsten Flensberg

Publications and source records attributed to Karsten Flensberg.

At least 91 records · Page 5Linked to original sources

arXiv2012

Introduction to topological superconductivity and Majorana fermions

This short review article provides a pedagogical introduction to the rapidly growing research field of Majorana fermions in topological superconductors. We first discuss in some details the simplest "toy model" in which Majoranas appear, namely a one-dimensional tight-binding representation of a p-wave superconductor, introduced more than ten years ago by Kitaev. We then give a general introduction to the remarkable properties of Majorana fermions in condensed matter systems, such as their intrinsically non-local nature and exotic exchange statistics, and explain why these quasiparticles are suspected to be especially well suited for low-decoherence quantum information processing. We also discuss the experimentally promising (and perhaps already successfully realized) possibility of creating topological superconductors using semiconductors with strong spin-orbit coupling, proximity-coupled to standard s-wave superconductors and exposed to a magnetic field. The goal is to provide an introduction to the subject for experimentalists or theorists who are new to the field, focusing on the aspects which are most important for understanding the basic physics. The text should be accessible for readers with a basic understanding of quantum mechanics and second quantization, and does not require knowledge of quantum field theory or topological states of matter.

cond-mat.mes-hall↗

arXiv2012

Parity qubits and poor man's Majorana bound states in double quantum dots

We study a double quantum dot connected via a common superconducting lead and show that this system can be tuned to host one Majorana bound state (MBS) on each dot. We call them "poor man's Majorana bound states" since they are not topologically protected, but otherwise share the properties of MBS formed in topological superconductors. We describe the conditions for the existence of the two spatially separated MBS, which include breaking of spin degeneracy in the two dots, with the spins polarized in different directions. Therefore, we propose to use a magnetic field configuration where the field directions on the two dot form an angle. By control of this angle the cross Andreev reflection and the tunnel amplitudes can be tuned to be approximately equal, which is a requirement for the formation of the MBS. We show that the fermionic state encoded in the two Majoranas constitutes a parity qubit, which is non-local and can only be measured by probing both dots simultaneously. Using a many-particle basis for the MBS, we discuss the role of interactions and show that inter-dot interactions always lift the degeneracy. We also show how the MBS can be probed by transport measurements and discuss how the combination of several such double dot systems allows for entanglement of parity qubits and measurement of their dephasing times.

cond-mat.mes-hall↗

arXiv2012

Finite-bias conductance anomalies at a singlet-triplet crossing

Quantum dots and single-molecule transistors may exhibit level crossings induced by tuning external parameters such as magnetic field or gate voltage. For Coulomb blockaded devices, this shows up as an inelastic cotunneling threshold in the differential conductance, which can be tuned to zero at the crossing. Here we show that, in addition, level crossings can give rise to a nearly vertical step-edge, ridge or even a Fano-like ridge-valley feature in the differential conductance inside the relevant Coulomb diamond. We study a gate-tunable quasidegeneracy between singlet and triplet ground states, and demonstrate how these different shapes may result from a competition between nonequilibrium occupations and weak (spin-orbit) mixing of the states. Our results are shown to be in qualitative agreement with recent transport measurements on a Mn complex [E. A. Osorio, et al., Nano Lett. 10, 105 (2010)]. The effect remains entirely general and should be observable in a wide range of Coulomb blockaded devices.

cond-mat.mes-hall↗

arXiv2012

Using hybrid topological-spin qubit systems for two-qubit-spin gates

We investigate a hybrid quantum system involving spin qubits, based on the spins of electrons confined in quantum dots, and topological qubits, based on Majorana fermions. In such a system, gated control of the charge on the quantum dots allows transfer of quantum information between the spin and topological qubits, and the topological system can be used to facilitate transfer of spin qubits between spatially separated quantum dots and to initialize entangled spin-qubit pairs. Here, we show that the coupling to the topological system also makes it possible to perform entangling two-qubit gates on spatially separated spin qubits. The two-qubit gates are based on a combination of topologically protected braiding operations, gate-controlled charge transfer between the dots and edge Majorana modes, and measurements of the state of the topological qubits.

cond-mat.mes-hall↗

arXiv2012

Cotunneling renormalization in carbon nanotube quantum dots

We determine the level-shifts induced by cotunneling in a Coulomb blockaded carbon nanotube quantum dot using leading order quasi-degenerate perturbation theory within a single nanotube quartet. It is demonstrated that otherwise degenerate and equally tunnel-coupled $K$ and $K'$ states are mixed by cotunneling and therefore split up in energy except at the particle/hole-symmetric midpoints of the Coulomb diamonds. In the presence of an external magnetic field, we show that cotunneling induces a gate-dependent $g$-factor renormalization, and we outline different scenarios which might be observed experimentally, depending on the values of both intrinsic $KK'$ splitting and spin-orbit coupling.

cond-mat.mes-hall↗

arXiv2012

Emerging Dirac and Majorana fermions for carbon nanotubes with proximity-induced pairing and spiral magnetic field

We study the low-energy bandstructure of armchair and small-bandgap semiconducting carbon nanotubes with proximity-induced superconducting pairing when a spiral magnetic field creates strong effective spin-orbit interactions from the Zeeman term and a periodic potential from the orbital part. We find that gapless Dirac fermions can be generated by variation of a single parameter. For a semiconducting tube with the field in the same plane, a non-degenerate zero mode at momentum k=0 can be induced, allowing for the generation of topologically protected Majorana fermion end states.

cond-mat.mes-hall↗

arXiv2012

Spin-orbit-induced strong coupling of a single spin to a nanomechanical resonator

We theoretically investigate the deflection-induced coupling of an electron spin to vibrational motion due to spin-orbit coupling in suspended carbon nanotube quantum dots. Our estimates indicate that, with current capabilities, a quantum dot with an odd number of electrons can serve as a realization of the Jaynes-Cummings model of quantum electrodynamics in the strong-coupling regime. A quantized flexural mode of the suspended tube plays the role of the optical mode and we identify two distinct two-level subspaces, at small and large magnetic field, which can be used as qubits in this setup. The strong intrinsic spin-mechanical coupling allows for detection, as well as manipulation of the spin qubit, and may yield enhanced performance of nanotubes in sensing applications.

cond-mat.mes-hall↗

arXiv2012

Dephasing and Hyperfine Interaction in Carbon Nanotubes Double Quantum Dots: Disordered Case

We study theoretically the \emph{return probability experiment}, used to measure the dephasing time $T_2^*$, in a double quantum dot (DQD) in semiconducting carbon nanotubes (CNTs) with spin-orbit coupling and disorder induced valley mixing. Dephasing is due to hyperfine interaction with the spins of the ${}^{13}$C nuclei. Due to the valley and spin degrees of freedom four bounded states exist for any given longitudinal mode in the quantum dot. At zero magnetic field the spin-orbit coupling and the valley mixing split those four states into two Kramers doublets. The valley mixing term for a given dot is determined by the intra-dot disorder and therefore the states in the Kramers doublets belonging to different dots are different. We show how nonzero single-particle interdot tunneling amplitudes between states belonging to different doublets give rise to new avoided crossings, as a function of detuning, in the relevant two particle spectrum, crossing over from the two electrons in one dot states configuration, $(0,2)$, to the one electron in each dot configuration, $(1,1)$. In contrast to the clean system, multiple Landau-Zener processes affect the separation and the joining stages of each single-shot measurement and they affect the outcome of the measurement in a way that strongly depends on the initial state. We find that a well-defined return probability experiment is realized when, at each single-shot cycle, the (0,2) ground state is prepared. In this case, valley mixing increases the saturation value of the measured return probability, whereas the probability to return to the (0,2) ground state remains unchanged. Finally, we study the effect of the valley mixing in the high magnetic field limit; for a parallel magnetic field the predictions coincide with a clean nanotube, while the disorder effect is always relevant with a magnetic field perpendicular to the nanotube axis.

cond-mat.mes-hall↗

arXiv2011

Quantum information transfer between topological and spin qubit systems

We propose a method to coherently transfer quantum information, and to create entanglement, between topological qubits and conventional spin qubits. Our suggestion uses gated control to transfer an electron (spin qubit) between a quantum dot and edge Majorana modes in adjacent topological superconductors. Because of the spin polarization of the Majorana modes, the electron transfer translates spin superposition states into superposition states of the Majorana system, and vice versa. Furthermore, we show how a topological superconductor can be used to facilitate long-distance quantum information transfer and entanglement between spatially separated spin qubits.

cond-mat.supr-con↗

arXiv2011

Scheme to measure Majorana fermion lifetimes using a quantum dot

We propose a setup to measure the lifetime of the parity of a pair of Majorana bound states. The proposed experiment has one edge Majorana state tunnel coupled to a quantum dot, which in turn is coupled to a metallic electrode. When the Majorana Fermions overlap, even a small relaxation rate qualitatively changes the non-linear transport spectrum, and for strong overlap the lifetime can be read off directly from the height of a current peak. This is important for the usage of Majorana Fermions as a platform for topological quantum computing, where the parity relaxation is a limiting factor.

cond-mat.mes-hall↗

arXiv2011

Dephasing and Hyperfine Interaction in Carbon Nanotubes Double Quantum Dots: The Clean Limit

We consider theoretically ${}^{13}$C-hyperfine interaction induced dephasing in carbon nanotubes double quantum dots with curvature induced spin-orbit coupling. For two electrons initially occupying a single dot, we calculate the average return probability after separation into the two dots, which have random nuclear-spin configurations. We focus on the long time saturation value of the return probability, $P_\infty$. Because of the valley degree of freedom, the analysis is more complex than in, for example, GaAs quantum dots, which have two distinct $P_\infty$ values depending on the magnetic field. Here the prepared state and the measured state is non-unique because two electrons in the same dot are allowed in six different states. Moreover, for one electron in each dot sixteen states exist and therefore are available for being mixed by the hyperfine field. The return probability experiment is found to be strongly dependent on the prepared state, on the external magnetic field---both Zeeman and orbital effects - and on the spin-orbit splitting. The lowest saturation value, being $P_\infty$=1/3, occurs at zero magnetic field for nanotubes with spin-orbit coupling and the initial state being the groundstate, this situation is equivalent to double dots without the valley degree of freedom. In total, we report nine dynamically different situations that give $P_\infty$=1/3, 3/8, 2/5, 1/2 and for valley anti-symmetric prepared states in an axial magnetic field, $P_\infty$=1. When the groundstate is prepared the ratio between the spin-orbit splitting and the Zeeman energy due to a perpendicular magnetic field can tune the effective hyperfine field continuously from being three dimensional to two dimensional giving saturation values from $P_\infty$=1/3 to 3/8.

cond-mat.mes-hall↗

arXiv2010

Interaction-induced negative differential resistance in asymmetric molecular junctions

Combining insights from quantum chemistry calculations with master equations, we discuss a mechanism for negative differential resistance (NDR) in molecular junctions, operated in the regime of weak tunnel coupling. The NDR originates from an interplay of orbital spatial asymmetry and strong electron-electron interaction, which causes the molecule to become trapped in a non-conducting state above a voltage threshold. We show how the desired asymmetry can be selectively introduced in individual orbitals in e.g., OPE-type molecules by functionalization with a suitable side group, which is in linear conjugation to one end of the molecule and cross-conjugated to the other end.

cond-mat.mes-hall↗

arXiv2010

Non-Abelian operations on Majorana fermions via single charge control

We demonstrate that non-Abelian rotations within the degenerate groundstate manifold of a set of Majorana fermions can be realized by the addition or removal of single electrons, and propose an implementation using Coulomb blockaded quantum dots. The exchange of electrons generates rotations similar to braiding, though not in real space. Unlike braiding operations, rotations by a continuum of angles are possible, while still being partially robust against perturbations. The quantum dots can also be used for readout of the state of the Majorana system via a charge measurement.

cond-mat.mes-hall↗

arXiv2010

Tunneling characteristic of a chain of Majorana bound states

We consider theoretically tunneling characteristic of a junction between a normal metal and a chain of coupled Majorana bound states generated at crossings between topological and non-topological superconducting sections, as a result of, for example, disorder in nanowires. While an isolated Majorana state supports a resonant Andreev process, yielding a zero bias differential conductance peak of height 2e^2/h, the situation with more coupled Majorana states is distinctively different with both zeros and 2e^2/h peaks in the differential conductance. We derive a general expression for the current between a normal metal and a network of coupled Majorana bound states and describe the differential conductance spectra for a generic set of situations, including regular, disordered, and infinite chains of bound states.

cond-mat.mes-hall↗

arXiv2010

Gate-dependent spin-orbit coupling in multi-electron carbon nanotubes

Understanding how the orbital motion of electrons is coupled to the spin degree of freedom in nanoscale systems is central for applications in spin-based electronics and quantum computation. We demonstrate this coupling of spin and orbit in a carbon nanotube quantum dot in the general multi-electron regime in presence of finite disorder. Further, we find a strong systematic dependence of the spin-orbit coupling on the electron occupation of the quantum dot. This dependence, which even includes a sign change is not demonstrated in any other system and follows from the curvature-induced spin-orbit split Dirac-spectrum of the underlying graphene lattice. Our findings unambiguously show that the spin-orbit coupling is a general property of nanotube quantum dots which provide a unique platform for the study of spin-orbit effects and their applications.

cond-mat.mes-hall↗

arXiv2010

Transport via coupled states in a C60 peapod quantum dot

We have measured systematic repetitions of avoided crossings in low temperature three-terminal transport through a carbon nanotube with encapsulated C60 molecules. We show that this is a general effect of the hybridization of a host quantum dot with an impurity. The well-defined nanotube allows identification of the properties of the impurity, which we suggest to be a chain of C60 molecules inside the nanotube. This electronic coupling between the two subsystems opens the interesting and potentially useful possibility of contacting the encapsulated molecules via the tube.

cond-mat.mes-hall↗

arXiv2009

Electrical manipulation of spin states in a single electrostatically gated transition-metal complex

We demonstrate an electrically controlled high-spin (S=5/2) to low-spin (S=1/2) transition in a three-terminal device incorporating a single Mn2+ ion coordinated by two terpyridine ligands. By adjusting the gate-voltage we reduce the terpyridine moiety and thereby strengthen the ligand-field on the Mn-atom. Adding a single electron thus stabilizes the low-spin configuration and the corresponding sequential tunnelling current is suppressed by spin-blockade. From low-temperature inelastic cotunneling spectroscopy, we infer the magnetic excitation spectrum of the molecule and uncover also a strongly gate-dependent singlet-triplet splitting on the low-spin side. The measured bias-spectroscopy is shown to be consistent with an exact diagonalization of the Mn-complex, and an interpretation of the data is given in terms of a simplified effective model.

cond-mat.mes-hall↗

arXiv2008

Interplay between interference and Coulomb interaction in the ferromagnetic Anderson model with applied magnetic field

We study the competition between interference due to multiple single-particle paths and Coulomb interaction in a simple model of an Anderson-like impurity with local-magnetic-field-induced level splitting coupled to ferromagnetic leads. The model along with its potential experimental relevance in the field of spintronics serves as a nontrivial benchmark system where various quantum transport approaches can be tested and compared. We present results for the linear conductance obtained by a spin-dependent implementation of the density matrix renormalization group scheme which are compared with a mean-field solution as well as a seemingly more advanced Hubbard-I approximation. We explain why mean-field yields nearly perfect results, while the more sophisticated Hubbard-I approach fails, even at a purely conceptual level since it breaks hermiticity of the related density matrix. Furthermore, we study finite bias transport through the impurity by the mean-field approach and recently developed higher-order density matrix equations. We find that the mean-field solution fails to describe the plausible results of the higher-order density matrix approach both quantitatively and qualitatively as it does not capture some essential features of the current-voltage characteristics such as negative differential conductance.

cond-mat.mes-hall↗