Pawel Szumniak

We study theoretically the detection of the topological phase transition occurring in Rashba nanowires with proximity-induced superconductivity using a quantum dot. The bulk states lowest in energy of such a nanowire have a spin polarization parallel or antiparallel to the applied magnetic field in the topological or trivial phase, respectively. We show that this property can be probed by the quantum dot created at the end of the nanowire by external gates. By tuning one of the two spin-split levels of the quantum dot to be in resonance with nanowire bulk states, one can detect the spin polarization of the lowest band via transport measurement. This allows one to determine the topological phase of the Rashba nanowire independently of the presence of Majorana bound states.

We consider a Rashba nanowire with a proximity gap which can be brought into the topological phase by tuning external magnetic field or chemical potential. We study spin and charge of the bulk quasiparticle states when passing through the topological transition for open and closed systems. We show, analytically and numerically, that the spin of bulk states around the topological gap reverses its sign when crossing the transition due to band inversion, independent of the presence of Majorana fermions in the system. This spin reversal can be considered as a bulk signature of topological superconductivity that can be accessed experimentally. We find a similar behavior for the charge of the bulk quasiparticle states, also exhibiting a sign reversal at the transition. We show that these signatures are robust against random static disorder.

We consider a system of weakly coupled wires with quantum Hall effect (QHE) and in the presence of a spatially periodic modulation of the chemical potential along the wire, equivalent to a charge density wave (CDW). We investigate the competition between the two effects which both open a gap. We show that by changing the ratio between the amplitudes of the CDW modulation and the tunneling between wires, one can switch between non-topological CDW-dominated phase to topological QHE-dominated phase. Both phases host edge states of chiral and non-chiral nature robust to on-site disorder. However, only in the topological phase, the edge states are immune to disorder in the phase shifts of the CDWs. We provide analytical solutions for filling factor $\nu=1$ and study numerically effects of disorder as well as present numerical results for higher filling factors.

We investigate numerically charge, spin, and entanglement dynamics of two electrons confined in a gated semiconductor nanowire. The electrostatic coupling between electrons in the nanowire and the charges in the metal gates leads to a self-trapping of the electrons which results in soliton-like properties. We show that the interplay of an all-electrically controlled coherent transport of the electron solitons and of the exchange interaction can be used to realize ultrafast SWAP and entangling $\sqrt{\text{SWAP}}$ gates for distant spin qubits. We demonstrate that the latter gate can be used to generate a maximally entangled spin state of spatially separated electrons. The results are obtained by quantum mechanical time-dependent calculations with exact inclusion of electron-electron correlations.

A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state which are induced by resonantly oscillating Rashba spin-obit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.

In this paper several nanodevices which realize basic single heavy-hole qubit operations are proposed and supported by time-dependent self-consistent Poisson-Schrodinger calculations using a four band heavy-hole–light-hole model. In particular we propose a set of nanodevices which can act as Pauli X, Y, Z quantum gates and as a gate that acts similar to a Hadamard gate (i.e., it creates a balanced superposition of basis states but with an additional phase factor) on the heavy-hole spin qubit. We also present the design and simulation of a gated semiconductor nanodevice which can realize an arbitrary sequence of all these proposed single quantum logic gates. The proposed devices exploit the self-focusing effect of the hole wave function which allows for guiding the hole along a given path in the form of a stable solitonlike wave packet. Thanks to the presence of the Dresselhaus spin-orbit coupling, the motion of the hole along a certain direction is equivalent to the application of an effective magnetic field which induces in turn a coherent rotation of the heavy-hole spin. The hole motion and consequently the quantum logic operation is initialized only by weak static voltages applied to the electrodes which cover the nanodevice. The proposed gates allow for an all electric and ultrafast (tens of picoseconds) heavy-hole spin manipulation and give the possibility to implement a scalable architecture of heavy-hole spin qubits for quantum computation applications.

A novel spintronic nanodevice is proposed that is able to manipulate the single heavy-hole spin state in a coherent manner. It can act as a single quantum logic gate. The heavy-hole spin transformations are realized by transporting the hole around closed loops defined by metal gates deposited on top of the nanodevice. The device exploits Dresselhaus spin-orbit interaction, which translates the spatial motion of the hole into a rotation of the spin. The proposed quantum gate operates on subnanosecond time scales and requires only the application of a weak static voltage which allows for addressing heavy-hole spin qubits individually. Our results are supported by quantum mechanical time-dependent calculations within the four-band Luttinger-Kohn model.

In this paper we propose and simulate operation of a nanodevice, which enables the electron spin accumulation and very precise read-out of its final value. We exploit the dependence of the electron trajectory on its spin state due to the spin-orbit coupling in order to distinguish between different spin orientations.

An idea for construction of two spintronic single-electron nanodevices is presented and supported by a quantum-mechanical simulation of their operation. The first device selects electrons of a given spin orientation and the other performs the spin read out. The operation of proposed devices exploits the spin-dependent deflection of electron trajectories induced by the spin-orbit Rashba coupling and does not require application of an external magnetic field. The operation of the nanodevice requires application of weak voltages applied to the electrodes only.