Origin and Transport Signatures of Spin-Orbit Interactions in One- and Two-Dimensional SrTiO$_3$-Based Heterostructures

We study origin of Rashba spin-orbit interaction at SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces by considering the interplay between atomic spin-orbit coupling and inversion asymmetry at the surface or interface. We show that, in a simple tight-binding model involving 3d $t_{2g}$ bands of Ti ions, the induced spin-orbit coupling in the $d_{xz}$ and $d_{yz}$ bands is cubic in momentum whereas the spin-orbit interaction in the $d_{xy}$ band has linear momentum dependence. We also find that the spin-orbit interaction in one-dimensional channels at LaAlO$_3$/SrTiO$_3$ interfaces is linear in momentum for all bands. We discuss implications of our results for transport experiments on SrTiO$_3$ surfaces and LaAlO$_3$/SrTiO$_3$ interfaces. In particular, we analyze the effect of a given spin-orbit interaction term on magnetotransport of LaAlO$_3$/SrTiO$_3$ by calculating weak anti-localization corrections to the conductance and to universal conductance fluctuations.

Transport properties of topological superconductor-Luttinger liquid junctions: a real-time Keldysh approach

Inspired by a recent experimental observation of the zero-bias tunneling conductance in superconductor-semiconductor nanowire devices, we consider here transport properties of the junctions consisting of a nanowire (Luttinger liquid) coupled to a topological superconductor characterized by the presence of Majorana zero-energy end states. The presence of the Majorana modes leads to a quantization of the zero-bias tunneling conductance at zero temperature. In order to understand this phenomenon, we have developed a framework, based on real-time Keldysh technique, which allows one to compute tunneling conductance at finite temperature and voltage in a realistic experimental setup. Our approach allows one to understand this transport phenomenon from a more general perspective by including the effect of interactions in the nanowire, which sometimes results in a drastic departure from the non-interacting predictions. Thus, our results provide a key insight for the tunneling experiments aiming at detecting Majorana particles in one-dimensional nanowire devices.

Magnetic and Superconducting Ordering at LaAlO3/SrTiO3 Interfaces

We formulate a model for magnetic and superconducting ordering at LaAlO3/SrTiO3 interfaces containing both localized magnetic moments and itinerant electrons. Though these both originate in Ti 3d orbitals, the former may be due to electrons more tightly-bound to the interface while the latter are extended over several layers. Only the latter contribute significantly to metallic conduction and superconductivity. In our model, the interplay between the two types of electrons, which is argued to be ferromagnetic, combined with strong spin-orbit coupling of the itinerant electrons, leads to magnetic ordering. Furthermore, we propose a model for interfacial superconductivity, consisting of random superconducting grains in the bulk STO driven, via coupling to the interface conduction band, towards long-ranged or quasi-long-ranged order. Most interestingly, the magnetic order and strong spin orbit coupling can lead in this manner to unconventional interfacial superconductivity, yielding a possible realization of Majorana physics.

Topological Protection of Majorana Qubits

We study the stability of the topological quantum computation proposals involving Majorana fermions against thermal fluctuations. We use a minimal realistic model of a spinless px+ipy superconductor and consider effect of excited midgap states localized in the vortex core as well as of transitions above the bulk superconducting gap on the quasiparticle braiding, interferometry-based qubit read-out schemes, and quantum coherence of the topological qubits. We find that thermal occupation of the midgap states does not affect adiabatic braiding operations but leads to a reduction in the visibility of the interferometry measurements. We also consider quantum decoherence of topological qubits at finite temperatures and calculate their decay rate which is associated with the change of the fermion parity and, as such, is exponentially suppressed at temperatures well below the bulk excitation gap. Our conclusion is that the Majorana-based topological quantum computing schemes are indeed protected by the virtue of the quantum non-locality of the stored information and the presence of the bulk superconducting gap.

Momentum relaxation in a semiconductor proximity-coupled to a disordered s-wave superconductor: effect of scattering on topological superconductivity

We study the superconducting proximity effect between a conventional semiconductor and a disordered s-wave superconductor. We calculate the effective momentum relaxation rate in the semiconductor due to processes involving electron tunneling into a disordered superconductor and scattering off impurities. The magnitude of the effective disorder scattering rate is important for understanding the stability of the topological (chiral p-wave) superconducting state that emerges in the semiconductor, since disorder scattering has a detrimental effect and can drive the system into a non-topological state. We find that the effective impurity scattering rate involves higher-order tunneling processes and is suppressed due to the destructive quantum interference of quasi-particle and quasi-hole trajectories. We show that, despite the fact that both the proximity-induced gap and the effective impurity scattering rate depend on interface transparency, there is a large parameter regime where the topological superconducting phase is robust against disorder in the superconductor. Thus, we establish that the static disorder in the superconductor does not suppress the proximity induced topological superconductivity in the semiconductor.

Majorana Fermions in Semiconductor Nanowires

We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor and calculate the topological phase diagram as a function of the chemical potential and magnetic field. The non-trivial topological state corresponds to a superconducting phase supporting an odd number of pairs of Majorana modes localized at the ends of the wire, whereas the non-topological state corresponds to a superconducting phase with no Majoranas or with an even number of pairs of Majorana modes. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality, but also allows having higher carrier density in the nanowire. Consequently, multiband nanowires are better-suited for stabilizing the topological superconducting phase and for observing the Majorana physics. We present a detailed study of the parameter space for multiband semiconductor nanowires focusing on understanding the key experimental conditions required for the realization and detection of Majorana fermions in solid-state systems. We include various sources of disorder and characterize their effects on the stability of the topological phase. Finally, we calculate the local density of states as well as the differential tunneling conductance as functions of external parameters and predict the experimental signatures that would establish the existence of emergent Majorana zero-energy modes in solid-state systems.

Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order

We show that long-ranged superconducting order is not necessary to guarantee the existence of Majorana fermion zero modes at the ends of a quantum wire. We formulate a concrete model which applies, for instance, to a semiconducting quantum wire with strong spin-orbit coupling and Zeeman splitting coupled to a wire with algebraically-decaying superconducting fluctuations. We solve this model by bosonization and show that it supports Majorana fermion zero modes. We argue that a large class of models will also show the same phenomenon. We discuss the implications for experiments on spin-orbit coupled nanowires coated with superconducting film and for LaAlO3/SrTiO3 interfaces.

Interacting topological phases in multiband nanowires

We show that semiconductor nanowires coupled to an s-wave superconductor provide a playground to study effects of interactions between different topological superconducting phases supporting Majorana zero-energy modes. We consider quasi-one dimensional system where the topological phases emerge from different transverse subbands in the nanowire. In a certain parameter space, we show that there is a multicritical point in the phase diagram where the low-energy theory is equivalent to the one describing two coupled Majorana chains. We study effect of interactions as well as symmetry-breaking perturbations on the topological phase diagram in the vicinity of this multicritical point. Our results shed light on the stability of the topological phase around the multicritical point and have important implications for the experiments on Majorana nanowires.

Loss of superfluidity by fermions in the boson Hubbard model on an optical lattice

The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of the bosons to the higher Bloch bands, coupled with the contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discuss implications for cold atom experiments where the expansion of the Mott lobes by fermions has been conclusively established.