Arijit Saha

We study the phenomenon of adiabatic quantum charge pumping in systems supporting fractionally charged fermionic bound states, in two different setups. The first quantum pump setup consists of a charge-density-modulated quantum wire, and the second one is based on a semiconducting nanowire with Rashba spin-orbit interaction, in the presence of a spatially oscillating magnetic field. In both these quantum pumps transport is investigated in a N-X-N geometry, with the system of interest (X) connected to two normal-metal leads (N), and the two pumping parameters are the strengths of the effective wire-lead barriers. Pumped charge is calculated within the scattering matrix formalism. We show that quantum pumping in both setups provides a unique signature of the presence of the fractional-fermion bound states, in terms of asymptotically quantized pumped charge. Furthermore, we investigate shot noise arising due to quantum pumping, verifying that quantized pumped charge corresponds to minimal shot noise.

We theoretically study transport through a semiconducting Rashba nanowire (NW) in the presence of uniform and spatially modulated magnetic fields. The system is fully gapped, and the interplay between the spin orbit interaction and the magnetic fields leads to fractionally charged fermion (FF) bound states of the Jackiw-Rebbi type at each end of the nanowire. We investigate the transport and noise behavior of a N=NW=N system, where the wire is contacted by two normal leads (N), and we look for possible signatures that could help in the experimental detection of such states. We find that the differential conductance and the shot noise exhibit a subgap structure which fully reveals the presence of the FF state. Alternatively, another confirmation of the presence of the FFs is provided by a conductance measurement in an Aharonov-Bohm setup, where the FFs are responsible for oscillations with double period. Our predictions can be tested in InSb/InAs nanowires and are within reach of the present technology.

We study the behavior of persistent current of relativistic electrons on a one dimensional ring in presence of attractive/repulsive scattering potentials. In particular, we investigate the persistent current in accordance with the strength as well as the number of the scattering potential. We find that in presence of single scatterer the persistent current becomes smaller in magnitude than the scattering free scenario. This behaviour is similar to the non-relativistic case. Even for a very strong scattering potential, finite amount of persistent current remains for a relativistic ring. In presence of multiple scatterer we observe that the persistent current is maximum when the scatterers are placed uniformly compared to the current averaged over random configurations. However if we increase the number of scatterers, we find that the random averaged current increases with the number of scatterers. The latter behaviour is in contrast to the non-relativistic case.

Effects due to the proximity of a superconductor has motivated a lot of research work in the last several decades both from theoretical and experimental point of view. In this review we are going to describe the physics of systems containing normal metal-superconductor interface. Mainly we discuss transport properties through such hybrid structures. In particular, we describe the effects of electron electron interaction on transport through such superconducting junction of multiple one-dimensional quantum wires. The latter can be described in terms of a non-Fermi liquid theory called Luttinger liquid. In this review, from the application point of view, we also demonstrate the possible scenarios for production of pure spin current and large tunnelling magnetoresistance in such hybrid junctions and analyze the influence of electron-electron interaction on the stability of the production of pure spin current.

The physics of a quantum dot with electron electron interactions is well captured by the so called Universal Hamiltonian if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close the the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution (Pis'ma v ZhETF 92, 202 (2010)).

We consider the phenomenon of quantum charge pumping of electrons across a superconducting double barrier structure in graphene in the adiabatic limit. In this geometry, quantum charge pumping can be achieved by modulating the amplitudes (Delta_1 and Delta_2) of the gaps associated with the two superconducting strips. We show that the superconducting gaps give rise to a transmission resonance in the Delta_1-Delta_2 plane, resulting in a large value of pumped charge, when the pumping contour encloses the resonance. This is in sharp contrast to the case of charge pumping in a normal double barrier structure in graphene, where the pumped charge is very small, due to the phenomenon of Klein tunneling. We analyse the behaviour of the pumped charge through the superconducting double barrier geometry as a function of the pumping strength and the phase difference between the two pumping parameters, for various angles of the incident electron.

We study resonant tunneling through a superconducting double barrier structure in graphene as a function of the system parameters. At each barrier, due to the proximity effect, an incident electron can either reflect as an electron or a hole (specular as well as retro Andreev reflection in graphene). Similarly, transport across the barriers can occur via electrons as well as via the crossed (specular and/or retro) Andreev channel, where a hole is transmitted nonlocally to the other lead. In this geometry, in the subgap regime, we find resonant suppression of Andreev reflection at certain energies, due to the formation of Andreev bound levels between the two superconducting barriers, where the transmission probability T for electrons incident on the double barrier structure becomes unity. The evolution of the transport through the superconducting double barrier geometry as a function of the incident energy for various angles of incidence shows the damping of the resonance as normal reflection between the barriers increases.

We study resonant transport through a superconducting double barrier structure. At each barrier, due to the proximity effect, an incident electron can either reflect as an electron or a hole (Andreev reflection). Similarly, transport across the barrier can occur via direct tunneling as electrons as well as via the crossed Andreev channel, where a hole is transmitted. In the subgap regime, for a symmetric double barrier system (with low transparency for each barrier), we find a new T=1/4 resonance (T is the transmission probability for electrons incident on the double barrier structure) due to interference between electron and hole wave-functions between the two barriers, in contrast to a normal double barrier system which has the standard transmission resonance at T=1. We also point out as an application that the resonant value of T=1/4 can produce pure spin current through the superconducting double barrier structure.

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parameterization of a S-matrix representing small deviations from a given fixed point S-matrix (obtained earlier in Phys. Rev. B 77, 155418 (2008)), and we then perform a comprehensive stability analysis. In particular, for the non-trivial fixed point which has intermediate values of transmission, reflection, Andreev reflection and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are non-linear functions of V(0) and V(2k_{F}) (where V(k) represents the Fourier transform of the inter-electron interaction potential at momentum k). We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

We study transport through a single channel t-stub geometry strongly coupled to a superconducting reservoir. In contrast to the standard stub geometry which has both transmission resonances and anti-resonances in the coherent limit, we find that due to the proximity effect, this geometry shows neither a T=1 resonance (T is the transmission probability for electrons incident on the t-stub) nor a T=0 anti-resonance as we vary the energy of the incident electron. Instead, we find that there is only one resonant value at T=1/4, where charge transport vanishes while the spin transport is perfect.

We consider quantum charge pumping of electrons across a superconducting double barrier structure in the adiabatic limit. The superconducting barriers are assumed to be reflection-less so that an incident electron on the barrier can either tunnel through it or Andreev reflect from it. In this structure, quantum charge pumping can be achieved (a) by modulating the amplitudes, Delta_1 and Delta_2 of the two superconducting gaps or alternatively, (b) by a periodic modulation of the order parameter phases, phi_1 and \phi_2 of the superconducting barriers. In the former case, we show that the superconducting gap gives rise to a very sharp resonance in the transmission resulting in quantization of pumped charge, when the pumping contour encloses the resonance. On the other hand, we find that quantization is hard to achieve in the latter case. We show that inclusion of weak electron-electron interaction in the quantum wire leads to renormalisation group evolution of the transmission amplitude towards the perfectly transmitting limit due to proximity effects. Hence as we approach the zero temperature limit, we get destruction of quantized pumped charge. This is in sharp contrast to the case of charge pumping in a double barrier in a Luttinger liquid where quantized charge pumping is actually achieved in the zero temperature limit. We also propose an experimental set-up to study these effects.

We investigate transport properties of a superconducting junction of many ($N \ge 2$) one-dimensional quantum wires. We include the effect of electron electron interaction within the one-dimensional quantum wire using a weak interaction renormalization group procedure. Due to the proximity effect, transport across the junction occurs via direct tunneling as well as via the crossed Andreev channel. We find that the fixed point structure of this system is far more rich than the fixed point structure of a normal metal$-$superconductor junction ($N = 1$), where we only have two fixed points - the fully insulating fixed point or the Andreev fixed point. Even a two wire (N=2)system with a superconducting junction i.e. a normalmetal$-$superconductor$-$normal metal structure, has non-trivialfixed points with intermediate transmissions and reflections. We also include electron-electron interaction induced back-scattering in the quantum wires in our study and hence obtain non-Luttinger liquid behaviour. It is interesting to note that {\textsl{(a)}} effects due to inclusion of electron-electron interaction induced back-scattering in the wire, and {\textsl{(b)}} competition between the charge transport via the electron and hole channels across the junction, give rise to a non-monotonic behavior of conductance as a functionof temperature. We also find that transport across the junction depends on two independent interaction parameters. The first one is due to the usual correlations coming from Friedel oscillations for spin-full electrons giving rise to the well-known interaction parameter (${{\alpha = (g_2-2g_1)/2 \pi \hbar v_F}}$). The second one arises due to the scattering induced by the proximity of the superconductor and is given by(${{\alpha^\prime = (g_2 + g_1)/2 \pi \hbar v_F}}$).

We demonstrate possible scenarios for production of pure spin current and large tunnelling magnetoresistance ratios from elastic co-tunnelling and crossed Andreev reflection across a superconducting junction comprising of normal metal-superconductor-normal metal, where, the normal metal is a one-dimensional interacting quantum wire. We show that there are fixed points in the theory which correspond to the case of pure spin current. We analyze the influence of electron-electron interaction and see how it stabilizes or de-stabilizes the production of pure spin current. These fixed points can be of direct experimental relevance for spintronics application of normal metal-superconductor-normal metal junctions of one-dimensional quantum wires. We also calculate the power law temperature dependence of the crossed Andreev reflection enhanced tunnelling magnetoresistance ratio for the normal metal-superconductor-normal metal junction.

We study adiabatic charge pumping through a quantum dot placed at the junction of $N$ quantum wires. We explicitly map out the pattern of pumped charge as a function of the time-varying tunneling parameters coupling the wires to the dot and the phase between any two time varying parameters controlling the shape of the dot. We find that with $N-2$ time-independent well-coupled leads, the maximum pumped charge in the remaining two leads is strongly suppressed with increasing $N$, leading to the possibility of tuning of the pumped charge, by modulating the coupling of the $N-2$ leads.