arXiv subjects

Sumathi Rao

Publications and source records attributed to Sumathi Rao.

At least 55 records · Page 3Linked to original sources

arXiv2010

Resonant tunneling through superconducting double barrier structures in graphene

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.

cond-mat.mes-hall↗

arXiv2009

Resonant spin transport through a superconducting double barrier structure

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.

cond-mat.mes-hall↗

arXiv2009

Resonant charge and spin transport in a t-stub coupled to a superconductor

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.

cond-mat.mes-hall↗

arXiv2009

Enhancement of tunneling density of states at a junction of three Luttinger liquid wires

We study the tunneling density of states (TDOS) for a junction of three Tomonaga-Luttinger liquid wires. We show that there are fixed points which allow for the enhancement of the TDOS, which is unusual for Luttinger liquids. The distance from the junction over which this enhancement occurs is of the order of x = v/(2 ω), where v is the plasmon velocity and ωis the bias frequency. Beyond this distance, the TDOS crosses over to the standard bulk value independent of the fixed point describing the junction. This finite range of distances opens up the possibility of experimentally probing the enhancement in each wire individually.

cond-mat.mes-hall↗

arXiv2009

Effect of inter-edge Coulomb interactions on transport through a point contact in a ν= 5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a ν= 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, the stable fixed point corresponds to a point contact which is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G_H = {1/2} e^2/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G_H = {5/2} e^2/h) and the fully disconnected case (G_H = 0).

cond-mat.mes-hall↗

arXiv2009

A systematic stability analysis of the renormalisation group flow for the normal-superconductor-normal junction of Luttinger liquid wires

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.

cond-mat.mes-hall↗

arXiv2008

Duality between normal and superconducting junctions of multiple quantum wires

We study junctions of single-channel spinless Luttinger liquids using bosonisation. We generalize earlier studies by allowing the junction to be superconducting and find new charge non-conserving low energy fixed points. We establish the existence of $g \leftrightarrow 1/g$ duality (where $g$ is the Luttinger Liquid parameter) between the charge conserving (normal) junction and the charge non-conserving (superconducting) junction by evaluating and comparing the scaling dimensions of various operators around the fixed points in normal and superconducting sectors of the theory. For the most general two-wire junction, we show that there are two conformally invariant one-parameter families of fixed points which are also connected by a duality transformation. We also show that the stable fixed point for the two-wire superconducting junction corresponds to the situation where the crossed Andreev reflection is perfect between the wires. For the three-wire junction, we study, in particular, the superconducting analogs of the chiral, $D_P$ and the disconnected fixed points obtained earlier in the literature in the context of charge conserving three-wire junctions. We show that these fixed points can be stabilized for $g < 1$ (repulsive electrons) within the superconducting sector of the theory which makes them experimentally relevant.

cond-mat.mes-hall↗

arXiv2008

Renormalization group study of transport through a superconducting junction of multiple one-dimensional quantum wires

We investigate transport properties of a superconducting junction of many ($N \ge 2$) one-dimensional quantum wires. We include the effectofelectron-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 (${α= (g_2-2g_1)/2 π\hbar v_F}$). The second one arises due to the scattering induced by the proximity of the superconductor and is given by(${α^\prime = (g_2 + g_1)/2 π\hbar v_F}$).

cond-mat.mes-hall↗

arXiv2008

Spintronics with NSN Junction of one-dimensional quantum wires : A study of Pure Spin Current and Magnetoresistance

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.

cond-mat.mes-hall↗

arXiv2007

Adiabatic charge pumping through a dot at the junction of N quantum wires

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.

cond-mat.mes-hall↗

arXiv2006

Renormalization group study of the Kondo problem at a junction of several Luttinger wires

We study a system consisting of a junction of N quantum wires, where the junction is characterized by a scalar S-matrix, and an impurity spin is coupled to the electrons close to the junction. The wires are modeled as weakly interacting Tomonaga-Luttinger liquids. We derive the renormalization group equations for the Kondo couplings of the spin to the electronic modes on different wires, and analyze the renormalization group flows and fixed points for different values of the initial Kondo couplings and of the junction S-matrix (such as the decoupled S-matrix and the Griffiths S-matrix). We generally find that the Kondo couplings flow towards large and antiferromagnetic values in one of two possible ways. For the Griffiths S-matrix, we study one of the strong coupling flows by a perturbative expansion in the inverse of the Kondo coupling; we find that at large distances, the system approaches the ferromagnetic fixed point of the decoupled S-matrix. For the decoupled S-matrix with antiferromagnetic Kondo couplings and weak inter-electron interactions, the flows are to one of two strong coupling fixed points in which all the channels are strongly coupled to each other through the impurity spin. But strong inter-electron interactions, with K_ρ< N/(N+2), stabilize a multi-channel fixed point in which the coupling between different channels goes to zero. We have also studied the temperature dependence of the conductance at the decoupled and Griffiths S-matrices.

cond-mat.str-el↗

arXiv2006

A multi-channel fixed point for a Kondo spin coupled to a junction of Luttinger liquids

We study a system of an impurity spin coupled to a junction of several Tomonaga-Luttinger liquids using a renormalization group scheme. For the decoupled S-matrix at the junction, there is a range of Kondo couplings which flow to a multi-channel fixed point for repulsive inter-electron interactions; this is associated with a characteristic temperature dependence of the spin-flip scatterings. If the junction is governed by the Griffiths S-matrix, the Kondo couplings flow to a strong coupling fixed point where all the wires are decoupled.

cond-mat.str-el↗

arXiv2005

Non-linear sigma model approach to quantum spin chains

We introduce and motivate the study of quantum spin chains on a one-dimensional lattice. We classify the varieties of methods that have been used to study these models into three categories, - a) exact methods to study specific models b) field theories to describe fluctuations about the classical ordered phases and c) numerical methods. We then discuss the $J_1$-$J_2$-$δ$ model in some detail and end with a few comments on open problems.

cond-mat.stat-mech↗

arXiv2005

Inter-edge interactions and novel fixed points at a junction of quantum Hall line junctions

We show that novel fixed points (characterized by matrices which specify the splitting of the currents at the junction) can be accessed in a system which contains a junction of three quantum Hall line junctions. For such a junction of fractional quantum Hall edge states, we find that it is possible for both the flower (single droplet) and islands (three droplets) configurations to be stable in an intermediate region, for a range of values of the inter-edge repulsive interactions. A measurement of the tunneling conductance as a function of the gate voltage controlling inter-edge repulsions can give a clear experimental signal of this region.

cond-mat.mes-hall↗

arXiv2004

Effects of interaction on an adiabatic quantum electron pump

We study the effects of inter-electron interactions on the charge pumped through an adiabatic quantum electron pump. The pumping is through a system of barriers, whose heights are deformed adiabatically. (Weak) interaction effects are introduced through a renormalisation group flow of the scattering matrices and the pumped charge is shown to {\it always} approach a quantised value at low temperatures or long length scales. The maximum value of the pumped charge is set by the number of barriers and is given by $Q_{\rm max} = n_b -1$. The correlation between the transmission and the charge pumped is studied by seeing how much of the transmission is enclosed by the pumping contour. The (integer) value of the pumped charge at low temperatures is determined by the number of transmission maxima enclosed by the pumping contour. The dissipation at finite temperatures leading to the non-quantised values of the pumped charge scales as a power law with the temperature ($Q-Q_{\rm int} \propto T^{2α}$), or with the system size ($Q-Q_{\rm int} \propto L_s^{-2α}$), where $α$ is a measure of the interactions and vanishes at $T=0 ~(L_s=\infty)$. For a double barrier system, our result agrees with the quantisation of pumped charge seen in Luttinger liquids.

cond-mat.mes-hall↗

arXiv2004

Tunneling through two resonant levels: fixed points and conductances

We study point contact tunneling between two leads of a Tomonaga-Luttinger liquid through two degenerate resonant levels in parallel. This is one of the simplest cases of a quantum junction problem where the Fermi statistics of the electrons plays a non-trivial role through the Klein factors appearing in bosonization. Using a mapping to a `generalized Coulomb model' studied in the context of the dissipative Hofstadter model, we find that any asymmetry in the tunneling amplitudes from the two leads grows at low temperatures, so that ultimately there is no conductance across the system. For the symmetric case, we identify a non-trivial fixed point of this model; the conductance at that point is generally different from the conductance through a single resonant level.

cond-mat.mes-hall↗

arXiv2003

Renormalization group study of the conductances of interacting quantum wire systems with different geometries

We examine the effect of interactions between the electrons on the conductances of some systems of quantum wires with different geometries. The systems include a wire with a stub in the middle, a wire containing a ring which can enclose a magnetic flux, and a system of four wires which are connected in the middle through a fifth wire. Each of the wires is taken to be a weakly interacting Tomonaga-Luttinger liquid, and scattering matrices are introduced at all the junctions. Using a renormalization group method developed recently for studying the flow of scattering matrices for interacting systems in one dimension, we compute the conductances of these systems as functions of the temperature and the wire lengths. We present results for all three regimes of interest, namely, high, intermediate and low temperature. These correspond respectively to the thermal coherence length being smaller than, comparable to and larger than the smallest wire length in the different systems, i.e., the length of the stub or each arm of the ring or the fifth wire. The renormalization group procedure and the formulae used to compute the conductances are different in the three regimes. We present a phenomenologically motivated formalism for studying the conductances in the intermediate regime where there is only partial coherence. At low temperatures, we study the line shapes of the conductances versus the electron energy near some of the resonances; the widths of the resonances go to zero with decreasing temperature. Our results show that the conductances of various systems of experimental interest depend on the temperature and lengths in a non-trivial way when interactions are taken into account.

cond-mat.str-el↗

arXiv2003

Transport through multiply connected quantum wires

We study transport through multiply coupled carbon nano-tubes (quantum wires) and compute the conductances through the two wires as a function of the two gate voltages $g_1$ and $g_2$ controlling the chemical potential of the electrons in the two wires. We find that there is an {\it equilibrium} cross-conductance, and we obtain its dependence on the temperature and length of the wires. The effective action of the model for the wires in the strong coupling (equivalently Coulomb interaction) limit can also be mapped to a system of capacitively coupled quantum dots. We thus also obtain the conductances for identical and non-identical dots. These results can be experimentally tested.

cond-mat.mes-hall↗