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Siddhartha Lal

Publications and source records attributed to Siddhartha Lal.

44 records · Page 3Linked to original sources
arXiv2006

On transport in quantum Hall systems with constrictions

Motivated by recent experimental findings, we study transport in a simple phenomenological model of a quantum Hall edge system with a gate-voltage controlled constriction lowering the local filling factor. The current backscattered from the constriction is seen to arise from the matching of the properties of the edge-current excitations in the constriction ($ν_{2}$) and bulk ($ν_{1}$) regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model, finding that a competition between two tunneling process, related by a quasiparticle-quasihole symmetry, determines the fate of the low-bias transmission conductance. In this way, we find satisfactory explanations for many recent puzzling experimental results.

cond-mat.mes-hall↗
arXiv2005

Charge ordering in quasi-one-dimensional systems with frustrating interactions

Motivated by the co-existing charge and spin order found in strongly correlated ladder systems, we study an effective pseudospin model on a coupled two-leg ladder. A bosonisation analysis yields a rich phase diagram showing Wigner/Peierls charge order and Neel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled ladder systems.

cond-mat.str-el↗
arXiv2002

Junction of several weakly interacting quantum wires: a renormalization group study

We study the conductance of three or more semi-infinite wires which meet at a junction. The electrons in the wires are taken to interact weakly with each other through a short-range density-density interaction, and they encounter a general scattering matrix at the junction. We derive the renormalization group equations satisfied by the S-matrix, and we identify its fixed points and their stabilities. The conductance between any pair of wires is then studied as a function of physical parameters such as temperature. We discuss the possibility of observing the effects of junctions in present day experiments, such as the four-terminal conductance of a quantum wire and crossed quantum wires.

cond-mat.str-el↗
arXiv2001

Conductance through contact barriers of a finite length quantum wire

We use the technique of bosonization to understand a variety of recent experimental results on the conductivity of a quantum wire. The quantum wire is taken to be a finite-length Luttinger liquid connected on two sides to semi-infinite Fermi liquids through contacts. The contacts are modeled as (short) Luttinger liquids bounded by localized one-body potentials. We use effective actions and the renormalization group to study the effects of electronic interactions within the wire, the length of the wire, finite temperature and a magnetic field on the conductivity. We explain the deviations of the conductivity away from 2Ne^2/h in wires which are not too short as arising from renormalization effects caused by the repulsive interactions. We also explain the universal conductance corrections observed in different channels at higher temperatures. We study the effects of an external magnetic field on electronic transport through this system and explain why odd and even spin split bands show different renormalizations from the universal conductance values. We discuss the case of resonant transmission and of the possibility of producing a spin-valve which only allows electrons of one value of the spin to go through. We compare our results for the conductance corrections with experimental observations. We also propose an experimental test of our model of the contact regions.

cond-mat.str-el↗
arXiv2000

Transport through quasi-ballistic quantum wires: the role of contacts

We model one-dimensional transport through each open channel of a quantum wire by a Luttinger liquid with three different interaction parameters for the leads, the contact regions and the wire, and with two barriers at the contacts. We show that this model explains several features of recent experiments, such as the flat conductance plateaux observed even at finite temperatures and for different lengths, and universal conductance corrections in different channels. We discuss the possibility of seeing resonance-like structures of a fully open channel at very low temperatures.

cond-mat.str-el↗
arXiv1999

One-dimensional fermions with incommensuration

We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from pi, and delta, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/ δ--> 0, the number of states lying inside the q=0 gap is nonzero and equal to 2 δ/π^2. Thus the limit q --> 0 differs from q=0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain close to dimerization, we use bosonization to argue that similar results hold; as q --> 0, we find a nontrivial density of states near zero energy. However, the limit q --> 0 and q=0 give the same results near commensurate wave numbers which are different from pi. We apply our results to the Azbel-Hofstadter problem of electrons hopping on a two-dimensional lattice in the presence of a magnetic field. Finally, we discuss the complete energy spectrum of noninteracting fermions with incommensurate hopping by going up to higher orders in delta.

cond-mat.str-el↗
arXiv1999

Magnetization Properties of Some Quantum Spin Ladders

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/2 ladder, and a two-legged spin-1/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ spin-1/2 chain in a magnetic field; the second order terms give corrections to the XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.

cond-mat.str-el↗
arXiv1998

One-dimensional fermions with incommensurate hopping close to dimerization

We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from pi, and delta, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/delta ---> 0, the number of states lying inside the q = 0 gap is nonzero and equal to 2 delta / pi^2. Thus the limit q ---> 0 differs from q = 0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain, we use bosonization to argue that similar results hold.

cond-mat.stat-mech↗