arXiv subjects

Ganpathy Murthy

Publications and source records attributed to Ganpathy Murthy.

At least 73 records · Page 4Linked to original sources

arXiv2004

Collective edge modes in fractional quantum Hall systems

Over the past few years one of us (Murthy) in collaboration with R. Shankar has developed an extended Hamiltonian formalism capable of describing the ground state and low energy excitations in the fractional quantum Hall regime. The Hamiltonian, expressed in terms of Composite Fermion operators, incorporates all the nonperturbative features of the fractional Hall regime, so that conventional many-body approximations such as Hartree-Fock and time-dependent Hartree-Fock are applicable. We apply this formalism to develop a microscopic theory of the collective edge modes in fractional quantum Hall regime. We present the results for edge mode dispersions at principal filling factors $ν=1/3,1/5$ and $ν=2/5$ for systems with unreconstructed edges. The primary advantage of the method is that one works in the thermodynamic limit right from the beginning, thus avoiding the finite-size effects which ultimately limit exact diagonalization studies.

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arXiv2003

Edge reconstructions in fractional quantum Hall systems

Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are present. We present a {\it microscopic} calculation of the edge states in the fractional quantum Hall systems at various filling factors using the extended Hamiltonian theory of the fractional quantum Hall effect. We find that at $ν=1/3$ the quantum Hall edge undergoes a reconstruction as the background potential softens, whereas quantum Hall edges at higher filling factors, such as $ν=2/5, 3/7$, are robust against reconstruction. We present the results for the dependence of the edge states on various system parameters such as temperature, functional form and range of electron-electron interactions, and the confining potential. Our results have implications for the tunneling experiments into the edge of a fractional quantum Hall system.

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arXiv2003

Absence of U(1) spin liquids in two dimensions

Many popular models of fractionalized spin liquids contain neutral fermionic spinon excitations on a Fermi surface, carrying unit charges under a compact U(1) gauge force. We argue that instanton effects generically render such states unstable to confinement in two spatial dimensions, so that all elementary excitations are gauge neutral, and there is no spinon Fermi surface. Similar results are expected to apply to SU(2) spin liquids. However, fractionalized states can appear when the gauge symmetry is broken down to a discrete subgroup by the Higgs mechanism. Our argument generalizes earlier results on confinement in the pure gauge theory, and on the instability of the U(1) staggered flux and algebraic spin liquids with a Dirac spectrum for fermionic spinons.

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arXiv2003

Hamiltonian Theories of the FQHE

This paper reviews progress on the Fractional Quantum Hall Effect (FQHE) based on what we term hamiltonian theories, i.e., theories that proceed from the microscopic electronic hamiltonian to the final solution via a sequence of transformations and approximations, either in the hamiltonian or path integral approach, as compared to theories based on exact diagonalization or trial wavefunctions. We focus on the Chern-Simons (CS) approach in which electrons are converted to CS fermions or bosons that carry along flux tubes and our Extended Hamiltonian Theory (EHT) in which electrons are paired with pseudo-vortices to form composite fermions (CF) whose properties are a lot closer to the ultimate low-energy quasiparticles. We address a variety of qualitative and quantitative questions: In what sense do electrons really bind to vortices? What is the internal structure of the Composite Fermion and what does it mean? What exactly is the dipole picture? How are (approximate) transport gaps, zero-temperature magnetic transitions, the temperature dependent polarizations of gapped and gapless states, the NMR relaxation rate $1/T_1$ in gapless states, and gaps in inhomogeneous states computed? It is seen that though the CS and EHT approaches agree whenever a comparison is possible, results that are transparent in one approach are typically opaque in the other, making them truly complementary.

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arXiv2003

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $Δ$ within a few $Δ$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.

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arXiv2003

Diamagnetic Persistent Currents and Spontaneous Time-Reversal Symmetry Breaking in Mesoscopic Structures

Recently, new strongly interacting phases have been uncovered in mesoscopic systems with chaotic scattering at the boundaries by two of the present authors and R. Shankar. This analysis is reliable when the dimensionless conductance of the system is large, and is nonperturbative in both disorder and interactions. The new phases are the mesoscopic analogue of spontaneous distortions of the Fermi surface induced by interactions in bulk systems and can occur in any Fermi liquid channel with angular momentum $m$. Here we show that the phase with $m$ even has a diamagnetic persistent current (seen experimentally but mysterious theoretically), while that with $m$ odd can be driven through a transition which spontaneously breaks time-reversal symmetry by increasing the coupling to dissipative leads.

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arXiv2002

Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit

We show that problem of interacting electrons in a quantum dot with chaotic boundary conditions is solvable in the large-g limit, where g is the dimensionless conductance of the dot. The critical point of the $g=\infty$ theory (whose location and exponent are known exactly) that separates strong and weak-coupling phases also controls a wider fan-shaped region in the coupling-1/g plane, just as a quantum critical point controls the fan in at T>0. The weak-coupling phase is governed by the Universal Hamiltonian and the strong-coupling phase is a disordered version of the Pomeranchuk transition in a clean Fermi liquid. Predictions are made in the various regimes for the Coulomb Blockade peak spacing distributions and Fock-space delocalization (reflected in the quasiparticle width and ground state wavefunction).

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arXiv2002

Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions

Using a fermionic renormalization group approach we analyse a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by Random Matrix Theory, we find that interactions can induce phase transitions (or crossovers for finite systems) to regimes where fluctuations and collective effects dominate at low energies. Implications for experiments and numerical work on quantum dots are discussed.

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arXiv2002

Hamiltonian Theory of the Fractional Quantum Hall Effect: Effect of Landau Level Mixing

We derive an effective hamiltonian in the Lowest Landau Level (LLL) that incorporates the effects of Landau-level mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy. We then transcribe the hamiltonian to the composite fermion basis using our hamiltonian approach and compute the effect of LL mixing on transport gaps.

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arXiv2001

The Effects of Disorder on the $ν=1$ Quantum Hall State

A disorder-averaged Hartree-Fock treatment is used to compute the density of single particle states for quantum Hall systems at filling factor $ν=1$. It is found that transport and spin polarization experiments can be simultaneously explained by a model of mostly short-range effective disorder. The slope of the transport gap (due to quasiparticles) in parallel field emerges as a result of the interplay between disorder-induced broadening and exchange, and has implications for skyrmion localization.

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arXiv2001

Hamiltonian Theory of the FQHE: Conserving Approximation for Incompressible Fractions

A microscopic Hamiltonian theory of the FQHE developed by Shankar and the present author based on the fermionic Chern-Simons approach has recently been quite successful in calculating gaps and finite tempertature properties in Fractional Quantum Hall states. Initially proposed as a small-$q$ theory, it was subsequently extended by Shankar to form an algebraically consistent theory for all $q$ in the lowest Landau level. Such a theory is amenable to a conserving approximation in which the constraints have vanishing correlators and decouple from physical response functions. Properties of the incompressible fractions are explored in this conserving approximation, including the magnetoexciton dispersions and the evolution of the small-$q$ structure factor as $ν\to\half$. Finally, a formalism capable of dealing with a nonuniform ground state charge density is developed and used to show how the correct fractional value of the quasiparticle charge emerges from the theory.

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arXiv2001

Hamiltonian Theory of the Composite Fermion Wigner Crystal

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the excitation gaps of the Wigner Crystal states. We find that the Wigner Crystal states near $ν=1/5$ are quantitatively well described as crystals of Composite Fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.

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arXiv2000

Finite Temperature Magnetism in Fractional Quantum Hall Systems: Composite Fermion Hartree-Fock and Beyond

Using the Hamiltonian formulation of Composite Fermions developed recently, the temperature dependence of the spin polarization is computed for the translationally invariant fractional quantum Hall states at $ν=1/3$ and $ν=2/5$ in two steps. In the first step, the effect of particle-hole excitations on the spin polarization is computed in a Composite Fermion Hartree-Fock approximation. The computed magnetization for $ν=1/3$ lies above the experimental results for intermediate temperatures indicating the importance of long wavelength spin fluctuations which are not correctly treated in Hartree-Fock. In the second step, spin fluctuations beyond Hartree-Fock are included for $ν=1/3$ by mapping the problem on to the coarse-grained continuum quantum ferromagnet. The parameters of the effective continuum quantum ferromagnet description are extracted from the preceding Hartree-Fock analysis. After the inclusion of spin fluctuations in a large-N approach, the results for the finite-temperature spin polarization are in quite good agreement with the experiments.

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arXiv2000

Hall Crystal States at $ν=2$ and Moderate Landau Level Mixing

The $ν=2$ quantum Hall state at low Zeeman coupling is well-known to be a translationally invariant singlet if Landau level mixing is small. At zero Zeeman interaction, as Landau level mixing increases, the translationally invariant state becomes unstable to aninhomogeneous state. This is the first realistic example of a full Hall crystal, which shows the coexistence of quantum Hall order and density wave order. The full Hall crystal differs from the more familiar Wigner crystal by a topological property, which results in it having only linearly dispersing collective modes at small $q$, and no $q^{3/2}$ magnetophonon. I present calculations of the topological number and the collective modes.

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arXiv2000

Temperature dependence of the spin polarization in the fractional quantum Hall effects

Using a Hamiltonian formulation of Composite Fermions that I recently developed with R. Shankar, I compute the dependence of the spin polarization on the temperature for the translationally invariant fractional quantum Hall states at $ν=1/3$ and $ν=2/5$. I compare my results to experiments at $ν=1/3$ and find reasonably good agreement.

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arXiv1999

A Composite Fermion Hofstader Problem: Partially Polarized Density Wave States in the 2/5 FQHE

It is well-known that the 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with charge/spin density wave order for Composite Fermions is proposed to exist at intermediate values of the Zeeman coupling for 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R.Shankar and the author is used to demonstrate the stability of this state to single-particle excitations, and compute gaps. We compare our results with a very recent experiment which shows direct evidence for the existence of such a state, and also with more indirect evidence from past experiments.

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arXiv1999

Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions

A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the $ν=1/3$, 2/5, and 3/7 gapped fractions, and find approximate agreement with numerical results. I also analyse the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 2/5 and 3/7, and it is shown that the spin-polarized 2/5 state, in contrast to the spin-polarized 1/3 state, cannot be described as a simple quantum ferromagnet.

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arXiv1998

Scaling Relations for Gaps in Fractional Quantum Hall States

The microscopic approach of Murthy and Shankar, which has recently been used to calculate the transport gaps of quantum Hall states with fractions p/(2ps+1), also implies scaling relations between gaps within a single sequence (fixed s) as well as between gaps of corresponding states in different sequences. This work tests these relations for a system of electrons in the lowest Landau level interacting with a model potential cutoff at high momenta due to sample thickness.

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