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Bertrand I. Halperin

Publications and source records attributed to Bertrand I. Halperin.

121 records · Page 7Linked to original sources
arXiv1996

Composite Fermions with Orbital Magnetization

For quantum Hall systems, in the limit of large magnetic field (or equivalently small electron band mass $m_b$), the static response of electrons to a spatially varying magnetic field is largely determined by kinetic energy considerations. This response is not correctly given in existing approximations based on the Fermion Chern-Simons theory of the partially filled Landau level. We remedy this problem by attaching an orbital magnetization to each fermion to separate the current into magnetization and transport contributions, associated with the cyclotron and guiding center motions respectively. This leads to a Chern-Simons Fermi liquid description of the $ν=\frac{1}{2m}$ state which correctly predicts the $m_b$ dependence of the static and dynamic response in the limit $m_b \rightarrow 0$.

cond-mat↗
arXiv1996

Higher-Order Results for the Relation between Channel Conductance and the Coulomb Blockade for Two Tunnel-Coupled Quantum Dots

We extend earlier results on the relation between the dimensionless tunneling channel conductance $g$ and the fractional Coulomb blockade peak splitting $f$ for two electrostatically equivalent dots connected by an arbitrary number $N_{\text{ch}}$ of tunneling channels with bandwidths $W$ much larger than the two-dot differential charging energy $U_{2}$. By calculating $f$ through second order in $g$ in the limit of weak coupling ($g \rightarrow 0$), we illuminate the difference in behavior of the large-$N_{\text{ch}}$ and small-$N_{\text{ch}}$ regimes and make more plausible extrapolation to the strong-coupling ($g \rightarrow 1$) limit. For the special case of $N_{\text{ch}}=2$ and strong coupling, we eliminate an apparent ultraviolet divergence and obtain the next leading term of an expansion in $(1-g)$. We show that the results we calculate are independent of such band structure details as the fraction of occupied fermionic single-particle states in the weak-coupling theory and the nature of the cut-off in the bosonized strong-coupling theory. The results agree with calculations for metallic junctions in the $N_{\text{ch}} \rightarrow \infty$ limit and improve the previous good agreement with recent two-channel experiments.

cond-mat↗
arXiv1995

The Physical Significance of Singularities in the Chern--Simons Fermi Liquid Description of a Partially Filled Landau Level

We analyze the linear response of a half filled Landau level to long wavelength and low frequency driving forces, using Fermi liquid theory for composite fermions. This response is determined by the composite fermions quasi--particle effective mass, $m^*$, and quasi--particle Landau interaction function $f(θ-θ')$. Analyzing infra--red divergences of perturbation theory, we get an exact expression for $m^*$, and conjecture the form of the $f(θ-θ')$. We then conclude that in the limit of infinite cyclotron frequency, and small ${\bf q},ω$, the composite fermion excitation spectrum is continuous for $0<ω<γ\frac{e^2}{εh}q$, with $γ$ an unknown number. For fractional quantum Hall states near a half filled Landau level, we derive an exact expression for the energy gap.

cond-mat↗
arXiv1995

Singularities in the Fermi liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states

We consider a two dimensional electron system in an external magnetic field at and near an even denominator Landau level filling fraction. Using a fermionic Chern--Simons approach we study the description of the system's low energy excitations within an extension of Landau's Fermi liquid theory. We calculate perturbatively the effective mass and the quasi--particle interaction function characterizing this description. We find that at an even denominator filling fraction the fermion's effective mass diverges logarithmically at the Fermi level, and argue that this divergence allows for an {\it exact} calculation of the energy gaps of the fractional quantized Hall states asymptotically approaching these filling fractions. We find that the quasi--particle interaction function approaches a delta function. This singular behavior leads to a cancelation of the diverging effective mass from the long wavelength low frequency linear response functions at even denominator filling fractions.

cond-mat↗
arXiv1995

Relation between Barrier Conductance and Coulomb Blockade Peak Splitting for Tunnel-Coupled Quantum Dots

We study the relation between the barrier conductance and the Coulomb blockade peak splitting for two electrostatically equivalent dots connected by tunneling channels with bandwidths much larger than the dot charging energies. We note that this problem is equivalent to a well-known single-dot problem and present solutions for the relation between peak splitting and barrier conductance in both the weak and strong coupling limits. Results are in good qualitative agreement with the experimental findings of F. R. Waugh et al.

cond-mat↗
arXiv1994

Developments in the Theory of the Quantum Hall Effect, Proceedings of the 1994 Vancouver Semiconductor Conference

The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting with a Chern-Simons gauge field, have been useful for explaining and predicting observations at even-denominator filling fractions where quantized Hall plateaus are not observed, as well as for giving new insight into the most prominent fractional quantized Hall states at odd-denominator fractions. Other theoretical approaches have led to important advances in our understanding of edge-excitations for systems in a fractional quantized Hall state, of phases and phase transitions in bilayer systems, of tunneling phenomena in the quantum Hall regimes, and of disorder-induced transitions between ``neighboring'' quantum Hall plateaus. Some highlights of these developments will be reviewed.

cond-mat↗
arXiv1994

Explanation for the Resistivity Law in Quantum Hall System

We consider a 2D electron system in a strong magnetic field, where the local Hall resistivity $ρ_{xy}(\vec r)$ is a function of position and $ρ_{xx}(\vec r)$ is small compared to $ρ_{xy}$. Particularly if the correlations fall off slowly with distance, or if fluctuations exist on several length scales, one finds that the macroscopic longitudinal resistivity $R_{xx}$ is only weakly dependent on $ρ_{xx}$ and is approximately proportional to the magnitude of fluctuations in $ρ_{xy}$. This may provide an explanation of the empirical law $R_{xx} \propto B \frac{dR_{xy}}{dB}$ where $R_{xy}$ is the Hall resistance, and $B$ is the magnetic field.

cond-mat↗
arXiv1994

Response Function of the Fractional Quantized Hall State on a Sphere I: Fermion Chern-Simons Theory

Using a well known singular gauge transformation, certain fractional quantized Hall states can be modeled as integer quantized Hall states of transformed fermions interacting with a Chern-Simons field. In previous work we have calculated the electromagnetic response function of these states at arbitrary frequency and wavevector by using the Random Phase Approximation (RPA) in combination with a Landau Fermi Liquid approach. We now adopt these calculations to a spherical geometry in order to facilitate comparison with exact diagonalizations performed on finite size systems.

cond-mat↗
arXiv1993

Understanding Far-Infrared Absorption in the S=1 Antiferromagnetic Chain Compound NENP

Infrared transmission measurements on the $S=1$ antiferromagnetic chain compound NENP in applied magnetic fields show a sharp absorption line at the field-shifted Haldane gap. This violates a wave-vector selection rule of the Hamiltonian normally used for NENP, as the gap excitations occur at the Brillouin zone boundary. We argue that the crystal structure admits terms which can explain the absorption lines. In addition, in an applied field, staggered orientations of the g-tensors produce a staggered magnetic field. This can explain the observation of a finite gap at all applied fields.

cond-mat↗
arXiv1993

Finite-Wavevector Electromagnetic Response of Fractional Quantized Hall States

A fractional quantized Hall state with filling fraction $ν= p/(2mp+1)$ can be modeled as an integer quantized Hall state of transformed fermions, interacting with a Chern-Simons field. The electromagnetic response function for these states at arbitrary frequency and wavevector can be calculated using a semiclassical approximation or the Random Phase Approximation (RPA). However, such calculations do not properly take into account the large effective mass renormalization which is present in the Chern-Simons theory. We show how the mass renormalization can be incorporated in a calculation of the response function within a Landau Fermi liquid theory approach such that Kohn's theorem and the $f$-sum rules are properly satisfied. We present results of such calculations.

cond-mat↗
arXiv1993

Theories for v=1/2 in Single- and Double-Layer Systems

Recent experiments have shown that a quantized Hall plateau can occur in double layer systems at total filling factor v=1/2, though there is no plateau at v=1/2 in a normal single layer system. For the single layer system, considerable insight has been provided by a theory based on the fermion Chern-Simons picture, where the electrons are transformed into fermions that carry two flux quanta of a Chern-Simons gauge field. A similar picture can be used to characterize ground states which have been proposed for the two layer system.

cond-mat↗