Fermi Liquid Of Composite Fermions Research Articles

Trial wave functions for a composite Fermi liquid on a torus

We study the two-dimensional electron gas in a magnetic field at filling fraction $\nu=\frac{1}{2}$. At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.

Numerical study of anisotropy in a composite Fermi liquid

We perform density-matrix renormalization group studies of a two-dimensional electron gas in a high magnetic field and with an anisotropic band mass. At half-filling in the lowest Landau level, such a system is a Fermi liquid of composite fermions. By measuring the Fermi surface of these composite fermions, we determine a relationship between the anisotropy of composite fermion dispersion, $\alpha_{CF}$, and the original anisotropy $\alpha_F$ of the fermion dispersion at zero magnetic field. For systems where the electrons interact via a Coulomb interaction, we find $\alpha_{CF}=\sqrt{\alpha_F}$ within our numerical accuracy. The same result has been found concurrently in recent experiments. We also show results with other forms of the electron-electron interaction; this allows us (a) to benchmark our procedure against known exact results and (b) to show that the relationship between the anisotropies is dependent on the form of the interaction.

Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions.

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.

Measurement of the specific heat of a fractional quantum Hall system

Using a time-resolved phonon absorption technique, we have measured the relative specific heat of a two-dimensional electron system in the fractional quantum Hall effect regime. For filling factors $\ensuremath{\nu}=5∕3$, $4∕3$, $2∕3$, $3∕5$, $4∕7$, $2∕5$, and $1∕3$ the specific heat displays a strong exponential temperature dependence in agreement with excitations across a quasiparticle gap. At filling factor $\ensuremath{\nu}=1∕2$ we were able to measure the relative specific heat of a composite fermion system. The observed nearly linear temperature dependence on temperature down to $T=0.14\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ agrees well with early predictions for a Fermi liquid of composite fermions.

Mutual Composite Fermion and Composite Boson approaches to balanced and imbalanced bi-layer quantum Hall system: An electronic analogy of the Helium 4 system

We use both Mutual Composite Fermion (MCF) and Composite Boson (CB) approach to study balanced and imbalanced Bi-layer Quantum Hall systems (BLQH) and make critical comparisons between the two approaches. We find the CB approach is superior to the MCF approach in studying ground states with different kinds of broken symmetries. In the phase representation of the CB theory, we first study the Excitonic superfluid (ESF) state. The theory puts spin and charge degree freedoms in the same footing, explicitly bring out the spin–charge connection and classify all the possible excitations in a systematic way. Then in the dual density representation of the CB theory, we study possible intermediate phases as the distance increases. We propose there are two critical distances d c1 < d c2 and three phases as the distance increases. When 0 < d < d c1, the system is in the ESF state which breaks the internal U(1) symmetry, when d c1 < d < d c2, the system is in an pseudo-spin density wave (PSDW) state which breaks the translational symmetry, there is a first-order transition at d c1 driven by the collapsing of magneto-roton minimum at a finite wavevector in the pseudo-spin channel. When d c2 < d < ∞, the system becomes two weakly coupled ν = 1/2 Composite Fermion Fermi Liquid (FL) state. There is also a first-order transition at d = d c2. We construct a quantum Ginzburg Landau action to describe the transition from ESF to PSDW which break the two completely different symmetries. By using the QGL action, we explicitly show that the PSDW takes a square lattice and analyze in detail the properties of the PSDW at zero and finite temperature. We also suggest that the correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature-dependent drag consistent with the experimental data. Then we study the effects of imbalance on both ESF and PSDW. In the ESF side, the system supports continuously changing fractional charges as the imbalance changes. In the PSDW side, there are two quantum phase transitions from the commensurate excitonic solid to an incommensurate excitonic solid and then to the excitonic superfluid state. We also comment on the effects of disorders and compare our results with the previous work. The very rich and interesting phases and phase transitions in the pseudo-spin channel in the BLQH is quite similar to those in 4He system with the distance playing the role of the pressure. A BLQH system in a periodic potential is also discussed. The Quantum Hall state to Wigner crystal transition in single layer Quantum Hall system is studied.

Transport properties between quantum Hall plateaus.

We propose a unified transport theory for the two-dimensional electron gas in the dissipative quantum Hall regime in the presence of a long-range disorder. We find that the evolution of the longitudinal conductivity peaks as a function of the disorder can be described by a single parameter ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}1}$ which is determined by the typical gradient of the electron-density fluctuations. In the case of a relatively strong disorder we utilize the edge-states-network model to describe transport in a half-filled Landau level. In the fractional quantum Hall regime we apply the network model to the system of composite fermions, finding the universal values of the resistivity at even-denominator filling fractions. The breakdown of the network model takes place at weak disorder because the edge channels develop into wide compressible strips and at strong disorder because of the destruction of the incompressible strips, isolating the edge channels. We find the limits of the applicability of the network model in terms of \ensuremath{\beta}. In the limit of very weak disorder the system is effectively a Fermi liquid of composite fermions. We calculate the conductivity in this regime by considering the motion of noninteracting fermions in a spatially varying magnetic field arising from the density fluctuations. The resistivity is found to scale linearly with the magnetic field with the slope given by ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}1}$. Although the presence of nonlocal transport makes measurements of the resistivity difficult, we find qualitative and, in some cases, quantitative agreement with experiment.