Session L2: Physics of Interacting Particles in Two Dimensional Electron Systems at Half-Filling

Do composite fermions satisfy Luttinger's area rule?

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion Fermi sea [1] arises as a non-perturbative 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. We show [2] that in the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent degree, the Fermi wave vectors at filling factors $\nu$ and $1-\nu$ are the same, and are generally consistent with the experimental findings of Kamburov {\em et al.} [3]. Our calculations [2] suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule. We further determine the area of the spin unpolarized composite-fermion Fermi sea, for which the Fermi seas at $\nu$ and $1-\nu$ are not related by particle hole symmetry. [1] B.I. Halperin, P.A. Lee, N. Read, PRB 47, 7312 (1993). [2] A. C. Balram, C. T\H{o}ke, J. K. Jain, Phys. Rev. Lett. 115, 186805 (2015). [3] D. Kamburov {\em et al.} Phys. Rev. Lett. {\bf 113}, 196801 (2014).   

Spontaneous time reversal symmetry breaking in atomically confined two-dimensional impurity bands in silicon and germanium

Three-dimensional bulk-doped semiconductors, in particular phosphorus (P)-doped silicon (Si) and germanium (Ge), are among the best studied systems for many fundamental concepts in solid state physics, ranging from the Anderson metal-insulator transition to the many-body Coulomb interaction effects on quantum transport. Recent advances in material engineering have led to vertically confined doping of phosphorus (P) atoms inside bulk crystalline silicon and germanium, where the electron transport occurs through one or very few atomic layers, constituting a new and unique platform to investigate many of these phenomena at reduced dimensions. In this talk I shall present results of extensive quantum transport experiments in delta-doped silicon and germanium epilayers, over a wide range of doping density that allow independent tuning of the on-site Coulomb interaction and hopping energy scales. We find that low-frequency flicker noise, or the $1/f$ noise, in the electrical conductance of these systems is exceptionally low, and in fact among the lowest when compared with other low-dimensional materials. This is attributed to the physical separation of the conduction electrons, embedded inside the crystalline semiconductor matrix, from the charged fluctuators at the surface. Most importantly, we find a remarkable suppression of weak localization effects, including the quantum correction to conductivity and universal conductance fluctuations, with decreasing doping density or, equivalently, increasing effective on-site Coulomb interaction. In-plane magneto-transport measurements indicate the presence of intrinsic local spin fluctuations at low doping although no signatures of long range magnetic order could be identified. We argue that these results indicate a spontaneous breakdown of time reversal symmetry, which is one of the most fundamental and robust symmetries of nonmagnetic quantum systems. While the microscopic origin of this spontaneous time reversal symmetry breaking remains unknown, we believe this indicates a new many-body electronic phase in two-dimensionally doped silicon and germanium with a half-filled impurity band.   

The half-filled Landau level and topological insulator surfaces

The metallic state of the half-filled Landau level - described originally in pioneering work by Halperin , Lee, and Read as a liquid of composite fermions - was proposed recently by Son to be described by a particle-hole symmetric effective field theory distinct from that in the prior literature. This talk will develop a simple picture of the particle-hole symmetric composite fermion through a modification of older pictures as electrically neutral ``dipolar" particles. This picture, and the proposed particle-hole symmetric theory, will be further substantiated through a recently developed deep connection between the half-filled Landau level and correlated surface states of certain three dimensional topological insulators. The phenomenology of composite fermi liquids (with or without particle-hole symmetry) will be revisited. It will be shown that their heat/electrical transport dramatically violates the conventional Wiedemann-Franz law but satisfies a modified one. References: 1. Chong Wang and T. Senthil, “Half-filled Landau Level, Topological Insulator Surfaces, and Three Dimensional Quantum Spin Liquids,” cond-mat arXiv:1507.08290 (2015).   

Experimental Observations of Particle-hole Asymmetry for Composite Fermions

In this talk, I will present our experimental study of the breaking of particle-hole symmetry for composite fermions (CFs), quasi-particles formed by attaching two flux quanta to each electron at large perpendicular magnetic fields. We measure the Fermi contour of the spin-polarized CFs near $\nu=1/2$ via commensurability oscillations, and find an asymmetry of the Fermi wave vector for $\nu<1/2$ and $>1/2$. In particular, we find that the deduced wave vector is smaller for $\nu>1/2$ compared to $\nu<1/2$, and on both sides consistent with the density of minority carriers in the lowest Landau level. We also study the spin-polarization transitions of fractional quantum Hall states near $\nu=3/2$ and 1/2; these states are particle-hole conjugates of each other and are expected to have the same polarization energies. Our systematic results clearly show the transition energies are about three times larger for states near $\nu=3/2$ compared to those near $\nu=1/2$. Work done in collaboration with D. Kamburov, M. A. Mueed, S. Hasdemir, A. Wojs, J.K. Jain, L.N. Pfeiffer, K.W. West, K.W. Baldwin, and M. Shayegan.   

A model wavefunction for the composite Fermi liquid: its geometry and entanglement.

I will describe a model wavefunction for the composite Fermi liquid in a partially-filled Landau level, recently formulated in a torus geometry (Shao et al., Phys. Rev. Lett. 114, 206402 (2015)), that allows a manifold of gapless composite Fermi-liquid states to be characterized, parametrized by an analog of the ``occupation number'' that defines the Fermi surface in a free-electron gas. Unlike incompressible FQHE states, which only occur in an inversion-symmetric momentum sector, these CFL states occur in each distinct momentum sector allowed by the periodic boundary condition. The fundamental wavefunction of this type describes a system with $\nu$ = 1/2, but multiplication by (or division by) a Vandermonde factor describes states at $\nu$ = $1/m$. The CFL states are characterized by an ``intrinsic metric" which determines the shape of the Fermi surface, and corresponds to the shape of the ``flux-attachment'' that forms the composite fermion. The wavefunction is well-suited for Monte-Carlo calculations, as it is analogous to a determinant form used by Jain in spherical geometry. The violation of ``area-law" (perimeter-law) entanglement found in Monte-Carlo calculations will be described.