Engineering topics

Balram, Ajit C.

Publications and source records attributed to Balram, Ajit C..

8 records

DOE OSTI2024

Fingerprints of composite fermion Lambda levels in scanning tunneling microscopy

A composite fermion (CF) is a topological quasiparticle that emerges from a nonperturbative attachment of vortices to electrons in strongly correlated two-dimensional materials. Similar to noninteracting fermions that form Landau levels in a magnetic field, CFs can fill analogous “Lambda” levels, giving rise to the fractional quantum Hall (FQH) effect of electrons. Here, we show that Lambda levels can be directly visualized through the characteristic peak structure in the signal obtained via spectroscopy with scanning tunneling microscopy (STM) on a FQH state. Complementary to transport, which probes the low-energy properties of CFs, we show that high-energy features in STM spectra can be interpreted in terms of Lambda levels. We numerically demonstrate that STM spectra can be accurately modeled using Jain's CF theory. Our results show that STM provides a powerful tool for revealing the anatomy of FQH states and identifying physics beyond the noninteracting CF paradigm.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Composite Fermion Pairing Induced by Landau Level Mixing

Pairing of composite fermions provides a possible mechanism for fractional quantum Hall effect at even denominator fractions and is believed to serve as a platform for realizing quasiparticles with non-Abelian braiding statistics. We present results from fixed-phase diffusion Monte Carlo calculations which predict that substantial Landau level mixing can induce a pairing of composite fermions at filling factors v = 1/2 and v = 1/4 in the l = -3 relative angular momentum channel, thereby destabilizing the composite-fermion Fermi seas to produce non-Abelian fractional quantum Hall states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene

Motivated by the observation of even denominator fractional quantum Hall effect in the n = 3 Landau level of monolayer graphene [Kim et al., Nat. Phys. 15, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f-wave pairing. Analogous calculation suggests the possibility of a p-wave pairing of composite fermions at half filling in the n = 2 graphene Landau level, whereas no pairing instability is found at half filling in the n = 0 and n = 1 graphene Landau levels. The relevance of these results to experiments is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Revisiting excitation gaps in the fractional quantum Hall effect

Recent systematic measurements of the quantum well width dependence of the excitation gaps of fractional quantum Hall states in high mobility samples open the possibility of a better quantitative understanding of this important issue. Here we present what we believe to be accurate theoretical gaps including the effects of finite width and Landau level (LL) mixing. While theory captures the width dependence, there still remains a deviation between the calculated and the measured gaps, presumably caused by disorder. It is customary to model the experimental gaps of the n/(2n ± 1) states as Δ n/(2n+1) = Ce 2 /[(2n ± 1)ϵl]-Γ, where ϵ is the dielectric constant of the background semiconductor and l is the magnetic length; the first term is interpreted as the cyclotron energy of composite fermions and Γ as a disorder-induced broadening of composite-fermion LLs. Fitting the gaps for various fractional quantum Hall states, we find that Γ can be nonzero even in the absence of disorder.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Origin of the $ν$ = 1/2 fractional quantum Hall effect in wide quantum wells

The nature of the fractional quantum Hall effect at ν = 1/2, observed in wide quantum wells al- most three decades ago, is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which assumes that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase diffusion Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, and also to two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations find that the one-component composite-fermion Fermi sea and the one-component Pfaffian states are very close in energy for a range of quantum well widths and densities, suggesting that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state. Furthermore, we hope that this will motivate further experimental studies of this state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Unconventional Z n parton states at ν=7/3: Role of finite width

A recent work [Balram, Jain, and Barkeshli, Phys. Rev. Res. 2, 013349 (2020)] has suggested that an unconventional state describing Zn superconductivity of composite bosons, which supports excitations with charge 1/(3n) of the electron charge, is energetically better than the Laughlin wave function at \nu=7/3 in GaAs systems. All experiments to date, however, are consistent with the latter. To address this discrepancy, we study the effect of finite width on the ground state and predict a phase transition from an unconventional Zn state at small widths to the Laughlin state for widths exceeding ~1.5 magnetic lengths. Here, we also determine the parameter region where an unconventional state is stabilized in the one-third filled zeroth Landau level in bilayer graphene. The roles of Landau level mixing and spin are also considered.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Interplay between fractional quantum Hall liquid and crystal phases at low filling

The nature of the state at low Landau-level filling factors has been a long-standing puzzle in the field of the fractional quantum Hall effect (FQHE). While theoretical calculations suggest that a crystal is favored at filling factors $\nu$≲1/6, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $\nu$ 1/7, 2/11, 2/13, 3/19, 1/9, 2/15, and 2/17, which belong to the standard sequences $\nu$ =n/(6n ± 1) and $\nu$=n/(8n ± 1). To address this paradox, we investigate the nature of some of the low-$\nu$ states, specifically $\nu$= 1/7, 2/13, and 1/9, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. Finally, this suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Theoretical phase diagram of two-component composite fermions in double-layer graphene

Theory predicts that double layer systems realize “two-component composite fermions,” which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid and crystal states as a function of the layer separation. Recent experiments in double layer graphene have revealed a large number of layer-correlated fractional quantum Hall states in the lowest Landau level, many of which have not been studied quantitatively in previous theoretical works. We consider the competition between various liquid and crystal states at several of these filling factors (specifically, the states at total filling factors ν = 3/7, 4/9, 6/11, 4/7, 3/5, 2/3, and 4/5) to determine the theoretical phase diagram as a function of the layer separation. We compare our results with experiments and identify various observed states. In particular, we show that at small layer separations the states at total fillings ν = 3/7 and ν = 3/5 are partially pseudospin polarized, where pseudospin refers to the layer index. For certain fractions, such as ν = 3/7, interlayer correlations are predicted to survive to surprisingly large interlayer separations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗