32 research outputs found
A "problem of time" in the multiplicative scheme for the -site hopper
Quantum Measure Theory (QMT) is an approach to quantum mechanics, based on
the path integral, in which quantum theory is conceived of as a generalised
stochastic process. One of the postulates of QMT is that events with zero
quantum measure do not occur, however this is not sufficient to give a full
picture of the quantum world. Determining the other postulates is a work in
progress and this paper investigates a proposal called the Multiplicative
Scheme for QMT in which the physical world corresponds, essentially, to a set
of histories from the path integral. This scheme is applied to Sorkin's
-site hopper, a discrete, unitary model of a single particle on a ring of
sites, motivated by free Schr\"odinger propagation. It is shown that the
multiplicative scheme's global features lead to the conclusion that no
non-trivial, time-finite event can occur.Comment: 24 pages, 2 figures. Now published in J. Phys. A: Math. Theor. under
CC-BY. New version expands section 3.1 and corrects typo
Soft pair excitations and double-log divergences due to carrier interactions in graphene
Interactions between charge carriers in graphene lead to logarithmic renormalization of observables mimicking the behavior known in (3+1)-dimensional quantum electrodynamics (QED). Here we analyze soft electron-hole (e-h) excitations generated as a result of fast charge dynamics, a direct analog of the signature QED effect—multiple soft photons produced by the QED vacuum shakeup. We show that such excitations are generated in photon absorption, when a photogenerated high-energy e-h pair cascades down in energy and gives rise to multiple soft e-h excitations. This fundamental process is manifested in a double-log divergence in the emission rate of soft pairs and a characteristic power-law divergence in their energy spectrum of the form 1/ω ln(ω/Δ). Strong carrier-carrier interactions make pair production a prominent pathway in the photoexcitation cascade
Pairing in magic-angle twisted bilayer graphene: role of phonon and plasmon umklapp
Identifying the microscopic mechanism for superconductivity in magic-angle twisted bilayer graphene (MATBG) is an outstanding open problem. While MATBG exhibits a rich phase-diagram, driven partly by the strong interactions relative to the electronic bandwidth, its single-particle properties are unique and likely play an important role in some of the phenomenological complexity. Some of the salient features include an electronic bandwidth smaller than the characteristic phonon bandwidth and a non-trivial structure of the underlying Bloch wavefunctions. We perform a systematic theoretical study of the cooperative effects due to phonons and plasmons on pairing in order to disentangle the distinct role played by these modes on superconductivity. We consider a variant of MATBG with an enlarged number of fermion flavors, N≫1, where the study of pairing instabilities reduces to the conventional (weak-coupling) Eliashberg framework. In particular, we show that certain umklapp processes involving mini-optical phonon modes, which arise physically as a result of the folding of the original acoustic branch of graphene due to the moiré superlattice structure, contribute significantly towards enhancing pairing. We also investigate the role played by the dynamics of the screened Coulomb interaction on pairing, which leads to an enhancement in a narrow window of fillings, and study the effect of external screening due to a metallic gate on superconductivity. We propose a smoking-gun experiment to detect resonant features associated with the phonon-umklapp processes in the differential conductance and also discuss experimental implications of a pairing mechanism relying on plasmons
Pairing in magic-angle twisted bilayer graphene: role of phonon and plasmon umklapp
Identifying the microscopic mechanism for superconductivity in magic-angle
twisted bilayer graphene (MATBG) is an outstanding open problem. While MATBG
exhibits a rich phase-diagram, driven partly by the strong interactions
relative to the electronic bandwidth, its single-particle properties are unique
and likely play an important role in some of the phenomenological complexity.
Some of the salient features include an electronic bandwidth smaller than the
characteristic phonon bandwidth and a non-trivial structure of the underlying
Bloch wavefunctions. We perform a theoretical study of the cooperative effects
due to phonons and plasmons on pairing in order to disentangle the distinct
role played by these modes on superconductivity. We consider a variant of MATBG
with an enlarged number of fermion flavors, , where the study of
pairing instabilities reduces to the conventional (weak-coupling) Eliashberg
framework. In particular, we show that certain umklapp processes involving
mini-optical phonon modes, which arise physically as a result of the folding of
the original acoustic branch of graphene due to the moir\'e superlattice
structure, contribute significantly towards enhancing pairing. We also
investigate the role played by the dynamics of the screened Coulomb interaction
on pairing, which leads to an enhancement in a narrow window of fillings, and
study the effect of external screening due to a metallic gate on
superconductivity. At strong coupling the dynamical pairing interaction leaves
a spectral mark in the single particle tunneling density of states. We thus
predict such features will appear at specific frequencies of the umklapp
phonons corresponding to the sound velocity of graphene times an integer
multiple of the Brillouin zone size.Comment: 20 pages, 8 figure
Visualizing structure of correlated ground states using collective charge modes
The variety of correlated phenomena in moir\'e systems is incredibly rich,
spanning effects such as superconductivity, a generalized form of
ferromagnetism, or even charge fractionalization. This wide range of quantum
phenomena is partly enabled by the large number of internal degrees of freedom
in these systems, such as the valley and spin degrees of freedom, which
interplay decides the precise nature of the ground state. Identifying the
microscopic nature of the correlated states in the moir\'e systems is, however,
challenging, as it relies on interpreting transport behavior or
scanning-tunneling microscopy measurements. Here we show how the real-space
structure of collective charge oscillations of the correlated orders can
directly encode information about the structure of the correlated state,
focusing in particular on the problem of generalized Wigner crystals in moir\'e
transition metal dichalcogenides. Our analysis builds upon our earlier result
[10.1126/sciadv.adg3262] that the presence of a generalized Wigner crystal
modifies the plasmon spectrum of the system, giving rise to new collective
modes. We focus on scanning near-field optical microscopy technique (SNOM),
fundamentally a charge-sensing-based method, and introduce a regime under which
SNOM can operate as a probe of the spin degree of freedom.Comment: 12 pages, 4 figure