arXiv subjects

Daniel Bulmash

Publications and source records attributed to Daniel Bulmash.

25 records · Page 2Linked to original sources

arXiv2018

Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics

We present a theoretical framework for a class of generalized $U(1)$ gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then lead to a class of generalized Gauss law constraints. The charge and magnetic excitations in these theories have restricted, subdimensional dynamics, providing a generalization of recently studied higher-rank symmetric $U(1)$ gauge theories to the case where arbitrary spatial rotational symmetries are broken. These theories can describe situations where charges exist at the corners of fractal operators, thus providing a continuum effective field theoretic description of Haah's code and Yoshida's Sierpinski prism model. We also present a $3+1$-dimensional $U(1)$ theory that does not have a non-trivial discrete $\mathbb{Z}_p$ counterpart.

cond-mat.str-el↗

arXiv2017

Strongly Interacting Phases of Metallic Wires in Strong Magnetic Field

We investigate theoretically an interacting metallic wire with a strong magnetic field directed along its length and show that it is a new and highly tunable one-dimensional system. By considering a suitable change in spatial geometry, we map the problem in the zeroth Landau level with Landau level degeneracy $N$ to one-dimensional fermions with an $N$-component pseudospin degree of freedom and $SU(2)$-symmetric interactions. This mapping allows us to establish the phase diagram as a function of the interactions for small $N$ (and make conjectures for large $N$) using renormalization group and bosonization techniques. We find pseudospin-charge separation with a gapless $U(1)$ charge sector and several possible strong-coupling phases in the pseudospin sector. For odd $N$, we find a fluctuating pseudospin-singlet charge density wave phase and a fluctuating pseudospin-singlet superconducting phase which are topologically distinct. For even $N>2$, similar phases exist, although they are not topologically distinct, and an additional, novel pseudospin-gapless phase appears. We discuss experimental conditions for observing our proposals.

cond-mat.str-el↗

arXiv2016

Quantum Oscillations in Weyl and Dirac Semimetal Ultra-Thin Films

We show that a thin film of Weyl or Dirac semimetal with a strong in-plane magnetic field becomes a novel two-dimensional Fermi liquid with interesting properties. The Fermi surface in this system is strongly anisotropic, which originates from a combination of chiral bulk channels and the Fermi arcs. The area enclosed by the Fermi surface depends strongly on the in-plane magnetic field component parallel to the Weyl/Dirac node splitting, which leads to unusual behavior in quantum oscillations when the magnetic field is tilted out of the plane. We estimate the oscillation frequencies and the regimes where such effects could be seen in Cd$_3$As$_2$, Na$_3$Bi, and TaAs.

cond-mat.mes-hall↗

arXiv2015

Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals

We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools - semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals - we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically calculated quantum oscillations for generic Weyl semimetals with distinctly curved Fermi arcs on the two surfaces. Based on these methods, we identify a 'magic' magnetic-field angle where quantum oscillations become independent of sample thickness, with striking experimental implications. We also analyze the stability of these quantum oscillations to disorder, and show that the high-field oscillations are expected to persist in samples whose thickness parametrically exceeds the quantum mean free path.

cond-mat.mes-hall↗

arXiv2015

The almost mobility edge in the almost Mathieu equation

Harper's equation (aka the "almost Mathieu" equation) famously describes the quantum dynamics of an electron on a one dimensional lattice in the presence of an incommensurate potential with magnitude $V$ and wave number $Q$. It has been proven that all states are delocalized if $V$ is less than a critical value $V_c=2t$ and localized if $V> V_c$. Here, we show that this result (while correct) is highly misleading, at least in the small $Q$ limit. In particular, for $V E_c$, form a set of narrow bands with exponentially small bandwidths $ \sim t\ \exp[-(2πα/Q)]$ (where $α$ is an energy dependent number of order 1) separated by band-gaps $ \sim t Q$. Thus, the states with $|E|> E_c$ are "almost localized" in that they have an exponentially large effective mass and are easily localized by small perturbations. We establish this both using exact numerical solution of the problem, and by exploiting the well known fact that the same eigenvalue problem arises in the Hofstadter problem of an electron moving on a 2D lattice in the presence of a magnetic field, $B=Q/2π$. From the 2D perspective, the almost localized states are simply the Landau levels associated with semiclassical precession around closed contours of constant quasiparticle energy; that they are not truly localized reflects an extremely subtle form of magnetic breakdown.

cond-mat.mes-hall↗

arXiv2015

Unified Topological Response Theory for Gapped and Gapless Free Fermions

We derive a scheme for systematically enumerating the responses of gapped as well as gapless systems of free fermions to electromagnetic and strain fields starting from a common parent theory. Using the fact that position operators in the lowest Landau level of a quantum Hall state are canonically conjugate, we consider a massive Dirac fermion in $2n$ spatial dimensions under $n$ mutually orthogonal magnetic fields and reinterpret physical space in the resulting zeroth Landau level as phase space in $n$ spatial dimensions. The bulk topological responses of the parent Dirac fermion, given by a Chern-Simons theory, translate into quantized insulator responses, while its edge anomalies characterize the response of gapless systems. Moreover, various physically different responses are seen to be related by the interchange of position and momentum variables. We derive many well-known responses, and demonstrate the utility of our theory by predicting spectral flow along dislocations in Weyl semimetals.

cond-mat.mes-hall↗

arXiv2014

Prediction of a Weyl Semimetal in Hg$_{1-x-y}$Cd$_x$Mn$_y$Te

We study strained Hg$_{1-x-y}$Cd$_x$Mn$_y$Te in a magnetic field using a $\bm{k}\cdot\bm{p}$ model and predict that the system is a Weyl semimetal with two nodes in an experimentally reasonable region of the phase diagram. We also predict two signatures of the Weyl semimetal phase which arise from tunability of the Weyl node splitting. First, we find that the Hall conductivity is proportional to the average Mn ion spin and thus is strongly temperature dependent. Second, we find an unusual magnetic field angle dependence of the Hall conductivity; in particular, we predict a peak in $σ_{xy}$ as a function of field angle in the $xz$-plane and a finite $σ_{yz}$ as the $x$-component of the field goes to 0.

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