Criticality across the energy spectrum from random artificial gravitational lensing in two-dimensional Dirac superconductors

Ghorashi, Sayed Ali Akbar; Karcher, Jonas F.; Davis, Seth; Foster, Matthew S.

doi:10.1103/physrevb.101.214521

Cited by 13 publications

(44 citation statements)

References 83 publications

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“…Since the tilt of the Dirac cone can be attributed to an underlying spacetime metric, the ability to tune the tilt parameter is tantamount to controllability of the ensuing solid-state spacetime structure by electric forces. Dirac materials subject to gravitational disorder [29,30] find their materialization in the present context when the carbon is randomly for boron.…”

mentioning

confidence: 92%

Tunning the tilt of a Dirac cone by atomic manipulations: application to 8Pmmn borophene

Yekta¹,

Hadipour²,

Jafari³

2021

Preprint

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We decipher the microscopic mechanism of the formation of tilt in the two-dimensional Dirac cone of 8P mmn borophene sheet. With the aid of ab initio calculations, we identify relevant low-energy degrees of freedom on the 8P mmn lattice and find that these atomic orbitals reside on an effective honeycomb lattice (inner sites), while the high-energy degrees of freedom reside on the rest of the 8P mmn lattice (ridge sites). Local chemical bonds formed between the low-and high-energy sublattices provide the required off-diagonal coupling between the two sectors. Elimination of high-energy ridge sites gives rise to a remarkably large effective further neighbor hoppings on the coarse grained (honeycomb) lattice of inner sites that determine the location and tilt of the Dirac cone. This insight based on real space renormalization of the 8P mmn lattice enables us to design atomic scale substitutions that can lead to desired change in the tilt of the Dirac cone. We furthermore encode the process of renormalization into an effective tight-binding model on a parent honeycomb lattice that facilitates numerical modeling of various effects such as disorder/interactions/symmetry-breaking for tilted Dirac cone fermions of 8P mmn structure. The tilt parameters determine a spacetime metric, and therefore the ability to vary the tilt over distances much larger than the atomic separations opens up a paradigm for fabricating arbitrary solid-state spacetimes.

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mentioning

confidence: 92%

Tunning the tilt of a Dirac cone by atomic manipulations: application to 8Pmmn borophene

Yekta¹,

Hadipour²,

Jafari³

2021

Preprint

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“…Thus, it is also a quadratic function of the shifted qi = q i + c i /2. But in these variables x λ must be even due to the first type of the Weyl group actions (11), which restricts it to…”

Section: Generalized Mulifractalitymentioning

confidence: 99%

“…It was also shown that the multifractality survives in the presence of Coulomb interaction [9]. Recently, the multifractality was used as an efficient tool to detect and explore the emergent criticality of 2D surface states of topological superconductors [10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Generalized multifractality at spin quantum Hall transition

Karcher,

Charles,

Gruzberg

et al. 2021

Preprint

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Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized multifractality in 2D systems, with the main focus on the spin quantum Hall (SQH) transition in superconductors of symmetry class C. Relations and differences with the conventional integer quantum Hall (IQH) transition are also studied. Using the field-theoretical formalism of non-linear sigma-model, we derive the pure-scaling operators representing generalizing multifractality and then "translate" them to the language of eigenstate observables. Performing numerical simulations on network models for SQH and IQH transitions, we confirm the analytical predictions for scaling observables and determine the corresponding exponents. Remarkably, the generalized-multifractality exponents at the SQH critical point strongly violate the generalized parabolicity of the spectrum, which implies violation of the local conformal invariance at this critical point.

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“…The minimal realization of a class DIII surface consists of a single Majorana cone; in this case, disorder can only modulate the velocity components of the cone. Since it couples to the stress tensor, we call this "quenched gravitational disorder" (QGD) [24]. Although class CI and AIII 2D Dirac models with gauge disorder could be robustly realized as TSC surface states, these were originally studied two decades ago in the context of the high-T c cuprate superconductors [25].…”

Section: Introductionmentioning

confidence: 99%

“…Although class CI and AIII 2D Dirac models with gauge disorder could be robustly realized as TSC surface states, these were originally studied two decades ago in the context of the high-T c cuprate superconductors [25]. Indeed, by suppressing interpair, internode, and/or intranode elastic impurity scattering in a 2D d-wave superconductor, one can realize all three minimal surface models in classes CI [26,27,28,29,30], AIII [31,32], and DIII [24].…”

Section: Introductionmentioning

confidence: 99%

How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down

Karcher

Foster

2021

Annals of Physics

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Criticality across the energy spectrum from random artificial gravitational lensing in two-dimensional Dirac superconductors

Cited by 13 publications

References 83 publications

Tunning the tilt of a Dirac cone by atomic manipulations: application to 8Pmmn borophene

Tunning the tilt of a Dirac cone by atomic manipulations: application to 8Pmmn borophene

Generalized multifractality at spin quantum Hall transition

How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down

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