Circuit realization of a tilted Dirac cone: Platform for fabrication of curved spacetime geometry on a chip

Motavassal, Ahmad; Jafari, S. A.

doi:10.1103/physrevb.104.l241108

Cited by 11 publications

(7 citation statements)

References 33 publications

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“…This metric encodes the long-distance structure of the complicated and rich content of the 8pmmn lattice. Putting it another way, the 8pmmn point group symmetry of the atomic scales becomes a metric at long wavelength scales [20,21]. Therefore, as long the system has quasiparticles, even the strong electron-electron interactions responsible for the formation of the hydrodynamic regime are not able to destroy this metric structure if the lattice is not melted.…”

Section: Discussionmentioning

confidence: 99%

“…In colculsion, we promote partial derivative to covariant derivative and write the hydrodynamic Eq. ( 18) in a non-trivial background metric (2) perturbed by perturbations (21) to (24) and keep the leading order terms. Doing so the energy and momentum equations for the perfect fluid become…”

Section: Electromagnetic Force and Spatial Gradients Of Temperaturementioning

confidence: 99%

“…As can be seen, the role assumed by ζ in the above equation is significantly richer than a simple anisotropy of the space alone. In fact, this metric is associated with the long-distance structure of the underlying (in the case of the 8pmmn borophene) lattice and does not depend on whether the particles (excitations) are being studied are fermionic or bosonic [20,21].…”

Section: Introductionmentioning

confidence: 99%

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Electron currents from gradual heating in tilted Dirac cone materials

2023

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Materials hosting tilted Dirac/Weyl fermions provide an emergent spacetime structure for the solid state physics. They admit a geometric description in terms of an effective spacetime metric. Using this metric that is rooted in the long-distance behavior of the underlying lattice, we formulate the hydrodynamic theory for tilted Dirac/Weyl materials in 2+12+1 spacetime dimensions. We find that the mingling of space and time through the off-diagonal components of the metric gives rise to: (i) heat and electric currents proportional to the temporal gradient of temperature, \partial_t T∂tT and (ii) a non-zero Hall-like conductance \sigma^{ij}\propto \zeta^i\zeta^jσij∝ζiζj where \zeta^jζj parameterize the tilt in jj’th space direction. The finding (i) above that can be demonstrated in the laboratory, implies that the non-trivial emergent spacetime geometry in these materials empowers them with a fascinating capability to harness naturally available sources of \partial_t T∂tT of hot deserts to produce electric current. We further find a tilt-induced non-Drude contribution to conductivity which can be experimentally disentangled from the usual Drude pole.

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Section: Discussionmentioning

confidence: 99%

Section: Electromagnetic Force and Spatial Gradients Of Temperaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electron currents from gradual heating in tilted Dirac cone materials

2023

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“…This approach was first considered in (3+1)-dimensional Weyl semimetals [58], opening the door to the investigation of black holes and gravitational lensing in a solid-state setting. In many systems with tilted Dirac cones, the spatial dependence of the tilt parameter can be achieved through various means, such as externally applied electric fields [65], magnetic/pseudo-magnetic fields [66,67], chemical substitution [68] and, in the case of a tunable circuit realization of tilted Dirac cone systems, by spatially varying the capacitor and inductor sizes [69]. The presence of a space-dependent tilt parameter in these systems allows for the exploration of nontrivial spacetime geometry and gravitomagnetic effects.…”

Section: Introductionmentioning

confidence: 99%

Bipolar electron waveguides in two-dimensional materials with tilted Dirac cones

Hartmann,

Portnoi

2024

Phys. Scr.

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We show that the (2+1)-dimensional massless Dirac equation, which includes a tilt term, can be reduced to the biconfluent Heun equation for a broad range of scalar confining potentials, including the well-known Morse potential. Applying these solutions, we investigate a bipolar electron waveguide in 8--$Pmmn$ borophene, formed by a well and barrier, both described by the Morse potential. We demonstrate that the ability of two-dimensional materials with tilted Dirac cones to localize electrons in both a barrier and a well can be harnessed to create pseudogaps in their electronic spectrum. These pseudogaps can be tuned through varying the applied top-gate voltage. Potential opto-valleytronic and terahertz applications are discussed.

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“…The remarkable fact is that, the above metric that emerges as the long-distance behavior of certain lattices or certain graphs, is independent of what excitation is being propagated on the lattice/graph. The circuit realization of the above metric [18] on a honeycomb graph is obtained by coarse-graining of the 8P mmn lattice [19].…”

Section: Introductionmentioning

confidence: 99%

Kinetic theory of tilted Dirac cone materials

A.¹,

Torabian²,

A.³

2022

Preprint

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We formulate the Boltzmann kinetic equations for interacting tilted Dirac fermions in two space dimensions characterized by a tilt parameter 0 ≤ ζ < 1. Solving the linearized Boltzmann equation, we find that the broadening of the Drude pole is enhanced by κ, where the κ is interaction-induced enhancement factor. The intensity of the Drude pole is also anisotropically enhanced by (1−ζ 2 ) −1 . The ubiquitous "redshift" factors (1 − ζ 2 ) 1/2 can be regarded as a manifestation of an underlying spacetime structure in such solids. The additional broadening κ indicates that interaction effects are more pronounced for electrons in a ζ-deformed Minkowski spacetime of tilted Dirac fermions.

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Circuit realization of a tilted Dirac cone: Platform for fabrication of curved spacetime geometry on a chip

Cited by 11 publications

References 33 publications

Electron currents from gradual heating in tilted Dirac cone materials

Electron currents from gradual heating in tilted Dirac cone materials

Bipolar electron waveguides in two-dimensional materials with tilted Dirac cones

Kinetic theory of tilted Dirac cone materials

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