Blue Phase III: Topological Fluid of Skyrmions

Pišljar, Jaka; Ghosh, Sharmistha; Turlapati, Srikanth; Rao, N. V. S.; Škarabot, Miha; Mertelj, Alenka; Petelin, Andrej; Nych, A.; Marinčič, Matevž; Pusovnik, Anja; Ravnik, Miha; Muševič, Igor

doi:10.1103/physrevx.12.011003

Cited by 24 publications

(26 citation statements)

References 80 publications

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“…To extract from (19d) the remaining distortion characteristics (b 1 , b 2 ), we need to identify the distortion frame (n 1 , n 2 , n) of a generic field in (17). Letting…”

Section: Standard Computations Show Thatmentioning

confidence: 99%

“…For a director field n as in (17), whose gradient has been computed in (18), and for the perturbation field v described in (58), the following computational ingredients were needed in the main text to arrive from the general formula for the second variation of Frank's elastic free energy in (51) at the special form needed when the unperturbed field in n = n ET , div n = 0, (B5a)…”

Section: B Radial Perturbationsmentioning

confidence: 99%

“…They are attributed to a lattice of line defects that orderly traverse the medium (in different spatial arrangements in the phases labeled BPI and BPII) and to a disordered network in the amorphous phase BPIII (see pp. 68 and 407 of [16] for a quick, but effective introduction to this topic, and [17] for one of the latest most illuminating models). The name double twist was coined in [18] (see also [19] for a fuller presentation of the elastic theory of blue phases), but the spatial arrangement of the director field that gives rise to it had already been precognized in [20].…”

Section: Introductionmentioning

confidence: 99%

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Stability Against the Odds: the Case of Chromonic Liquid Crystals

Paparini¹,

Virga²

2022

Preprint

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The ground state of chromonic liquid crystals, as revealed by a number of recent experiments, is quite different from that of ordinary nematic liquid crystals: it is twisted instead of uniform. The common explanation provided for this state within the classical elastic theory of Frank demands that one Ericksen's inequality is violated. Since in general such a violation makes Frank's elastic freeenergy functional unbounded below, the question arises as to whether the twisted ground state can be locally stable. We answer this question in the affirmative. In reaching this conclusion, a central role is played by the specific boundary conditions imposed in the experiments on the boundary of rigid containers and by a general formula that we derive here for the second variation of Frank's elastic free energy.

show abstract

“…To extract from (19d) the remaining distortion characteristics (b 1 , b 2 ), we need to identify the distortion frame (n 1 , n 2 , n) of a generic field in (17). Letting…”

Section: Standard Computations Show Thatmentioning

confidence: 99%

Section: B Radial Perturbationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability Against the Odds: the Case of Chromonic Liquid Crystals

Paparini¹,

Virga²

2022

Preprint

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show abstract

“…Lavrentovich 2003) for a quick, but effective introduction to this topic, and (Pišljar et al 2022) for one of the latest most illuminating models). The name double twist was coined in Meiboom et al (1981) (see also (Meiboom et al 1983) for a fuller presentation of the elastic theory of blue phases), but the spatial arrangement of the director field that gives rise to it had already been precognized in Saupe (1969).…”

Section: Ground Statementioning

confidence: 99%

Stability Against the Odds: The Case of Chromonic Liquid Crystals

Paparini

Virga

2022

J Nonlinear Sci

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The ground state of chromonic liquid crystals, as revealed by a number of recent experiments, is quite different from that of ordinary nematic liquid crystals: it is twisted instead of uniform. The common explanation provided for this state within the classical elastic theory of Frank demands that one Ericksen’s inequality is violated. Since in general such a violation makes Frank’s elastic free-energy functional unbounded below, the question arises as to whether the twisted ground state can be locally stable. We answer this question in the affirmative. In reaching this conclusion, a central role is played by the specific boundary conditions imposed in the experiments on the boundary of rigid containers and by a general formula that we derive here for the second variation in Frank’s elastic free energy.

show abstract

“…Skyrmions may also exist in chiral soft matter such as cholesteric liquid crystals. 8–10 The twisting energy in cholesteric liquid crystals is similar to the Dzyaloshinsky–Moriya interaction in chiral ferromagnets, causing twisting of orientation and forming the ordered skyrmionic state called blue phase. 11 It is an interesting question how skyrmions are generated in chiral active systems lacking the Dzyaloshinsky–Moriya interaction.…”

Section: Introductionmentioning

confidence: 99%