Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene

Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron in...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Semenoff, Gordon W. [verfasserIn] Zhou, Fei

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2011

Schlagwörter:	Field Theories in Lower Dimensions Spontaneous Symmetry Breaking

Anmerkung:	© SISSA, Trieste, Italy 2011

Übergeordnetes Werk:	Enthalten in: Journal of high energy physics - Berlin : Springer, 1997, 2011(2011), 7 vom: 07. Juli
Übergeordnetes Werk:	volume:2011 ; year:2011 ; number:7 ; day:07 ; month:07

Links:	Volltext

DOI / URN:	10.1007/JHEP07(2011)037

Katalog-ID:	SPR030402077

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allfields	10.1007/JHEP07(2011)037 doi (DE-627)SPR030402077 (SPR)JHEP07(2011)037-e DE-627 ger DE-627 rakwb eng Semenoff, Gordon W. verfasserin aut Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2011 Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry. Field Theories in Lower Dimensions (dpeaa)DE-He213 Spontaneous Symmetry Breaking (dpeaa)DE-He213 Zhou, Fei aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2011(2011), 7 vom: 07. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2011 year:2011 number:7 day:07 month:07 https://dx.doi.org/10.1007/JHEP07(2011)037 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2011 2011 7 07 07
spelling	10.1007/JHEP07(2011)037 doi (DE-627)SPR030402077 (SPR)JHEP07(2011)037-e DE-627 ger DE-627 rakwb eng Semenoff, Gordon W. verfasserin aut Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2011 Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry. Field Theories in Lower Dimensions (dpeaa)DE-He213 Spontaneous Symmetry Breaking (dpeaa)DE-He213 Zhou, Fei aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2011(2011), 7 vom: 07. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2011 year:2011 number:7 day:07 month:07 https://dx.doi.org/10.1007/JHEP07(2011)037 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2011 2011 7 07 07
allfields_unstemmed	10.1007/JHEP07(2011)037 doi (DE-627)SPR030402077 (SPR)JHEP07(2011)037-e DE-627 ger DE-627 rakwb eng Semenoff, Gordon W. verfasserin aut Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2011 Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry. Field Theories in Lower Dimensions (dpeaa)DE-He213 Spontaneous Symmetry Breaking (dpeaa)DE-He213 Zhou, Fei aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2011(2011), 7 vom: 07. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2011 year:2011 number:7 day:07 month:07 https://dx.doi.org/10.1007/JHEP07(2011)037 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2011 2011 7 07 07
allfieldsGer	10.1007/JHEP07(2011)037 doi (DE-627)SPR030402077 (SPR)JHEP07(2011)037-e DE-627 ger DE-627 rakwb eng Semenoff, Gordon W. verfasserin aut Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2011 Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry. Field Theories in Lower Dimensions (dpeaa)DE-He213 Spontaneous Symmetry Breaking (dpeaa)DE-He213 Zhou, Fei aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2011(2011), 7 vom: 07. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2011 year:2011 number:7 day:07 month:07 https://dx.doi.org/10.1007/JHEP07(2011)037 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2011 2011 7 07 07
allfieldsSound	10.1007/JHEP07(2011)037 doi (DE-627)SPR030402077 (SPR)JHEP07(2011)037-e DE-627 ger DE-627 rakwb eng Semenoff, Gordon W. verfasserin aut Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2011 Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry. Field Theories in Lower Dimensions (dpeaa)DE-He213 Spontaneous Symmetry Breaking (dpeaa)DE-He213 Zhou, Fei aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2011(2011), 7 vom: 07. Juli (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2011 year:2011 number:7 day:07 month:07 https://dx.doi.org/10.1007/JHEP07(2011)037 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2011 2011 7 07 07
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topic_title	Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene Field Theories in Lower Dimensions (dpeaa)DE-He213 Spontaneous Symmetry Breaking (dpeaa)DE-He213
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title	Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene
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title_sort	magnetic catalysis and quantum hall ferromagnetism in weakly coupled graphene
title_auth	Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene
abstract	Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry. © SISSA, Trieste, Italy 2011
abstractGer	Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry. © SISSA, Trieste, Italy 2011
abstract_unstemmed	Abstract We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2) × U(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry. © SISSA, Trieste, Italy 2011
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title_short	Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene
url	https://dx.doi.org/10.1007/JHEP07(2011)037
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Magnetic catalysis and quantum Hall ferromagnetism in weakly coupled graphene

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